The Divine Proportion: Does It Have a Materialistic Explaination?

JasonChin writes:

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But Phi appears far more often than these numbers

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No, it doesn't. It certainly doesn't appear more often than pi or e.Quick question: Suppose you have a bunch of parallel, straight lines, each one unit apart. You have a bunch of toothpicks, each one unit long. You drop them onto the lines. What are the odds that the pick will cross a line?That's right...pi/4.Now think about it...why might pi have something to do with this?

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and always in the same context, I.E. proportions.

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Let me see if I understand this correctly: You're amazed that a number that is calculated from proportions tends to pop up when dealing with proportions?That's like being amazed that pi comes up when talking about circles (that's a big hint to my question above.)The golden ratio can be approximated by dividing the n+1th and nth terms of the Fibonacci series as n goes to infinity.Now, the Fibonacci series comes up a lot in nature simply due to its intrinsic physical qualities: Add the previous two. That's a very simple thing to do biologically. Want to visualize a Nautilus shell? You can make it with a Fibonacci series:Start with two 1x1 squares side by side. You thus have a 2x1 rectangle. To add another square to the long edge, you need a square that is the sum of the two previous ones: 2x2. Well, now you have a 2x3 rectangle. To add another square to the long edge, you need a square that is the sum of the two previous ones, 3x3. Well, now you have a 3x5 rectangle. As you keep spiraling around and around, you're adding squares that follow the Fibonacci series. And if you draw a quarter circle in each square so that the pathway lines up, that's the spiral of the Nautilus shell.But notice what you did: You calculated the golden ratio simply by adding squares together in a spiral pattern, each one the size of the big side of what you had before. There is nothing mysterious about this. It's a simple necessity of mathematics. There's no other way it could be.

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Rrhain
WWJD? JWRTFM!

crashfrog responds to me:

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This card is restricted in Type 1 play, by the way.

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I know. I believe I have the only one in existence, though, so you don't have to worry about it too much. It's quite powerful (should actually have a casting cost), but it is quite dangerous. Unless you have a way to store all that mana, it'll kill you from mana burn.It's great for a combination of Fibonacci Series, Capacitor (which will store it), and Diffraction Grating (which will turn it into a specific color).

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Rrhain
WWJD? JWRTFM!