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Mathematical Proof π is by Design

My aim is to demonstrate a unique series of steps to calculate π 3.141592653... A fascinating number, because it is the mathematical ratio upon which the whole physical universe is designed! The finding of the related number 3.141602671... was important because it provided the correct starting point.

This page is a bit lengthy but it is a record of my finds and the various steps taken to arrive at a point very close to the location of π. The precise and remarkable π conclusion continues in The exact value of π.


Straight lines are our attempts to physically measure the reality of non-physical and invisible energy waves. This idea is suggested by the 3-4-5 Pythagorean right triangle where sections 3 and 4 denote straight lines, and section 5 that energy wave or arc/spiral section. A rotating, right twisting, vortex phenomenon.

ratios of π and phi

While working on the Squaring the Circle and Stonehenge pages I discovered a 1.8 split ratio of 35.71... and 64.28...%, which represents the number 3.141602671...! It is the split result between two concrete working numbers 3.144654088... Squaring the Circle, and 3.139907440... Stonehenge.
The number 3.141602671... is linked to π, and together form a 3.5 ratio!

I also observed that both ratios of π and phi grow towards the center ' 1 ' at .001, .0001, .00001 etc. the closer the number values approach each other. And it appears that the number 1 gets closer and further away at the same time. However, the lines never touch but only pass each other with 1 always in the center, while the e-ratio at this stage remains at a constant 2.722222... (122.5 / 45).

ratio constant

A repeating ratio occurs regardless of size when subtracting two phi numbers from each other, divided by a third one and working towards the center. To do this, take a group of three of those phi numbers in a row, add the bottom two numbers and divide into the top one. The number 2.72... is close to e-constant 2.71...

Furthermore, 100% divided by 2.722222... = 36.73469...%, minus 100 = 63.26530...%. Those numbers are very close to the 37 and 63 percent approximation split as used in today's ' e ' probability calculations.
(e is used in growth calculations, such as economic or growth of populations etc.)

balanced ratios

The ratio presented in circular form as counter and clockwise spirals.
It is like looking into a vortex or tube where the yin and yang symbol comes to mind as well as balanced ratios.

perfect ratios

Important information to consider:
The top of the vertical red line at 3125 mm (tip of the pyramid) at 3.2 represents the visible physical limit, as was explained in the Squaring the Circle page. The correct π 3.1415926... at 3182.83130505...mm as measured from the base of the pyramid, is located within the small blue diamond shape signifying the unseen realm!
Straight lines are an illusion and the red line measured from the bottom of the pyramid and crossing over into the unseen realm at 3.2 toward the location of π, represents an arc or spiral section!



Overlaying the spirals ratio diagram onto the 5000 x 5000 mm Magic square of the Sun, and zeroing in on π and its companion number 3.141602671..., both of which are located within the small blue diamond set on the tip of the pyramid! Entering the small blue diamond shape and zeroing in ever closer to π and ultimately establishing the exact value of π, will take up the rest of this page as well as the next page.
I chose the 5000 mm square and cube outside edge measurement from start to finish for simplicity sake, but any other dimension could be used since ratios are what matter.

When multiplying or dividing any horizontal or vertical line length involved within the square (cube) the results become simple numbers, and it is a quick method to test and see if a calculation has gone wrong. However, this does not work with diagonal lines because they all represent arc sections!

For example, 5000 mm divided by 3125 mm (the height of the pyramid as represented by the red line) is 1.6.

I mainly use 3125 from here on as my number to divide other numbers into to get that simple number, which I will put in brackets. Any number involved in the magic square or cube could be used here such as 5000, 3125, 777, 125, 1.
(The Babylonians pegged one of the earliest π numbers at 3.125)

diamond shape

Several measurements involved in the diamond shape. Think of these drawings as 3-dimensional.


The diamond shape is as tall as the capstone it is sitting on, 125 mm.

circle split

Where the blue lines intersect marks the location of the circle split 35.714285714... and 64.28571428...%.

This information is connected to Daniel's days page.


From the tip of the pyramid at 3125 mm to the blue 16X triangle is 57.705965909090...mm (3182.705...mm total)
(63.4765625 / 1.1 = 57.705965909090...)


Before proceeding, I would like to show an interesting feature. The orange lines in the diagram represent the 5x5x5 (5000 x 5000 x 5000 mm) cube, red 6x6x6 cube, and yellow a 7x7x7 cube. Imagine this as a painting with a frame around it. The orange 5x5x5 square represents the inside of the frame, red 6x6x6 the center, and the outside of the frame is represented by the yellow 7x7x7 square. The blue dotted π lines pass through numbers 13 and 18 located on the inside of 5x5x5 frame, the center of the 6x6x6 frame and the outside of the 7x7x7 frame.

Seven represents spiritual perfection, six has to do with man (male and female) the number of imperfection and the human number, five the number for grace, and triple 444 is the world number, and so on. For more on this read: Number in Scripture: Its Supernatural Design and Spiritual Significance by E. W. Bullinger (1837-1913).

From the base of the pyramid to the intersecting blue dotted lines close to the location of π is 3181.831325 mm, add 3125 mm= 6307.831325...2= 39788736.024651255625. Divide this number into 125000000 for answer 3.1415926* 337... Note that this is correct only to the number 6, but I am going to step by step fine tune to the number of π.

When I saw that the dotted line numbers 13 and 18 intersected close to π, I was reminded of Revelation 13:18 where it talks of the mark of the beast. Verse 18 "Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six." Literally, the biometric ID number is a “number...that of a man” (Revelation 13:18). "Of a Man Definition: a human being, whether male or female, generically, to include "all" human individuals." (From the Linked Word Project excellent Bible study tool.)

As mentioned elsewhere, some of you may know that a calendar is just one aspect of the Great Pyramid where dates of past and future events written in stone can be measured accurately, and π is a specific point in time!

blue dotted π lines and blue dotted π lines

These next measurements are from the base of each triangle to the intersecting blue dotted π lines, as they are reduced in size. Shown here are the first two examples: The largest triangle is right side up and has a red post, the next triangle (reversed) is half the height (not volume) and has a blue post, and so on towards the center.

Diagram A


Diagram A

Diagram A: The triangles lined up, so that all are of the same size. Within the fifth triangle (16x) π is now in the upper half of the pyramid, compared to the previous four where it was in the bottom half of each triangle.

Diagram A


Diagram B

Diagram B: As you can see in the previous diagrams, the dotted lines do not hit the tops and bottoms of the triangles perfectly! So now, the length of each post is based on a set of lines hitting the tops and bottoms of the pyramids perfectly, as shown in this set of diagrams.

Diagram B

This diagram shows the overlay of diagrams A and B. The red lines represent the results from diagram A and the blue dotted lines represent the results from diagram B. The blue horizontal line is what we are going to focus on next. It is the difference between the results of A and B. I call it the gap.

To the right and in the 32x triangle is a short vertical green line (circled), and will be explained next.

the gap

The "gap" and a closer look at the red-circled area.

gap width

The total gap width is .023873185...mm. The short vertical green line in the earlier diagram is .23873185...mm (13090). It is a drop by a factor of 10.
Top of gap .126826298... minus bottom .125334224...= .0014920741...(2094400) times 16= .023873185...mm.

Showing that π is located within the .000402680...mm gap. The method was explained earlier. From the base of the main pyramid to the base of the 16X triangle is 3182.70596590...mm. Add .12535939...mm (top of the .000402680... section)= 3182.83132530...mm, add 3125= 6307.83130505...2= 39788735.77297459... Then divide this number into 125000000 for the answer π # 3.1415926*334... Using the same method for the bottom of the .000402680...mm section it is .125334224...mm for a π # 3.1415926*58... The exact π # 3.1415926*53589... is located between the two numbers!

.00148715... X 16= Gap space to π .02379451...

two numbers

gap ratios

.020536692...mm / .002933813...mm = 7 and .020536692...mm / .000402680...mm = 51

.002933813...mm / .000402680...mm = 7.2857142857... (51 / 7)

reducing triangle sizes

This example is based on previous measurements by reducing triangle sizes, however the gap or bandwidth in this method is .02754598342...mm (777 / 28207.3792).
The split (not using the red line) is between .0156093906...mm (3125 / 200200) and .011936592...mm (3125 / 261800).

The thin red line represents the "13:18 " π junction based on the intersecting blue dotted π lines.

5th triangle

As mentioned already, within the 5th triangle (16x) the band width and π are now in the upper half of the pyramid, compared to the previous four where it was in the bottom half of each triangle.
The band completely misses the 32x triangle and any further triangles from here on.

Working within the .000402680...mm gap and continuing towards π is somewhat like approaching the center of an hour glass or the edge of a knife blade.

the split of 80.46875

.125334224...(777 / 6199.424) + 0.000004915...(3125 / 635740160)=  0.125339140129...

the red line

The correct π # 3.141592653... sits just below the red line. This line divides 80.46875 and 19.53125 percent, so that π is a little more than 80.46875 % and a little less than 19.53125 %.

To be more precise
80.468463897705078125% = .125338694492...= 3.14159265*403486...
80.46875%                        = .125339140129...= 3.1415926535*9096...
00.000000000000029384858097488348901575404318685127667675662076...% (3125 / 106347289125316800)
80.469036102294921875% = .125339585765...= 3.141592653*14707...

19.53125 / 25781205= 0.00000075757707989211520563138922... + 80.46875%
Difference= 0.000000000000029384858097488348901575404318685127667675662076...% ( π inside this gap)
19.53125 / 25781206= 0.00000075757705050725710814304032... + 80.46875%

Before continuing with this I want to share some interesting observations concerning the 19.53125 / 80.46875 split.

flip back 19.53125

From 100% flip back 19.53125 to 80.46875, from there flip back 19.53125 to 60.9375, then flip back 39.0625 to 21.875, and finally from 21.875 flip back 78.125 to -56.25 past the center point.




This is self-explanatory because the measurements (ratios) are the same as in the above diagram.


number sequence

number sequence

Follow the number sequence 60.9375 minus 19.53125 = 41.40625 / 19.53125 = "2.12"
41.40625 x 2 = 82.8125 mm


The blue rings line up perfectly in this hourglass/cup shape form when inserting the 2.12 blue ring component! Imagine this as 3-d where the circle is a sphere and π is close to the 80.46875 line.

35.714... / 64.285... % represents 3.1416026716...
02.590... / 97.409... % represents 3.1415926535...

97.40909103... / 75.76262636...= 1.285714285 X 7= 9
97.40909103... / 21.64646467...= 4.5
75.76262636... / 21.64646467...= 3.5

This side view shows the horizontal and vertical relationship between the two π numbers.
And when rotating the diagram 90° it matches the shape that is contained within the Sun Magic Square.

great pyramid 111

More links to the hourglass/cup shape forms and the Great Pyramid.

13 and 18

Zeroing further toward the center point π within the triangles using a series of diagrams to reveal a kite shape, and the measurements contained within it. The first drawing shows the intersecting dotted lines passing through grid points 13 and 18, and in the next drawings joined by other lines that intersect triangle points.

toward the center

kite shaped

kite shape

Compare to the Tree of Life drawing.

tree of life

kite hovering

plumbob shaped



This unit at .02029220779…mm tall is 154000 times smaller than the 3125 mm pyramid height, and 6160 times smaller than the 125 mm height of the diamond shape!


red and blue

The red line measured from the top of the kite shape down to the location of π is .001487157...mm

Continuing within the 19.53125 / 80.46875 split


The half gap measurement of 0.000286102294921875 is the same number cited in the book De Steenen Spreeken.

0.000000000000029384858097488348901575404318685127667675662...= 100% = (3125 / 106347289125316800)

In these closing steps I found the unique split in 0.0000000000000293848580... and observed repeating patterns in the strings of numbers where every section is 12 digits long in 3 out of 4 strings of numbers.

repeating patterns

97.3554... / 0.0000000000000286077466...= 3403113252010137.6
02.6445... / 0.0000000000000007771114...= 3403113252010137.6

106347289125316800 / 3403113252010137.6= 31.25 x 4= >>> 125 <<<
31.25 x 1.25= "39.0625")............................................31.25 x 32= 1000 or 125 x 8= 1000

At this juncture approximately .05% from π the patterns seemed to have stopped and it puzzled me. After getting back on track, there were just a few remaining steps all the way to the precise location of π. It concluded in some amazing but not surprising mathematics and geometry!

Page two. The exact value of π !


Additional information up to the 97.3554017462544758977984348022977984348022977984348022...% split:

Calculating e constant:
97.3554... / 02.6445...= 36.812926... %
Subtracted from 100 %= 63.187073... %

Close to the 37 and 63 percent approximation split as used in today's e probability calculations!

100 / 36.812926...= 2.716437..., and the official e constant = 2.718281... (A difference of about .05% at this point)

97.35540.../ 4096= gap space .023768408...close to π. [4096= 642(Square), (32 Absent), 163(Cube), 84, 46, 212, 1]

97.355401746254475897...% A difference of approximately .05% from π:
97.40909103400243723...= π4π 3.14159265358979323...

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