Squaring The Circle With ONLY Compass & Square (No Measurement Markings)

In 2021 I had a breakthrough discovery on the Da Vinci squaring of the circle.

For centuries this has been a mathematical challenge: Squaring the Circle with ONLY a Compass and Square (a Straight Edge with NO MARKINGS on it Whatsoever) in a FINITE Number of Steps.

Well, here it is. I will also post a video following this of me hand ✍️ drawing this representation of Divine Balance (Masculine and Feminine Energies) with NO Markings on my straight edge and along with the straight edge, using only a pencil and compass. Finally, after many millenia, this ancient method is available to the world at large. I encourage you to try drawing this yourself and absorbing its significance (for our time) into your awareness.

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Robert Edward Grant

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[RockMe]

Something incredibly stimulating watching you draw that out with that music in the background and your soft tone of voice. Thank you! 😍

[BrunildaLibera]

I am so incredibly grateful for this robert. Its a gift to get to draw this... Thank you for sharing all the knowledge freely like you do. Not only the content but your atitude also deeply o inspires me.

[pvdguitars]

Dear Robert,
By assuming the radius of the circle = 1, then you can demonstrate - using trigonometry (Pythagorean rules, sin rule, ...) that:
The top angle of the triangle is 45 degrees, thus :
1. The base side of the triangle (=side of the square) = 2sin(22.5°)/sin(67.5°) which corresponds also to 2(√2 - 1)
2. The perimeter of the square is thus (4xside)= 16(√2 - 1), approx. 6.627417
3. The area of the square is thus (side)^2 = 16 (3 - 2√2), approx. 2.745166
Consequently:
a) Perimeter: P[square] is 12.61865% larger than P[circle]=2π (6.28319 ...)

b) Area: A[square] is 5.47862 % smaller than A[circle]=π (3.14159...)
Your approach is a perfect match for the DaVinci Vitruvian man. Spot on!
There is an easier way to draw the circle/square by using a square edge and a compass (Masonic approach); identical result though.
I can share my calculations if you wish (including some fascinating mathematical connections with the Vesica Pisces, the mother of geometries and the Fibonacci sequence (golden ratio Phi)).

Kind regards, Philippe

[kennethbeal]

Thank you! X marks the spot! :) Noticed an enhancement you might make: for this exercise, as you used a compass, a square, *and* the paper manufacturer's precision. In other words, you used the edge of the paper to line up the first (and a later) line.

Instead, you could draw an initial horizontal line[1], and then use that as the "starting edge, " so that the solution is completely 'self-contained" as it were, angle-wise. Thanks again!

[1] -- Like, rotate the paper 45 degrees, or rip the edges off so they're not uniform, etc.

[scottdellinger]

The true test was only to use a straight edge and a compass. Using the end of a ruler as a square is a cheat.

[anthony]

i think about your work all the time and thank you for your time

[dpapazoni]

A single edged razor blade also works geat for sharpening the lead on your compass.

[LoLhEnRy]

this reminds me of the visual pathway of the brain images we see. How the view is inverted. i also noticed this is the esoteric sigil of lucifer inverted. I wonder what the triangle in the middle has to do with how we view perception. The X in the middle is almost that of a focal point. This looks like a map the the brain to me. Thank you for uploading.

[flammen]

Why am I watching this? I should be asleep.

[wagdan]

The angle seen from the upper triangle is 47 degrees.
47 degrees from the compass + 90 degrees from the square equals 137
❤ 137=YHWH ❤

[ThoughtCannon]

Would you kindly show the results of your final measurements with this technique?

[triceunity]

Your hands, your voice.. and the squaring of the circle by you with you is heaven.. 🔵♥️🟥

[pvdguitars]

Even with the naked eye, you can see that neither the area nor the circumference of the circle matches the square. Without trigonometry math proof, the drawing is misleading.

[fenixgirl]

as you drew this i kept thinking of the image done by DiVinci...showing the golden ratio...could that also be the squaring of a circle in that image as well?

[anthony]

you used the bottom of the paper as a reference why don't you use your own square lines you draw.

[MelindaConroy-ch]

I literally sit here with tears from the articulation of your work, Robert! You've GOT to know DeVinci watches IN AWE from above your shoulder!!!

[anthony]

what does it take to center the circle?

[DANIELBRADLEY]

Wait…so you need a perfectly square piece of paper and the ruler has to have a perfectly square edge too??? That doesn’t seem right…they said just straight edge and compass, not perfectly right angle square and compass… 🧐

[anthony]

the square to the circle degree off set

[healmejohnredcorn]

Can you point me to the lovely symphony being played