Location: Minnesota, United States

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Friday, November 05, 2004

blogAclass: Math Problem Solving

Yesterday in Math Problem Solving we went through one of Professor Below's presentations. This one was called Divine Design: The Divine Proportion and basically it covered Fibonacci Numbers, the Golden Rectangle, and how it all related to God's design. First off here are some quote and bible passages that were given throughout the presentation to back up the math and science.

Math is man's attempt to prove God's hand in the universe.
For the word of God is right; and all his works are done in truth.
Psalm 33:4
Job 38:22-24
Romans 1:20

Anyway, starting from the beginning, Fibonacci numbers are an infinite sequence of rational numbers in which each term is the sum of the two preceding terms.

ex. 1,1,2,3,5,8,13,21.....

Moving onward the Golden rectangle which looks like this:

When you divide the length by the height you get 1.6180339 and seriously this number NEVER ENDS, it just keeps going on forever. There is no other number like that, when you square it doubles exactly (2.6180339) and when you divide it by one you get exactly one less (0.6180339). Another interesting thing about the Golden Rectangle is whenever you take away a rectangle chunk it is still a Golden Rectangle no matter how much you split it.
The golden rectangle has been used for centuries in architecture from as far back as 2400BC. With the ancient Egyptians and 432BC with the ancient Greeks in the building of the Parthenon. If you take the three pyramids each of the slant heights is very close to a golden rectangle. Menkare has a slant height of 1.562, Khafre has a slant height of 1.664, and Khufu has a slant height of 1.6195.
An interesting measurement you can do yourself to show how the Golden Rectangle is used in nature is to divide the widest part of your arm by the thinnest, it should be pretty close to 1.6180339. Another example is a DNA molecule, the height of a DNA molecule is 21 actroms (spelling prolly wrong) and the width is 34 actroms. A final picture example of this is the Chambered Nautilus:

Erm, don't know how well that went, I spose not too well, let me know in the comments, I need better notes and a better flow I think, and something to wrap it up. Hope you liked it.