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 Post subject: Pi Riddle
PostPosted: Tue Mar 27, 2012 10:53 am 
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Hey Folks,

Earlier this month, Gene posted an homage to Pi day (3.14), and I offered up a Pi riddle as a response. Unfortunately, that thread was somehow lost to the ethersphere, so I asked Mango to let me post it here.

Did you know that the base dimensions of the Great Pyramid of Giza are a function of Pi? Why would a square footprint be a function of Pi?


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PostPosted: Wed Mar 28, 2012 10:01 am 
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Someplace in the recesses I think I have heard that. The Base has a dimension of length or perimeter which could be used in calculating some function of Pi. :confused:

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PostPosted: Thu Mar 29, 2012 12:53 pm 
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I cheated a bit and found an answer. The ratio of the perimeter to the height is 2Pi.


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PostPosted: Thu Mar 29, 2012 1:44 pm 
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Hey Hebertoo,

Sorry, wrong question. While you are correct that the ration of the height to the base is a function of Pi, you haven't answered the question of
why the dimensions of the base itself (a square) are a function of Pi.

You are free to try again. :D

Tom

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PostPosted: Thu Mar 29, 2012 3:33 pm 
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John Boy wrote:
I actually found two references to Pi and one to PI (both caps)

The first is the relationship between Pi and Phi (golden ratio) that is expressed in the fundamental proportions of the Great Pyramid.

The second is way too hard for me to paraphrase, so here it is directly

"If the height of the pyramid is taken as the radius of a circle, then the circumference of this circle is the same as the perimeter of the base. This provided the complimentary squaring of a circle and circling of a square. The key to this relationship is knowledge of the value of Pi and designing the angle of the pyramid to be exactly 51 degrees, 51 minutes, and 14.3 seconds."

The reference to PI (both caps) is Pyramid Inches, which is equal to 1.0011 present inches.

If you want to read more about this amazing structure, go here

http://www.timstouse.com/EarthHistory/E ... gfacts.htm
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Sorry John Boy.

Again, wrong question.
Thanks for playing, feel free to try again. :D

Tom

ps. I'm going to resist giving any hints for awhile, as the answer is painfully apparent once you hear it, and nearly any hint would give it away, and I've already said too much :roll:

Tom

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PostPosted: Thu Mar 29, 2012 4:35 pm 
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It's not because of the geometric formula for the area of a circle ...

pi X r^2 or pi are squared, is it? :D

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PostPosted: Thu Mar 29, 2012 5:20 pm 
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Hey John Boy,

Nope, sorry. There's no penalty for guessing though. :wink:

Tom

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PostPosted: Thu Mar 29, 2012 9:47 pm 
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The diameter of the largest circle enclosed by a square is equal to the length of one side of the square. D=L=C/II

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PostPosted: Thu Mar 29, 2012 10:32 pm 
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Hey Jess,

That's quite true, but also the answer to the wrong question.
Thanks for playing, the only limit to your participation is in your mind, or the mind of someone who actually knows the answer. :D

Tom

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PostPosted: Fri Mar 30, 2012 6:55 am 
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I vaguely remember something about the ratio of circle and square areas being related to the square root of II. Am I on the right track?

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PostPosted: Fri Mar 30, 2012 7:27 am 
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I think it may have something to do with the ancient Egyptian measurement system (Cubits, palms,fingers), and coincidentally with the approximation of 22/7 to PI.

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 Post subject: First Hint
PostPosted: Fri Mar 30, 2012 9:35 am 
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Hey Gene,

Nope, sorry, but thanks for playing. :D

Tom


ps. Okay, it's probably time for a hint.

Everyone should stop looking at Wikipedia, and Googling, and start to think out of the box a little. You are all over thinking this.

Remember, the ancients had no concept of Pi, or modern trigonometry. So the fact that the base dimension is a function of Pi is a coincidence, not a intended outcome.

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PostPosted: Fri Mar 30, 2012 11:00 am 
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does it have anthing to do with the "golden mean" or "golden ratio"


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PostPosted: Fri Mar 30, 2012 12:41 pm 
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Hey Brantleytl,

Nope, sorry.

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PostPosted: Fri Mar 30, 2012 9:32 pm 
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Take a look at this. Interesting reading.

http://www.theglobaleducationproject.or ... gpmath.php


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PostPosted: Fri Mar 30, 2012 11:15 pm 
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Hey John,

Pitrie's survey is quoted all over the web, and many people claim it as evidence of some mystical, if not logical, relationship with Pi.

So here's another hint (a big one):

Given the material limitations of the age, the dimensions of the pyramid's base are too precise to have been laid out with a linear tool like a tape.

There, now if that hasn't given it to you, I'll have to keep the soggy points for myself. :wink:

Tom

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PostPosted: Sat Mar 31, 2012 9:43 am 
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They drew a large circle on the ground and than used the radius to find the corners of the base for an accurate square. Using the center line of the circle at the intersection of CL and circumference in both directions.

Just a guess and I can't think of a way to describe what I mean.

Rog

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PostPosted: Sat Mar 31, 2012 11:02 am 
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Hey Rog,

Sorry, no. You are thinking more about the process though, and that's closer.

The answer is incredibly simple, maddeningly so.

Tom

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PostPosted: Sat Mar 31, 2012 5:16 pm 
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Pi are round, cake are square :D

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PostPosted: Sat Mar 31, 2012 5:21 pm 
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Okay,
Maybe not that simple. :D

Tom

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