Given a 120 centimeter Diameter multiplied by three, the length of the circle will be 360 centimeters.

Given 360 degrees to the circles length, each degree will be one centimeter in length.

And not one nor any number of mathematicians, geometer's or geniuses can alter or change the fact that; a circles length is exactly three times that of its diameter length.

__Elementary Foundation Stone Of Differential Geometry__Given a 120 centimeter Diameter multiplied by three, the length of the circle will be 360 centimeters.

Given 360 degrees to the circles length, each degree will be one centimeter in length.

And not one nor any number of mathematicians, geometer's or geniuses can alter or change the fact that; a circles length is exactly three times that of its diameter length.

As above no more than elementary/simple arithmetic has been used in the work that follows, and as such any average adult or teenager should be able to follow it, especially as the working has already been done.

__Readers Please Note__As above no more than elementary/simple arithmetic has been used in the work that follows, and as such any average adult or teenager should be able to follow it, especially as the working has already been done.

****

**Content**

Introduction - Numbers - Circles - TimeMeasuring the length of a Circle Sumeria 3000 BC Greek- Roman University (Catholic - Universal) Mathematics 2017 The Non - Imaginary (Abstract) Rational Length Of One Degree Simplest Method For Calculating The Area Of A Circle Archimedes Proposition 1 The Reality Of Shape Equals The Shape Of Reality 3 x r squared Squaring The Circle Whats In A Number Whats In A Name - The Area Of Time - 3 x r SquaredAreas Of Rings From The Cube To Its Sphere Twelve Steps To The Sphere Areas And Volumes Of Symmetrical Ovals And Ovoids The Number Of Degrees Of Latitude And Longitude To A Sphere The Area Of One Degree Of 64, 800 Degrees to The Surface of A Sphere |
Symmetry Of A CircleIrrationality Of 3.14159 Compass And Line Universal Geometry Ruler And Line Euclidean Geometry Minus Pi In Black And Yellow Relativity Axis Of Time Over Diameter Of Time e.mail:universometry@gmail. unialphaomega@hotmail.com© www.fromthecircletothesphere.net©www.geometry-mass-space-time.com |

**INTRODUCTION**

NUMBERS - CIRCLES - TIME

NUMBERS - CIRCLES - TIME

****

Over ancient times in Sumeria Persia, numbers developed from simply being attached to physical things into becoming used in the form of smaller fractional units of length to measure the dimensions of a body/object, and so allow mathematical calculations to be made in regard to the comparative sizes, and the intrinsic values of weight, volume, densities, etc. of bodies and of distances laying between them.

This measuring of distances between objects then naturally led on to the establishment of fixed landmarks and the mapping, of terrain, and later oceanic navigation using the fixed positions of the stars, which led on to the recognition that the stars formed fixed linear patterns (Constellations) that could be likened to the shapes of common things here on the Earth.

Gradually over time what had been simple arithmetic, moved on into the realms of discovering and working out the "natural rules of geometry" for calculating the dimensions and the angles of straight linear geometric shapes, and subsequently the relativity's laying between straight linear and curved differential geometry.

Given this knowledge

1. The Sumerians gave 0 to 360 degrees/divisions to a circle, and 0 to 360 degrees/divisions to one full rotation. Therefore a circle of 360 degrees could represent the Earth itself, and 360 degrees of the circles rotation could represent 360 degrees of the Earth's rotation.

2. Babylon was then given fixed point on the Earth, from which to measure how long it would take for the Earth to rotate 360 degrees relative to the fixed position of the Sun when it was directly overhead at midday and did not cast a shadow.

3. The measuring process would have involved the use of a stick or the like, to cast a moving-circling shadow as the Earth rotated relative to the fixed position of the Sun, and a large amount of fine sand passing through a small and exact sized orifice over the full period of one 360 degree rotation of the Earth.

4. The amount of sand representing 360 degrees of rotation would then have been divided into twenty four equal portions of sand, each portion of sand thereof representing 15 degrees of the Earth's 360 degrees of rotation.

Subsequently it would have been a simple matter for them to take one portion of sand and make a single sand timer with a duration period of 15 degrees of rotation, and thus the First Hour

However with the fall of Babylon and the defeat of the Persian Empire at the hands of Alexander of Macedonia and his Greek Tyrant/Fascist Generals, a great deal of this knowledge which had been accumulated over thousands of years was lost, and a great deal more that had been stored (

Over ancient times in Sumeria Persia, numbers developed from simply being attached to physical things into becoming used in the form of smaller fractional units of length to measure the dimensions of a body/object, and so allow mathematical calculations to be made in regard to the comparative sizes, and the intrinsic values of weight, volume, densities, etc. of bodies and of distances laying between them.

This measuring of distances between objects then naturally led on to the establishment of fixed landmarks and the mapping, of terrain, and later oceanic navigation using the fixed positions of the stars, which led on to the recognition that the stars formed fixed linear patterns (Constellations) that could be likened to the shapes of common things here on the Earth.

Gradually over time what had been simple arithmetic, moved on into the realms of discovering and working out the "natural rules of geometry" for calculating the dimensions and the angles of straight linear geometric shapes, and subsequently the relativity's laying between straight linear and curved differential geometry.

Given this knowledge

1. The Sumerians gave 0 to 360 degrees/divisions to a circle, and 0 to 360 degrees/divisions to one full rotation. Therefore a circle of 360 degrees could represent the Earth itself, and 360 degrees of the circles rotation could represent 360 degrees of the Earth's rotation.

2. Babylon was then given fixed point on the Earth, from which to measure how long it would take for the Earth to rotate 360 degrees relative to the fixed position of the Sun when it was directly overhead at midday and did not cast a shadow.

3. The measuring process would have involved the use of a stick or the like, to cast a moving-circling shadow as the Earth rotated relative to the fixed position of the Sun, and a large amount of fine sand passing through a small and exact sized orifice over the full period of one 360 degree rotation of the Earth.

4. The amount of sand representing 360 degrees of rotation would then have been divided into twenty four equal portions of sand, each portion of sand thereof representing 15 degrees of the Earth's 360 degrees of rotation.

Subsequently it would have been a simple matter for them to take one portion of sand and make a single sand timer with a duration period of 15 degrees of rotation, and thus the First Hour

*(Of Measured Earth rotation)*Of Time would have begun.However with the fall of Babylon and the defeat of the Persian Empire at the hands of Alexander of Macedonia and his Greek Tyrant/Fascist Generals, a great deal of this knowledge which had been accumulated over thousands of years was lost, and a great deal more that had been stored (

*and not yet been plagiarized*) in the Alexandrian Museum, was later burned and destroyed by the Romans.

*MEASURING THE LENGTH OF A CIRCLE*

SUMERIA 3000 BCSUMERIA 3000 BC

**SUMER (Wikipedia)**

Mathematics[edit]

The Sumerians developed a complex system of metrology c. 4000 BCE. This metrology advanced resulting in the creation of arithmetic, geometry, and algebra. From c. 2600 BCE onwards, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises and division problems. The earliest traces of the Babylonian numerals also date back to this period.[43] The period c. 2700 – 2300 BCE saw the first appearance of the abacus, and a table of successive columns which delimited the successive orders of magnitude of their sexagesimal number system.[44] The Sumerians were the first to use a place value numeral system. There is also anecdotal evidence the Sumerians may have used a type of slide rule in astronomical calculations. They were the first to find the area of a triangle and the volume of a cube.[45]

Geometry[edit] Babylonians knew the common rules for measuring volumes and areas. They measured the circumference of a circle as three times the diameter and the area as one-twelfth the square of the circumference, *

Mathematics[edit]

*Main article: Babylonian mathematics*The Sumerians developed a complex system of metrology c. 4000 BCE. This metrology advanced resulting in the creation of arithmetic, geometry, and algebra. From c. 2600 BCE onwards, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises and division problems. The earliest traces of the Babylonian numerals also date back to this period.[43] The period c. 2700 – 2300 BCE saw the first appearance of the abacus, and a table of successive columns which delimited the successive orders of magnitude of their sexagesimal number system.[44] The Sumerians were the first to use a place value numeral system. There is also anecdotal evidence the Sumerians may have used a type of slide rule in astronomical calculations. They were the first to find the area of a triangle and the volume of a cube.[45]

Geometry[edit] Babylonians knew the common rules for measuring volumes and areas. They measured the circumference of a circle as three times the diameter and the area as one-twelfth the square of the circumference, *

__which would be correct if__**π*is estimated as 3**Babylonian mathematics (also known as**

*Assyro-Babylonian mathematics*[1][2][3][4][5][6]) was any mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in 539 BC. Babylonian mathematical texts are plentiful and well edited.[7] In respect of time they fall in two distinct groups: one from the Old Babylonian period (1830-1531 BC), the other mainly Seleucid from the last three or four centuries BC. In respect of content there is scarcely any difference between the two groups of texts. Thus Babylonian mathematics remained constant, in character and content, for nearly two millennia.[7]

A Babylonian cuneiform tablet written some

Quote Wikipedia:__Reference Estimating the wealth; Encyclopedia Britannica.__A Babylonian cuneiform tablet written some

__3,000 years__ago treats problems about dams, wells, water clocks, and excavations. It also has an exercise in circular enclosures with an implied value of π pi = 3. The contractor for King Solomon's swimming pool, who made a pond 10 cubits across and 30 cubits around (1 Kings 7:23) used the same value.Quote Wikipedia:

*****

__which would be correct if__**π*is estimated as 3__Sumerian Method__**1. Diameter 120 cm's**

**2. Circumference 360 cm's**

**3. Circumference squared 129, 600 sq cm's**

**4. Divide 129, 600 by 12 = 10, 800 sq cm's to the area of the circle**

**GREEK - ROMAN UNIVERSITY**

*(CATHOLIC - UNIVERSAL)*

MATHEMATICS 2017

**Oxford English Dictionary 2017**

Mathematics: The

Abstract: Existing in thought or as an idea but not having a physical or concrete existence.

Abstraction:The quality of dealing with ideas rather than events; topics will vary in degrees of abstraction, something that exists only as an idea.

Rhetorical Question

What is the name and where is the Chief Human Abstractrician - Genius of supposedly pure mathematics, who decides when and which abstracts of "pure imaginary - theoretical mathematics", are relative and should be applicable to the physics and engineering, of the non - abstract physical and concrete existence of "

And so gave rise to this comment *

Thousands of years taken and spent by ancient Sumerian mathematicians in order to reach a pinnacle of mathematics, whereby they were able to both measure and find the areas of circles, and so consequently be able to invent the same measurable elements of time that we use to this day (A day of the days and the years that they invented).

And yet modern day mathematicians (?) possess such an astounding degree of arrogance that they choose to ignore and discount its veracity, in favor of their own purely imaginary and inane decimal abstractions.

Mathematics: The

__abstract science__of number, quantity, and space. Mathematics may be studied in its own right (pure mathematics) or as it is applied to other disciplines such as physics and engineering (applied mathematics).Abstract: Existing in thought or as an idea but not having a physical or concrete existence.

Abstraction:The quality of dealing with ideas rather than events; topics will vary in degrees of abstraction, something that exists only as an idea.

Rhetorical Question

What is the name and where is the Chief Human Abstractrician - Genius of supposedly pure mathematics, who decides when and which abstracts of "pure imaginary - theoretical mathematics", are relative and should be applicable to the physics and engineering, of the non - abstract physical and concrete existence of "

__Our World__" and "__The Universe__"?And so gave rise to this comment *

__which would be correct if__* obviously written by a Dunce.*π*is estimated as 3Thousands of years taken and spent by ancient Sumerian mathematicians in order to reach a pinnacle of mathematics, whereby they were able to both measure and find the areas of circles, and so consequently be able to invent the same measurable elements of time that we use to this day (A day of the days and the years that they invented).

And yet modern day mathematicians (?) possess such an astounding degree of arrogance that they choose to ignore and discount its veracity, in favor of their own purely imaginary and inane decimal abstractions.

****

**AUTHORS NON ABSTRACT**

RATIO

*NON IMAGINARY*RATIO

*(Rational)*LENGTH OF ONE**DEGREE**

****1.**

**Use**

**one right angle of the 120 x 120 cm square as a Diameter Line**

**2. M**

**ultiply the 120 cm Diameter Line by 3**

**3. The Circle is 360 cm long**

**4. The Circle has 360 degrees**

**5. Each Degree is 1 cm long**

*SIMPLEST METHOD FOR CALCULATING THE AREA OF A CIRCLE*

**Diameter 120 Centimetres x Diameter 120 Centimetres = 14, 400 Square Centimetres to the Square**

**1. Area of the Square "is" 14, 400 sq cm**

2. Area of the Circle "is" 4 x 2, 700 sq cm's

3. 4 x 2, 700 sq cm's "is" 10, 800 sq cm's

4. 10, 800 sq cm's "is" three quarters of the area to the 14, 400 sq cm square

5. The square area of "any" circle "is", three quarters of that defined by the squaring of its diameter

2. Area of the Circle "is" 4 x 2, 700 sq cm's

3. 4 x 2, 700 sq cm's "is" 10, 800 sq cm's

4. 10, 800 sq cm's "is" three quarters of the area to the 14, 400 sq cm square

5. The square area of "any" circle "is", three quarters of that defined by the squaring of its diameter

**Line.**

*ARCHIMEDES***287 - 212 BC**

**Proposition 1**.

**The area of any circle is equal to a right-angle triangle in which one of the sides about the triangle is equal to the radius, and the other to the circumference of the circle.**

**Archimedes Triangle**

**1. The base right-angle is equal to the radius 60 cm**

**2. The height of the right-angle is equal to the circumference of the circle**

**3.**

**The area of the circle is equal to the above right-angle triangle, which has one side about the triangle that is equal to the 60 cm radius, and the other to the 360 cm circumference of the circle.**

**Check**

**1, The area of the rectangle is 21, 600 sq cm's**

**2. The area of the right-angle triangle is 10, 800 sq cm's**

**3. The three quarter area of the 3 x r squared circle is 10. 800 sq cm's**

Quite clearly given that the Sumerian method, the Authors (Mine) methods and Archimedes method proposition 1, give exactly the same result of 10, 800 squares to the circle; one has to question how it was that Archimedes also came up with the contradictory formula of 22/7.

Quite clearly given that the Sumerian method, the Authors (Mine) methods and Archimedes method proposition 1, give exactly the same result of 10, 800 squares to the circle; one has to question how it was that Archimedes also came up with the contradictory formula of 22/7.

THE REALITY OF SHAPE

EQUALS

THE SHAPE OF REALITY

THE REALITY OF SHAPE

EQUALS

THE SHAPE OF REALITY

**Preamble**

This chapter is comprised entirely of some of the preliminary questions that I first had to formulate and consider, before it was possible for me to move on to the subject matters covered in the following chapters.

Readers may prefer to skip these questions and move on to the other chapters, however in regard to those who may be curious as to why I have chosen to include them, the reason is that they may serve to counteract the erroneous concepts that have arisen and prevailed over time, as a direct result of Euclid's and Archimedes limited linear based perceptions.

Oxford English Dictionary

This chapter is comprised entirely of some of the preliminary questions that I first had to formulate and consider, before it was possible for me to move on to the subject matters covered in the following chapters.

Readers may prefer to skip these questions and move on to the other chapters, however in regard to those who may be curious as to why I have chosen to include them, the reason is that they may serve to counteract the erroneous concepts that have arisen and prevailed over time, as a direct result of Euclid's and Archimedes limited linear based perceptions.

Oxford English Dictionary

**Circle: A round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (center).**

**Circumf****erence: 1. The enclosing boundary esp of a circle or other figure enclosed by a curve. 2. The distance around.**

****

**Boundary: A line that marks the limits of an area; a dividing line.**

**Shape: The external form or appearance of someone or something; the outline of an area or figure.**

**Approximate: Close to the actual, but not completely accurate or exact.**

**Pi:The sixteenth letter of the Greek alphabet "**

__translated"__as "P."**the numerical**

**("**

__decimal__**")**

**value of the ratio of the circumference of a circle to its diameter**

**(**

__approximately__**3.14159)**

**Rhetorical Questions**

**Diagram A****1. Are circles defined by their shape or the shape of their outline?****2. Are circular lengths measured by the lengths to their outlines, or the lengths to the edges of their actual forms?****3. Does diagram A show a black circle or an orange circle?****4. Does the area of the black "round shape" have a boundary line "dividing it" from the orange encircling area?****5. Does the area of the encircling orange area have a line "dividing"it from the "round shape" of the black area?****6. If it is considered that there is a boundary line dividing the black "round shape" from the encircling orange area;****a. Where is it?****b. What colour is it?****c. What is its length and width?****Diagram B relative to the Archimedes formula of Approximation Pi****Pi:The sixteenth letter of the Greek alphabet "**__translated"__as "P."**the numerical****("**__decimal__**")****value of the ratio of the circumference of a circle to its diameter****(**__approximately__**3.14159)****1. Does diagram B show one circle, two circles, or three circles?****2. Does a circumferential line measure the actual and factual length of the shape of a circle, or is a circumferential line only approximate to a circles actual and factual length?****3. Does the "round shape" of the the encircling/limiting/enclosing "Red Ring - Circumferential Area", possess a calculable area of length and width?****4. Does the irrational formula of Archimedes approximate to three diameter lengths?****5. Does the irrational formula of Archimedes approximate to the actual length of a circles edge?****6. Is the irrational the formula of Archimedes an irrational number, or does it consist of a rational number plus an irrational factor?****7. Is the whole number 3 rational or irrational?****8. Is the additional factor of****∙14159 of itself rational or irrational?****9. If the irrational factor of the irrational formula of Archimedes was subtracted from the irrational formula, would this leave a rational number. that could be subdivided into the rational - symmetrical edge length of a circle?****10. Given that a miss is as good as a mile; Does any irrational approximation possess any more worth, than any rational approximation?**

**Diagram C**

**1. Do the 360 degree spatial points of reference serve to define a circle or a round shape?****2. Do the 360 degree spatial points of reference serve to define a circle or a round shape and if so, does it possess a boundary line dividing it from the surrounding area (space) and if so; a. Where is it. What colour is it. 3. What is its length and width?****3. Given that in diagram C the 360 points of spatial reference do serve to define a round shape?****a. how many radiated points of spatial reference does it take to form a "round shape"?****b. How many points of spatial reference does it take to form a complete encircling "line" of spatial limitation (enclosure - containment - boundary) circumscribed around a "round shape"?****4. Given that all circles have "been nominated" as possessing "a minimum" of 360 points of spatial reference called degrees;****a. Do the 360 degrees of spatial reference vary (possess a value) in size?****b. Do the spaces between each of the 360 degrees equate to being of the same length?****c. When added together do the spaces between the 360 points of spatial reference/degrees, equate to a complete curvature of length?****d. Given that the spaces between the 360 points of spatial reference do equate to a complete curvature of length, is there any reason why the length of the complete curvature cannot be calculated, and if so why not?**

*3 x r squared***A**

**Diameter 120 Cm x 120 Cm = 14, 400 Sq Cm's to the Square**

**1. 60 cm radius squared = 3, 600 sq cm's**

**2. x by 3 =**

__10, 800__sq cm's**3. Area of the circle is 3/4 that of the**

__14, 400__sq cm square**B**

**14, 400 sq cm square divide by 4 = 3, 600 sq cm**

**Multiply by 3 =**

__10, 800__**sq cm**

**Area of the Circle is 3/4 the area, of the Square**

**C**

**1.**

**60 cm radius is squared, 3, 600 sq cm**

**2. 3, 600 sq cm is divided by 4 = 900 sq cm**

**3. 900 sq cm is then multiplied by 3 = 2, 700 sq cm**

**4. 2, 700 sq cm is then multiplied by 4, = 10, 800 sq cm's to the circle**

__Absolutes__**The**

__"non-linear" circumferential length__of the area to a circle; is six times that of the circles radius length, and three times that of the circles diameter length.**The**

__"non-linear" circumferential length__to the area of a circle; is three quarters of the length, to the perimeter, of the square of the circles diameter length.**The**

__"non-linear" area__of a circle, is three quarters of the area to that, of the area of the square of the circles diameter length.

SQUARING THE CIRCLE

SQUARING THE CIRCLE

**EUCLIDEAN PROGRESSION**

****

**In the above diagram it can be observed.**

That the area of the first two rectangular progressions of 5/12 & 4/12 when added together, form a rectangle measuring 9 x 12 squares with a square area of 108 squares, which is the same amount of area possessed by the three quarter square area of the yellow circle in the first diagram.

Which serves to define that given one right angle dimension that is of the same height (length/diameter) as that of a circle, by extension a rectangle can be formed, which contains (is made up of) the same amount (3/4 of the initial square) of area as that of a circle of the same height.

Which serves to further reinforce the

That the area of the first two rectangular progressions of 5/12 & 4/12 when added together, form a rectangle measuring 9 x 12 squares with a square area of 108 squares, which is the same amount of area possessed by the three quarter square area of the yellow circle in the first diagram.

Which serves to define that given one right angle dimension that is of the same height (length/diameter) as that of a circle, by extension a rectangle can be formed, which contains (is made up of) the same amount (3/4 of the initial square) of area as that of a circle of the same height.

Which serves to further reinforce the

__fact__, that the area of a circle is always three quarters that of the square of its diameter.

*WHAT'S IN A NUMBER - WHAT'S IN A NAME*

THE AREA OF TIME

3 x r SQUARED

THE AREA OF TIME

3 x r SQUARED

**To find the area of time we simply change the name of the measurements we are have been using, namely centimeters to that of Seconds of Time.**

And therefore the 120 x 120 centimeter square we have been using, becomes a Square Clock Face of Time measuring 120 x 120 seconds of time.

120 x 120 Seconds = 14, 400 Square Seconds of Time to the area of the Square Clock Face.

14, 400 Square Seconds of tme divided by 4 = 3, 600 Square Seconds of time to each 1/4 of the Square Clock Face.

And therefore the 120 x 120 centimeter square we have been using, becomes a Square Clock Face of Time measuring 120 x 120 seconds of time.

120 x 120 Seconds = 14, 400 Square Seconds of Time to the area of the Square Clock Face.

14, 400 Square Seconds of tme divided by 4 = 3, 600 Square Seconds of time to each 1/4 of the Square Clock Face.

**3, 600 Square Seconds multiplied by 3 = 10, 800 Square Seconds of Time.**

Therefore there are 10, 800 Square Seconds of Time, to the resultant Circle of Square Time.

Therefore there are 10, 800 Square Seconds of Time, to the resultant Circle of Square Time.

**Therefore as there are 3, 600 Standard Seconds to each Standard Hour of each 24 Hour Day**

The Square Area of each 24 Hour day, is equal to

6 Squares measuring 120 x 120 Seconds

or

8 Circles each measuring 3 Hours of Square Time.

In Sum

Time is a Sumerian Differential Geometry Measurement, which they applied a fixed point on the Earth's surface (Babylon then, today Greenwich) and related its 360 degrees of rotation, to that of the fixed face of the Sun.

The Square Area of each 24 Hour day, is equal to

6 Squares measuring 120 x 120 Seconds

or

8 Circles each measuring 3 Hours of Square Time.

In Sum

Time is a Sumerian Differential Geometry Measurement, which they applied a fixed point on the Earth's surface (Babylon then, today Greenwich) and related its 360 degrees of rotation, to that of the fixed face of the Sun.

*AREAS OF RINGS***8 Mile Diameter - Right Angle Square**

**We begin by first finding the area of each circle**

**1. Multiply the 2 mile diameter of the central circle by itself = 4 square miles to the square of the diameter, divide by 4 = 1 square mile x 3 = 3 square miles to the central circle.**

**2. Multiply the 4 mile diameter of the red circle by itself = 16 square miles to the square of the diameter, divide by 4 = 4 square miles x 3 = 12 square miles to the red circle.**

**3. Multiply the 6 mile diameter of the blue circle by itself = 36 square miles to the square of the diameter, divide by 4 = 9 square miles x 3 = 27 square miles to the blue circle.**

**4. Multiply the 8 mile diameter of the green circle by itself = 64 square miles to the square of the diameter, divide by 4 = 16 square miles x 3 = 48 square miles to the green circle.**

**5. Deduct the 3 square mile area of the central circle from the 12 square mile area of the red circle; = 9 square miles to the area of the red ring.**

**6. Deduct the 12 square mile area of the red circle from the 27 square mile area of the blue circle = 15 square miles to the area of the blue ring.**

**7. Deduct the 27 square mile area of the blue circle from the 48 square mile area of the green circle = 21 square miles to the area of the green ring.**

**8. Deduct the 48 square mile area of the green circle from 64 square mile area of the overall pale blue square, = 16 square miles to the remaining area of the square, which is 1/4 of the squares area.**

**Check**

**Central Circle = 3 square miles**

**Red Ring = 9 square miles**

**Blue Ring = 15 square miles**

**Green Ring = 21 square miles**

**Pale Blue Area**

__= 16__square miles**Total = 64 square miles**

FROM THE CUBE TO ITS SPHEREFROM THE CUBE TO ITS SPHERE

**From the Cube to its Cylinder**

**Diagrams 1 - 5 serve to depict the potential cylinder within a cube, diagrams 5 - 6 serve to show that when a three dimensional cylinder is rotated, so that its lateral length is face on to us, if we imagine it rather as being as a flat square, with the circle of the potential sphere within the cylinder being visibly apparent; we can see that when the four corners of the cylinder are carved away, the shape of the sphere will be released.**

**The diagram above depicts the three quarter area of the circle of the square relative to the potential cylinder lying within a 16 cm x 16 cm wooden cube. and in order to form the cylinder from the wooden cube; we place it on a wood lathe, and then rotate the cube and shave away the four lateral corners, which are equal one quarter of the cubes mass, leaving the three quarter mass of the cylinder remaining.**

**The two diagrams above serve to demonstrate both visually, and via our minds eye, that when the four-dimensional (lateral-Vertical-Angled- Curvature) cylinder is given an angled frontal aspect of view, and then turned towards us to a full face on view, and while at the same time mentally discarding its dimension of the curvature; the front facial view of the cylinder, then in visual effect, becomes a flat square.**

**Therefore if we use our minds eye, to imagine a circle of the same height and width, relative to the area of the square;**

**It then becomes apparent, that when we shave off the four corners of the square, which are in reality the corner ends to the cylinder, we will be in reality shaving away one quarter, of the mass of the cylinder.**

**The first diagram above serves to depict the cube fixed on a wood lathe, prior to carving away the four corners to form the cylinder; and the second diagram depicts the cylinder placed lengthwise and laterally away from us, prior to shaving away the corners of the circular face, to form the sphere.**

**This visual perspective then allows us to imagine, that as we use our chisel in a left and right circular motion, acting between and towards each of the two central spindles, we are shaving away the circular dark flat aspect, of the front of the cylinder.**

**And as we do so the round and darker frontal facial aspect of the cylinders length, will gradually move upwards and forwards away from us, and grow smaller, as the final curvature of the sphere, takes its full form.**

**In sum in regard to the mass of wood removed from the cube**

**With our first cut we removed one quarter of the mass of wood from the cube**

**With our second cut we removed one quarter of the mass of wood from the cube**

**Therefore we can say**

**A**

**circle is three quarters of the area of its square**

**A a cylinder is three quarters of its cube**

**A sphere is three quarters of its cylinder.**

**Confirmation by Mass - Weights**

**Given that the cube weighed 160 grams prior to being converted into a sphere**

**The cylinder would weigh 120 grams**

**The wood shavings would weigh 40 grams**

**Given that the cylinder weighed 120 grams**

**The wood shavings would weigh 30 grams**

**Confirming a cylinder is three quarters of its cube, a sphere is three quarters of its cylinder.**

TWELVE STEPS TO THE SPHERETWELVE STEPS TO THE SPHERE

**CUBE TO CYLINDER**

**Calculating the surface area and volume of a 6 centimetre diameter sphere, obtained from a 6 centimetre cube.**

**Note we use 6 centimetres rather than 120 cm, in order to make the numbers easier to follow.**

**1. Measure cube height to obtain a/its Diameter line = 6 cm**

**2. Multiply 6 cm x 6 cm to obtain the square area of one face of the cube; and also add them together to obtain the length of perimeter to the square face = Length 24 cm, Square area 36 sq cm.**

**3. Multiply the square area, by the length of diameter line to obtain the cubic capacity = 216 cubic cm.**

**4. Divide the cubic capacity by**

**4, to obtain one quarter of the cubic capacity of the cube = 54 cubic cm.**

**5. Multiply the one quarter cubic capacity by 3. to obtain the cubic capacity of the Cylinder = 162 cubic cm.**

**6. Multiply the area of one face of the cube by 6, to obtain the cubes surface area = 216 square cm.**

**7. Divide the cubes surface area by 4, to obtain one quarter of the cubes surface area = 54 square cm.**

**8. Multiply the one quarter surface area of the cube by 3, to obtain the three quarter surface area of the Cylinder = 162 square cm.**

CYLINDER TO SPHERE

CYLINDER TO SPHERE

**9. Divide the Cylinders cubic capacity by 4, to obtain one quarter of the cubic capacity of the Cylinder = 40 & a half cubic cm.**

**10. Multiply the one quarter cubic capacity by 3, to obtain the three quarter cubic capacity of the Sphere = 121 & a half cubic cm, to the volume of the Sphere.**

**11. Divide the Cylinders surface are by 4, to obtain one quarter of the surface area of the Cylinder = 40 & a half square cm.**

**12. Multiply the one quarter surface area by 3 to obtain the three quarter surface area of the Sphere = 121 & a half square cm, to the surface area of the Sphere.**

*AREAS AND VOLUMES*

*OF*

*SYMMETRICAL OVALS AND OVOIDS***Space volume and area are relatively interchangeable (see space - volume - Area - Mass after the next chapter) and when considered as such;**

**A symmetrical oval is a squashed circle**

**A symmetrical ovoid is a squashed sphere**

**When a straight flat downward pressure is applied to the centre of an inflated sphere/ball, resting on a flat solid surface, the air within the ball is displaced equally in all directions away from the the centre of gravity of the ball; as the passive resistance of the atomic tensile strength, of the solid surface below, causes the air pressure already within the ball, plus the pressure being applied to the ball, to equate in all directions away from the centre of gravity of the ball.**

**Resulting in an equal expansion of the balls envelope, in all directions away from the centre of gravity of the ball.**

**Therefore this same effect can be relatively be applied by the use of the minds eye, to the amount of space that exists within a circle, existent upon a flat surface.**

**Whereby by given the symmetrical confining stricture, to the line of the circles circumference, the simulated downward pressure, can only expand symmetrically, laterally, and geometrically along the increasingly oval length of the former symmetrical circular shape, as per the diagram below.**

**Therefore given that the diameter of the ball in the diagram above is 6 cm, the area of the square of the diameter will be 36 square cm; and the three quarter square area of the circle will be 27 square metres.**

**Therefore if the diameter length is compressed down to 3 cm**

**The area of half of the oval will be 13 and a half square cm, and the total area of the oval will be 27 square cm; which will be three quarters of the area to the ovals rectangle.**

**As the rectangles area would have consisted of 3 rows of one cm squares; totalling 36 square cm of area to the rectangle.**

**Therefore we can say**

**As a symmetrical circle is three quarters of its square, and its sphere is three quarters of its cylinder**

**So a symmetrical oval is three quarters of its rectangle, and its ovoid is three quarters of its cylinder**

**THE NUMBER OF DEGREES OF LATITUDE AND LONGITUDE**

**TO THE SURFACE OF A SPHERE****Square Degree**

From Wikipedia, the free encyclopedia

A square degree is a non-SI unit measure of solid angle. It is denoted in various ways, including deg2, sq.deg., (°)², and ☐°. Just as degrees are used to measure parts of a circle, square degrees are used to measure parts of a sphere. Analogous to one degree being equal to

or approximately 41 253 deg2. This is the total area of the 88 constellations in the list of constellations by area. The largest constellation, Hydra covers a solid angle of 1303 deg2, whereas the smallest, Crux covers 68 deg2.[1]

For example, observed from the surface of the Earth, the sun or the full moon has a diameter of approximately 0.5°, so it covers a solid angle of approximately 0.2 deg2 (≈

Assuming the Earth to be a sphere with a surface area of 510 000 000 km2, the area of Northern Ireland, 13 600 km2 represents a solid angle of 1.10 deg2.[2] Similarly, the area of Connecticut, 14 356 km2represents a solid angle of 1.16 deg2.[3]

From Wikipedia, the free encyclopedia

A square degree is a non-SI unit measure of solid angle. It is denoted in various ways, including deg2, sq.deg., (°)², and ☐°. Just as degrees are used to measure parts of a circle, square degrees are used to measure parts of a sphere. Analogous to one degree being equal to

*π*/180 radians, a square degree is equal to (*π*/180)2, or about 1/3283 or 3.0462×10−4 steradian (0.30462 msr). The number of square degrees in a whole sphere isor approximately 41 253 deg2. This is the total area of the 88 constellations in the list of constellations by area. The largest constellation, Hydra covers a solid angle of 1303 deg2, whereas the smallest, Crux covers 68 deg2.[1]

For example, observed from the surface of the Earth, the sun or the full moon has a diameter of approximately 0.5°, so it covers a solid angle of approximately 0.2 deg2 (≈

*π*(0.5/2)2 deg2), which is 4.8 × 10−6 of the total sky sphere.Assuming the Earth to be a sphere with a surface area of 510 000 000 km2, the area of Northern Ireland, 13 600 km2 represents a solid angle of 1.10 deg2.[2] Similarly, the area of Connecticut, 14 356 km2represents a solid angle of 1.16 deg2.[3]

**A Circular protractor has 180 Degrees to its "Vertical Height of Diameter Length"**

Which equates to there being 180

Therefore if the Vertical Height of the Sphere is given a rotation of 360 degrees

Which equates to there being 180

__Lateral Circles__of 360 degrees; to the "Vertical Height of the Earth__a__Sphere"Therefore if the Vertical Height of the Sphere is given a rotation of 360 degrees

**180 Vertical Degrees x 360 Degrees of Lateral Rotation = 64, 800 shared Vertical**

*(Longitude)*and Latitudinal Degrees to the surface area of the Earth__a__Sphere.

*THE AREA OF 1 DEGREE*

*OF*

*64, 800 DEGREES***a. Circle of 360**

**⁰**

**b. 6 Diameters 6 Square faces c. Shared Degrees d. 1 Square Face of Cube e. 8 Corners of Cube Removed**

**In the previous chapter in order to gain the number of degrees to the surface of a sphere; we rotated the 180**

**⁰ of**

**height of a protractor by 360**

**⁰, and in so doing defined that there are 180 lateral circles of 360⁰ to the height of a sphere; and therefore there are 64, 800⁰ to the surface area of a sphere.**

**However although this lateral rotational method of finding the number of degrees to the surface of a sphere, does indeed serve to define the number of 64, 000 degrees to the surface of a sphere; it does not serve to give each of those degrees an equal amount of surface area.**

**The reason being, that if we were to view such a hypothetical sphere from an overhead aspect of view, extending upwards from the spheres equator; each subsequent circle of 360⁰ to that of the circle of the equator, would appear to be smaller than the one below it.**

**Therefore in order to equate all of the degrees to each other, and equally over the surface of the sphere, we have to divide the number of 64,800 degrees into the overall surface area of the sphere.**

**And in order to achieve this via straight linear geometry, we begin by observing that the number of radii/degrees to a circle is the same number for its surrounding square; and relative to the solidarity of a sphere and its surrounding solid cube, this principle does not change.**

**To grasp this rather than think in terms of linear radii; think in terms of radiations extending directly outwards from the centre of a sphere, and continuing outwards through the surrounding body of the cube.**

**Given this aspect of observation it becomes clear, that if we convert the number of degrees to a circle into the same number of centimeters to find the surface area of the sphere; and then divide this surface area by 64, 800 degrees, this will give the area to each one of those degrees.**

**120 cm Height of Cube = 120 cm Diameter Sphere**

One face of the Six faces of a 120 cm cube = 14, 400 square centimeters

Six faces x 14, 400 square centimeters = 86, 400 square centimeters

86, 400 sq cm ÷ by 4 = 21, 600 square centimeters to one quarter of the surface area of the cube

21, 600 sq cm x 3 = 64, 800 square centimeters to the surface area of the ¾ Cylinder of the Cube

64, 800 sq cm ÷ by 4 = 16, 200 sq cm to one quarter of the cylinders surface area

16, 200 sq cm x 3 = 48, 600 square centimeters to the surface area of the ¾ Sphere of the Cylinder

48, 600 sq cm ÷ by 64, 800 degrees to the surface of the Sphere = 0∙75 or ¾ of one square centimeter to 1 degree of the surface, of the Sphere.

__Refer Back To 12 Steps To The Sphere__One face of the Six faces of a 120 cm cube = 14, 400 square centimeters

Six faces x 14, 400 square centimeters = 86, 400 square centimeters

86, 400 sq cm ÷ by 4 = 21, 600 square centimeters to one quarter of the surface area of the cube

21, 600 sq cm x 3 = 64, 800 square centimeters to the surface area of the ¾ Cylinder of the Cube

64, 800 sq cm ÷ by 4 = 16, 200 sq cm to one quarter of the cylinders surface area

16, 200 sq cm x 3 = 48, 600 square centimeters to the surface area of the ¾ Sphere of the Cylinder

48, 600 sq cm ÷ by 64, 800 degrees to the surface of the Sphere = 0∙75 or ¾ of one square centimeter to 1 degree of the surface, of the Sphere.

**Height 180 degrees plus three times 1/3rd Rotation's of 120 degrees (360) = 64, 800 degrees****Which serves to prove once again; that a circles length is 3 x its diameter length & its area is 3/4 that of its surrounding square.**

**And given that; 48, 600 sq cm ÷ by 64, 800 degrees to the surface of the Sphere =**

__¾ of one "Square Centimetre"__to the area of 1 degree of the surface, of the Sphere.**This also serves to inform us;**

**That the three-dimensional, 3/4 square centimetre shape of one degree of sphere surface; is in the shape of a circle.**

**Which equates to; the cross section of one**

__radiation__extending from the__centre__of the 120 cm sphere, being circular along its entire radiant length.**However in regard to equating and relating this aspect of spherical surface geometry to that of linear geometry; each degree just as with the three equal curved linear dimensions of a circle, needs to possess, three equal straight linear dimensions of an equilateral triangle.**

SYMMETRY OF A CIRCLESYMMETRY OF A CIRCLE

**A circular protractor has**

180 Degrees to its Diameter

360 Degrees to its Circumference

Therefore by giving 180 Centimetres to the length of Diameter

The Area to the "Square" of the Diameter is

32, 400 "Square Centimeters"

Rotate the 90 degree radius 360 Degrees; and the Area to the "Circle" of the Diameter is;

32, 400 "Circumnavigation Degrees"

Proving that the Circumferential length to a Circle has an "Exact Ratio" to its Radius (radii) length, and hence its Diameter length.

Therefore the "

Which is reinforced by the following; which serve to confirm that a Circles circumference length far from being irrational;

180 Degrees to its Diameter

360 Degrees to its Circumference

Therefore by giving 180 Centimetres to the length of Diameter

The Area to the "Square" of the Diameter is

32, 400 "Square Centimeters"

Rotate the 90 degree radius 360 Degrees; and the Area to the "Circle" of the Diameter is;

32, 400 "Circumnavigation Degrees"

Proving that the Circumferential length to a Circle has an "Exact Ratio" to its Radius (radii) length, and hence its Diameter length.

Therefore the "

*irrational/non-ratio*" formula of Pi cannot be considered or said to be; the ratio of a Circles circumference length, to Diameter length.Which is reinforced by the following; which serve to confirm that a Circles circumference length far from being irrational;

**Is perfectly symmetrical**

90⁰/cm radius x 360⁰ rotation = 32, 400 circumnavigation degrees

60⁰/cm radius x 360⁰ rotation = 21, 600 circumnavigation degrees

30⁰/cm radius x 360⁰ rotation = 10. 800 circumnavigation degrees

10⁰/cm radius x 360⁰ rotation = 3, 600 circumnavigation degrees

90⁰/cm radius x 360⁰ rotation = 32, 400 circumnavigation degrees

60⁰/cm radius x 360⁰ rotation = 21, 600 circumnavigation degrees

30⁰/cm radius x 360⁰ rotation = 10. 800 circumnavigation degrees

10⁰/cm radius x 360⁰ rotation = 3, 600 circumnavigation degrees

**360⁰/cm**

**÷ 5 = 72 ÷ 5 = 14.4 x 10 = 144 square centimetres ÷ 4 = 36 x 3 = 108 square centimetres to the circle**

**And this is why a circles circumference length, can be equally subdivided by any "whole number", into that number of exactly equal, and identical parts of the circle.**

**And any part of any circle multiplied by 360, will give 360 degrees to the circle with each degree exactly identical in curvature of length.**

*IRRATIONALITY Of 3.14159***When measuring the length of string against a straight ruler, after using it to measure the circumference of e.g. a cylinder; both the**

__stretched__longer outer circumferential length, and the shorter__constricted__circumferential length, are in effect measured as being one length; whereby it is in the longer stretched outer length of the string that is in fact being measured, as the shorter constricted length is included within the longer length.

*Oxford English Dictionary (OED)**Pi: Symbol of the*__"ratio"__of the circumference of a circle to its diameter, approximately 3.14159

*OED*

*IRRATIONAL: 1. Not logical or reasonable, not endowed with the power of reason. 2. Mathematics (of a number, quantity or expression)*__"not expressible as a ratio"__of two integers, and having an infinite and non-recurring expansion when expressed as a decimal. Examples are are the numbers pi and the square root of 2.**Quite clearly there is a contradiction in in terms regard to the definition of Pi in the OED.**

**On the one hand Pi is defined as being**

__"the symbol"__*(not number)*of__of the circumference of a circle; and then on the other hand it is defined as an__*"the ratio"**that is not expressible as a ratio of two integers.*__"irrational number"__

*OED*

*INTEGER: 1. A whole number; a number that is not a fraction. 2. A thing complete of itself.***And here is where the confusion has occurred; because Pi expressed in its original form as 22/7, is not a whole unit - number - integer of itself; nor is it a fraction, it is an improper fraction. Whereby the numerator above the line is comprised of 22 parts, and the denominator/**

__divisor__ below the line, is comprised of 7 parts of the 22 parts above the line.**Therefore when the divisor which is one whole unit consisting of 7 parts**

*, is used to divide the 22 parts above the line; it equates to 3 whole units - numbers - integers, and 1/7th of one whole unit of 7 remaining (in excess) or 3 & 1/7th units.*__(of one diameter unit of length)__**However in regard to the decimalisation of Pi, which gives Pi as being the approximate 3.14159, if we multiply this by 7, we obtain 21.99113 which is 0.00887 less than the original 22 parts/numbers over the divisor number of 7 below.**

*14 x 14 Square***Diameter 14 - Circumference 42 - Perimeter 56**

**14 squares x 14 squares = 196 squares to the area of the**

196 squares divide by 4 = 49 squares x 3 = 147 squares to the area of the

49 squares divide by 4 = 12 ½ (.5) squares to each corner of the square.

10 ½ (.5) squares x 12 squares = 126 to the inner rectangle of the triangle, divide by 2 = 63 squares to the

147 squares to the Circle minus 63 squares of the triangle = 84 squares to the 3 Non-linear/Mathematical Arcs of the Circle.

84 squares divide by 3 = 28 squares to each of the Non-linear Mathematical Arcs, of the

__Non-linear/Mathematical__Square.196 squares divide by 4 = 49 squares x 3 = 147 squares to the area of the

__Non-linear/Mathematical__Circle, with 49 squares remaining.49 squares divide by 4 = 12 ½ (.5) squares to each corner of the square.

10 ½ (.5) squares x 12 squares = 126 to the inner rectangle of the triangle, divide by 2 = 63 squares to the

__Non-linear/Mathematical__Triangle.147 squares to the Circle minus 63 squares of the triangle = 84 squares to the 3 Non-linear/Mathematical Arcs of the Circle.

84 squares divide by 3 = 28 squares to each of the Non-linear Mathematical Arcs, of the

__Non-linear//Mathematical__Circle.

*7 X 7 Square***Diameter 7 - Circumference 21 - Perimeter 28**

**7 squares x 7 squares = 49 squares to the area of the**

49 squares divide by 4 = 12 & 1/2 (.5) squares x 3 = 36 3/4 (.75) squares to the area of the

12 1/2 (.5) squares divide by 4 = 3 & 1/8 (.125) squares to each corner of the square.

5 & 1/4 (.25) squares x 6 squares = 31 & 1/2 squares to the inner rectangle of the triangle, divide by 2 = 15 & 3/4 (. 75) squares to the

31 & 3.4 (.75) squares to the Circle minus 15 & 3/4 (.75) squares of the triangle = 21 squares to the 3 Non-linear/Mathematical Arcs of the Circle.

21 squares divide by 3 = 7 squares to each of the Non-linear Mathematical Arcs, of the

__Non-linear/Mathematical__Square.49 squares divide by 4 = 12 & 1/2 (.5) squares x 3 = 36 3/4 (.75) squares to the area of the

__Non-linear/Mathematical__Circle, with = 12 & 1/2 (.5) squares remaining.12 1/2 (.5) squares divide by 4 = 3 & 1/8 (.125) squares to each corner of the square.

5 & 1/4 (.25) squares x 6 squares = 31 & 1/2 squares to the inner rectangle of the triangle, divide by 2 = 15 & 3/4 (. 75) squares to the

__Non-linear/Mathematical__Triangle.31 & 3.4 (.75) squares to the Circle minus 15 & 3/4 (.75) squares of the triangle = 21 squares to the 3 Non-linear/Mathematical Arcs of the Circle.

21 squares divide by 3 = 7 squares to each of the Non-linear Mathematical Arcs, of the

__Non-linear//Mathematical__Circle.**OED reiteration, Pi.**

*Pi: Symbol of the*__"ratio"__of the circumference of a circle to its diameter, approximately*3.14159.***Contrary to the OED definition of Pi being the ratio of the circumference of a circle to its diameter; Pi instead consists of 3 whole diameter lengths of 7 parts, with an excess of 1 part (1/7th) of a diameter remaining.**

**Therefore; if we give a circle a diameter length of 7 parts, and then square this to obtain the number of squares to its square, this equates to 49 parts to the square of the diameter; and 4 x 7 = 28 parts to its perimeter length.**

**Divide this by 4 = 12 & 1/4 (12.75) x 3 = 36 & 3/4 (36.75) squares to the circle of the diameter length; and 21 parts to its circumference length.**

**The reason why the original improper fraction of 22/7 and other close approximations of the ancient world arose; was because they relied upon a flexible length of string or flat tape, in order to gain a round objects curved circumference length. And when the length of the string was measured against a straight rule, it gave a false reading because its curvature of thickness, was also included within the straight linear measurement of its length.**

****

**In sum**

**The only way to gain the exact length of a circles circumference length, is mathematically by ratio; as this serves to exclude any physical applied means, of incurring an error.**

COMPASS AND LINECOMPASS AND LINE

**A compass has two armatures, with one arm having a scribing pencil tip to draw the line of the circle, and the other arm a sharp piercing steel tip which is used, to provide a stable fixed central point, around which the pencil tip can then be radiated.**

**Prior to drawing a circle, the two tips of the compass are separated to a measurement distance, that will subsequently form the**

__"single length - line of radius"__, that goes into make-up the__"bilinear"__diameter length of the circle.**However despite all methods used in order to enhance the accuracy of physically drawing a circle; the physical process of drawing a circle, is always flawed by the inaccuracies that are inherent and always creep in during the process of drawing a circle.**

In first place is the fact, that if even the smallest degree of inaccuracy occurs when measuring the distance between the two tips of the compass; the degree of inaccuracy is amplified as it is multiplied over the 360 degree length of the circle.

In first place is the fact, that if even the smallest degree of inaccuracy occurs when measuring the distance between the two tips of the compass; the degree of inaccuracy is amplified as it is multiplied over the 360 degree length of the circle.

**In second place is the fact, that as the steel tip of the compass pierces down into the drawing surface of the circle, the depth of its penetration in effect, serves to shorten the drawing surface distance, between the two tips of the compass.**

**third place is the fact, that the width of the surface area of the space that is taken up by the drawn line of the circle is dependant upon the sharpness of the pencil tip, and the thickness of the graphite tip widens as it is worn down over the length of drawing the circle.**

**In fourth place is the additional and overriding factor, that these factors and other factors of error that creep in during the drawing process of a circle; are repeated over and over again when e.g. as with a six sided hexagon, we sub-divide the circle into varying numbers and/or lengths of arc of the circumference.**

**However although it is impossible to physically draw a perfectly accurate circle, and as such define its exact length and surface area; this is not the case when we mathematically use the correct 3 to 1 ratio of circumferential to diameter length, which serves to exclude the**

__linear surface area__of the__outline__of the circle, from the overall equation.

UNIVERSAL GEOMETRY

UNIVERSAL GEOMETRY

**PILLARS OF CREATION - THE FUNDAMENTAL ENERGY AND RATIOS OF MATHEMATICS & GEOMETRY**

MICROCOSMIC NON-LINEAR DIFFERENTIAL GEOMETRY

MICROCOSMIC NON-LINEAR DIFFERENTIAL GEOMETRY

**MACRO-COSMIC NON- LINEAR DIFFERENTIAL GEOMETRY**

**MACRO-COSMIC LINEAR CONSTELLATIONS OF THE EUCLIDEAN MINDS EYE PERSPECTIVE**

RULER & LINE

EUCLIDEAN GEOMETRY

RULER & LINE

EUCLIDEAN GEOMETRY

**Euclidean Archimedean**

**Euclidean Definitions**

**1. A point is that which has no part:**

**Oxford English Dictionary. Point: That which in geometry has position but not magnitude, e.g the intersection of two lines**

**Author: If a point had no parts as per the Euclidean concept, then it could neither exist in the empirical physical realm as an apparently solid spatial point/state of matter, or as a geometrical/mathematical focal point, or spatial point within the realm of the minds eye of our**

*(Metaphysical)*imaginations.**2. A line is a breadth-less length:**

**Author: All physical geometric shapes are mathematically defined by the lengths/dimensions of their boundaries/extremities not by lines; and all drawn lines, possess a length and breadth that is comprised of particulates of matter. However within the metaphysical realm of mathematical/geometrical calculations, they**

*(should only; refer to next chapter Pi In Black & Yellow)*only possess a value of distance, not an area or a volume of substance.**3. The extremities of a line are points:**

**Author: The extremities of all lines (boundaries) are made up of non-linear in motion proximate's, of smaller particulate's and groups of particulates.**

**4. A straight line is a line which lies evenly on itself:**

**Author: A straight line is a macro-cosmic perception not a reality, as all things possess boundaries that are particulate in nature, and would appear as such when viewed from a microcosmic perspective.**

**5. A surface is that which has length and breadth only:**

**Author: A surface is the boundary of a structure, that is comprised of trillions of non-linear/multi-dimensional particulates, all of which are is a constant state of motion relative to each other.**

**6. The Extremities of a surface are line:**

**Author: As per previous.**

**To be continued**

Taking a break to do some gardening and set up sun shading during this the fourth hottest year on record, and highest recorded temperature of 14 degrees above average.

Taking a break to do some gardening and set up sun shading during this the fourth hottest year on record, and highest recorded temperature of 14 degrees above average.

MINUS Pi IN BLACK AND YELLOWMINUS Pi IN BLACK AND YELLOW

**Card A Card B**

**Card B Card A**

**Card B Card A Card A Card B**

**120 X 120 cm 120 X 120 cm**

**We have two square yellow cards measuring 120 cm's x 120 cm's**

Card A. has a black circle of 120 cm diameter, and has been cut into 4 equal quadrants of 60 cm squares

Card B. has four 60 cm diameter circles to each quadrant, and has been cut into 4 equal quadrants of 60 cm squares.

Card A. has a black circle of 120 cm diameter, and has been cut into 4 equal quadrants of 60 cm squares

Card B. has four 60 cm diameter circles to each quadrant, and has been cut into 4 equal quadrants of 60 cm squares.

__A. Black Areas__**1.**

**All black areas have an equal area to each other**

**2. Any number or type or black area combined will give an equal area**

**3.**

**All black areas combined will give an equal area**

__B. Yellow Areas__**1. All yellow areas have an equal area to each other**

2. Any number or type of yellow area combined will give an equal area

3. All yellow areas combined will give an equal area

1. Have an equal area

2. Any number and any combination of black and yellow areas, will give an equal area

3. All black and yellow areas combined, will give an equal area

4. All areas of the two cards combined, will give an equal area (288 squares)

2. Any number or type of yellow area combined will give an equal area

3. All yellow areas combined will give an equal area

__C. All Areas Of The Two Cards__1. Have an equal area

2. Any number and any combination of black and yellow areas, will give an equal area

3. All black and yellow areas combined, will give an equal area

4. All areas of the two cards combined, will give an equal area (288 squares)

__Logic__**1.**

**All of black and yellow areas of circle and square contain an equality of area**

**2. When an equal amount of area is deducted from an equal amount of area, it leaves an equal amount of area remaining**

**3.**

**Pi has a greater sum of inequality to its area, than that of the lesser sum of equality to the area of the circle**

**4.**

**Pi is a mathematical infringement into the area surrounding of a circle**

Pi represents the physical inequality of the thickness of a flexible length of measuring string or tape, or the width of the "area"

__In Sum__Pi represents the physical inequality of the thickness of a flexible length of measuring string or tape, or the width of the "area"

*(flat space)*of a flat line that has been drawn upon a surface, having inadvertently been included within the formula, rather than its flat space having been mathematically excluded from the formula.

*Gods Center is everywhere, Gods Circumference (Line) is nowhere.**Saint Bonaventure*

**RELATIVITY**

*AXIS OF TIME OVER DIAMETER OF TIME***The equatorial diameter of the Earth, as it rotates around its Earth axis is "**

__given__" as being 7, 926 miles.**The equatorial diameter of the Earth Time Meridian, as it rotates around its Earth axis is "**

__given__" as being 8, 000 miles.

__Therefore & Accordingly__**A. The equatorial circumference of the Earth, as it rotates around its Earth axis is**

__23, 778 miles.__**B. The equatorial circumference of the Earth Time Meridian as it rotates around its Earth Axis,**

__24 000__equatorial miles = to__24 Hours.__**C. The square of the diameter of the Earth Time Meridian, is**

__36, 000__equatorial miles = to__24 Hours.__**Which in terms of**

__mileage distance relative to time__would seem to be a contradiction, however it is not because;

__By Rotation__**A. 23, 778 miles = 360 Degrees of a Circle**

**B. 24, 000 miles = 360 Degrees of a Circle**

**C. 36, 000 miles = 360 Degrees of a Circle**

**The Common Denominator of all three (Linear) distances of mileage**

__by ratio__, is a*(conceptually mathematical)*constantly Rotating Circle - Cycle of__360 Degrees of 86, 400 Seconds of Time (ing)__.

__24 Hour - Rotational Motion over 24, 000 Mile - Fixed Linear Measure__**Linear Length of One Hour**

**1 Hour = 63, 360, 000 Inches divide by**

*(*

*60 Minutes x 60 seconds)*= 3, 600 seconds**63, 360, 000 Inches divide by 3, 600 seconds = 17, 600 inches per second**

**17, 600 inches divide by 12 = 1, 466 feet and 8 inches per second**

**1, 466 feet divide by 3 = 488 yards with 2 feet remaining**

**The Earth rotates at a rate of 488 yards, 2 feet and 8 inches per second, "**

__according to__"__24 Hours of Curved Motion of Distance__over__24,000 Fixed Linear Miles of Distance__.**The Equatorial diameter of the Earth is given as being 7926 miles, rather than the 8,000 diameter that it would need to have, in order to possess a 24, 000 mile, 360 degree circumferential length; rotating at a rate of 1, 000 miles per 15 degrees = 60 minutes to the hour.**

**Therefore it follows that the curved differential degrees of time, over the curved differential distance of the Earth's rotational circumferential length (or visa-vis); is not consistent with, but relative and approximate to our Euclidean straight linear concept of time.**

**7, 926 miles x 3 = 23, 778 miles per 24 hours**

**23, 778 x 1, 760 yards = 41, 849, 280 yards**

**x 3 = 125, 547, 849 feet**

**x 12 = 1, 506, 574, 080 inches**

**÷ by 24 hours = 62, 773, 920 inches per hour**

**÷ by 12 = 5, 231, 160 feet per hour**

**÷ by 3 = 1, 743, 720 yards**

**1, 743, 720 yards ÷ by 1, 760 = 990 miles per hour with 3/4 of one mile remaining**

**3/4 of one mile = 1, 320 yards per hour remaining**

**1, 320 yards**

**÷ by minutes = 22 yards per minute**

**Therefore given a curved rotational circumference length of 23, 778 miles over 360 degrees to each day; the Earth would have to increase its rate of rotation by 222 miles each day in order to fit in with and full-fill our straight linear concept of time.**

**Quite simply, straight linear measurements are gained by the use of straight rulers, with each equal linear increment along the length of the ruler, as such representing the length of any one of the four right-angles to a square. Therefore all straight linear lengths, are in effect being measured by using a series of equal right angle square lengths, each of which has the same value of measurement unit.**

**Circles curved circumferential lengths however do not possess any right angles, as their lengths are comprised of the 360 equal distances, that exist between each of the 360 radii termini that radiate from the centre of the circle.**

**And unlike the fixed straight linear square measurement/value units of a ruler, which have one consistent value of one square measurement unit each; the lengths of the 360 degrees to the overall curvature of a circle are dependent upon, and vary in length relative to the**

*(expansive or decreasing)*radiated lengths of the 360 radii, extending from the centre of the circle.**However as there is a constant ratio of a circles circumferential length, that is 6 times the length of the circles radius, and 3 times the length of its diameter; and there is a constant ratio of a squares length, that is 8 times the length of the circles radius, and 4 times the length of the circles diameter;**

**So it is, that it is possible to obtain by the rotation of the Earth's (Given) constant circle of 24, 000 miles of circumferential degree length; relative to its fixed solar position of 0/360 degrees;**

**A constant speed of 360 larger "**

__" = to a measured length of 24, 000 miles; over 360 smaller "__*Spatial Degrees*__" of the Earth's "actual" circumferential length;__*Terra Degrees***That have been further sub-divided, into 24 smaller lengths of "**

__15 Terra Degrees__*"*called one hour.

*PHENOMENON OF THE PYTHAGORAS THEOREM*

*Geometric Encounter With The Third Dimension*

**PYTHAGORAS 2582 - 2500 BC**

*In any right angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.*

**www.Maths forum: 370 proofs are given in the book "The Pythagoras Proposition" published by E S Loomis 1940.**

**www.BabylonianPythagoras: The earliest record of the Pythagoras Theorem appears on the Babylonian Susa Tablet dated between, 1,800 - 1,600 BC.**

**A B**

**In diagram A it can be seen that given a right-angle triangle with a base and vertical line measuring 12 squares, the square on the hypotenuse measures 17 x 17 squares, which equates to 289 squares.**

**However when the number of squares and half squares of this "45 degree" angle square on the hypotenuse, are counted; there are 264 whole squares + 48 half squares = 288 whole squares, to the "45" degree square on the hypotenuse.**

**While In diagram B of the 17 x 17 "vertical" square, it can be seen that there are 17 rows of 17 squares which amounts to 289 squares. Which is one square more than the sum of the squares on the other two sides of the right angle triangle.**

**Therefore given all of the proofs that have been given in regard to the Pythagoras over previous millennium's; one can only assume that, this phenomenon has either been missed or ignored, and placed in the too hard basket as a result.**

However regardless of what is true in regard to the past, or whether an answer can be found as to why this phenomenon occurs or not; it serves no constructive purpose to ignore it but rather to consider it, and/or leave it open for others to do so if they wish.

However regardless of what is true in regard to the past, or whether an answer can be found as to why this phenomenon occurs or not; it serves no constructive purpose to ignore it but rather to consider it, and/or leave it open for others to do so if they wish.

**A B**

**Diagram A above shows how by radiating the length of the hypotenuse of the 12 x 12 square to the vertical or to the lateral, the number of 17 squares to the hypotenuse length of the square is gained.**

**Diagram B shows the radiated length of the hypotenuse of a 12 x 12 square adds 5 squares to the vertical height of the right-angle, and the radiated length of the 17 x 17 square adding a further 7 squares to the vertical right angle, and in effect doubling the height and base width of the right-angle.**

**In diagram A above it can be seen, that the phenomenon of an extra amount of area to the square on the hypotenuse, is not isolated to just a 12 x 12 right-angle triangle; it also occurs with a 6 x 6 right-angle, where there is an extra 0.25 (1/4) square area, on the 8.5 (8 1/2) square of the hypotenuse.**

**In diagram B and relative to diagram A, it can be seen that although 8.5 x 8.5 squares equates to 72.25 squares of area; all three of the "45 degree angle" squares of the hypotenuse in the two diagrams;**

**contain the same area of of 72 squares within them. And any two of those three squares in sum, equate to the same number of squares on the other two sides of the right angle.**

**Baffling!**

**1. We have three 45 degree angle squares of the 8.5 hypotenuse, with the same lengths of right angle as the hypotenuse length, and as such each of their three areas are the same 72 squares.**

**2. We have a length of 8.5 squares to the length of each of their right angles, which when equated as 8.5 x 8.5 gives an area of 72.25, one quarter of a square extra.**

**3. When we equate the square of the hypotenuse length of 17 squares as 17 x 17 squares, this gives an area of 289, which is one square extra, to that of the sum of 288 squares on the other two sides of the right-triangle.**

__Empirical__**1. The areas of the 45 degree angle squares of the hypotenuse all concur in sum, with the sum of the areas of the squares on the other two sides.**

**2. The areas of e.g. the 17 x 17, "45 degree angle" square of the hypotenuse which is 288; does not concur in sum, with the sum of the 17 x 17, "90 degree angle" square, which contains one extra square in sum 289 squares.**

__Conclusion__**The dimensional lengths of angle and perspective, relative to the two vertical (perpendicular) and the lateral (horizontal) dimensions, are not precisely the same according to our linear measurements; hence angular dimensionality is indeed of itself, differential to that of vertical and horizontal dimensionality.**

**Therefore the questions is and remains, can this differential between the three dimensions be rationalised; or more simply how and why?**

__Oxford English Dictionary__**Circle: 1. A round plane figure whose boundary (the circumference) consists of points is equidistant from a fixed point (the centre). 2. The line enclosing such a figure.**

**Angle: The space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point they meet.**

**Degree: A unit of measurement of angles one three hundred and sixtieth of the circumference of a circle; set at an angle of 45 degrees.**

**Perspective: The art of drawing solid objects on a two-dimensional surface so as to give the right impression of their height, width, depth, and position in relation to each other when viewed from a particular point.**

**What becomes clearly apparent from examining these four definitions; is that when we think of and relate to the nature of a circle or circles, our minds are locked into relating to them in the form of the straight angles of linear geometry, rather than what a circle is and what its angles represent.**

**A drawn circle is basically a flat cross section of a sphere or a cylinder, which has been transposed onto a solid flat surface by the use of a**

__"radiated"__drawn line. And the__"radius"__, and angles of the drawn__"radii"__that go into the make up of a drawn circle, are basically straight and flat linear representations (mimicry's) of the__"three- dimensionally angled radiations"__that in nature extend from the centre of gravity of a sphere of influence*(e.g. the centre of gravity of the nucleus of an atom, or the centre's of gravity of particles, planetary bodies, solar bodies)*, or indefinably from the centre of gravity of a solid sphere.

*Note: The straight linear sub-divisional angles of degree, relative to that of the centre of a circle we draw on flat paper; relative to the real physical world, are representatives of 360 visual angles of perspective (Depth of vision through the surrounding atmospheric medium) from the centre of the circle, and 64, 800 degrees of perspective from the centre of a sphere, or a sphere of energetic influence.*

**Therefore when we draw a circle by rotating the terminal fixed distance point/pencil tip of a compass armature around the central fixed point/steel tip of its second armature; in effect what we are doing is orbiting the measured straight linear distance of the radius of one "spatial tracking" body, around a second centrally fixed spatial body, in order to create a visible and therefore measurable "static flat track line", of the circular "orbital motion" of the orbiting body around the central body/axis.**

**Having achieved the completion of a fixed visible "**

__" of the "__*circular static flat track line*__" of the orbiting body, we are then able to attach to its "__*motion**flat fixed on paper orbital track*"; 360 "*orbital motion body equivalents"*called degrees, which are equally spaced apart, and can then be used by the ratio of the scale of their arc lengths apart;**To that of the scale of length, to that of the straight line orbital radius**

*(radial/radiant-radiation)*length, to find the flat fixed straight line length, of the orbiting body;**Put more simply, to find the length of the non-linear circular orbit of the (an) orbiting body, and "**

__" into a "__*convert**it**" on paper.*__flat static straight linear length of scale__**However the problem with this conversion of the scale of circular motion, to that of a static straight linear scale of length, that has occurred over time;**

**Is that we have lost sight of the fact, that the linear fixed degrees that we geometrically apply to a static line of circle drawn on paper; are actually representatives of a scale of circular orbital motion, travelling over a curved length of distance, not a flat static straight line of distance, as measured by our human and varying scales of measurement's on paper.**

**Quite simply; degrees are a constant scale of orbital-circular motion; that by ratio, are applicable to all other smaller or larger orbital-circular rates of motion**

*(The symmetrical scale of one circle, is applicable to the symmetrical scale of every other circle)*.**Therefore it follows; that all scales of measurement we use, in order to convert a distance of circular motion (A Circle), over a static straight linear distance (Straight Line), must by ratio, be compatible with that of the scale of degrees, that apply to all forms of curved - circular - orbital - circles - cycles of motion.**

__Scale of Degrees__**Three hundred and sixty degrees go into the scale of one day.**

**One day consists of the orbital motion of one fixed point of 0/1 degree (Greenwich), travelling over the 360/0 degree curved circular distance of 24, 000 miles.**

**One hour consists of the orbital motion of that 0/1 degree (Greenwich) travelling over 15 degrees of a curved circular distance of 1, 000 miles.**

**Therefore**

**One Day = A Circle of 360 Degrees**

**24, 000 Miles**

**24 Hours**

**One Clock Hour = A Circle of 360 Degrees**

**1, 000 Miles**

**15 Degrees of Orbital Travel over Earth's Curved Distance**

**60 Minutes**

__To be continued__