Pi number

Jude Andre Charles

C.B. is b squared the height of the triangle? I would suppose the base instead as it comes up the shortest. But so far you have exactly the same results as I do.

C.B.

Jude Andre Charles
is b squared the height of the triangle? I would suppose the base instead as it comes up the shortest.

B is the long led and b² the short leg of the triangle. The height is 1, the hypotenuse.

Jude Andre Charles But so far you have exactly the same results as I do.

Yes, but my result is justified or demonstrated.
I’m working from the beginning with the exact value of π, disguised as 4b the perimeter of the square. This is the missing part in the work with the pyramid.

Jude Andre Charles

Before the end of the day, I will reproduce it on Desmos as a comparative assessment.

Jude Andre Charles

Do not doubt yourself. Your results are correct.

C.B.

Jude Andre Charles

Jude Andre Charles Do not doubt yourself. Your results are correct.

I know they are correct as you can easily corroborate it looking at the derivation.

Jude Andre Charles

C.B. We apply Pythagoras:

b4 + b2 – 1 = 0

And obtain the value of b or π/4:

b = 0.78615

How did you get there?

C.B.

Jude Andre Charles

I obtain b, area of the circle and b² area of the square and I use them as the legs of a right triangle and I take the diameter of the circle 1 as the hypotenuse and apply Pythagoras.
That’s it.

Jude Andre Charles

C.B. so from what I understanding, you are using the areas as basis for the legs of the triangle and then build around it both the circle and the square, is this correct?

C.B.

Jude Andre Charles

Jude Andre Charles so from what I understanding, you are using the areas as basis for the legs of the triangle and then build around it both the circle and the square, is this correct?

Not exactly. We have already the circle and the square. They are the premise of the derivation. We use the circle to inscribe in it the right triangle and have the diameter as the hypotenuse.

Jude Andre Charles

C.B. so of course the radius for the circle is pi/4, the length of the square is (2(pi/4)²).

But when I do the Pythagorean Theorem, I don't get 1. Is there a reason?

C.B.

Jude Andre Charles

No, the radius is 0.5.
Otherwise the perimeter of the circle can’t be π

C.B.

If you’re trying to understand this derivation now, forget for a moment everything else you have been doing regarding 3.1446. Otherwise you’ll get confused.
When you’re through with it then you can correlate it to the geometry of the pyramid.

Jude Andre Charles

C.B. I think I see where I might've confused you with my results. You results are based on the fact that the square has four faces. Mines are based on 8 faces (as per the Pyramid of Giza). I'll try redoing it again without the 8 faces confusion.

Jude Andre Charles

Not in order but you get the gist of it (no phi or 3.144606 in that one)

Jude Andre Charles

Tried it with 3.14460551103, although I used a variation of the equation for the Circumference. The rest is more or less the same.

C.B.

Sorry Charles, but I can’t follow.

Jude Andre Charles

C.B. how so?

C.B.

Jude Andre Charles
I can’t understand what you’re doing

Jude Andre Charles

C.B. I see. So an explanation would be in order. When I finish work I will explain it all.

C.B.

Ok.

Jude Andre Charles

C.B. OK im back. You will have to point out where you got confused. I will try to explain as best as I can. As a disclaimer, I am not a mathematician. This is merely a hobby, however, an important one IMO.

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