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Aim: What is the Golden Section?

Aim: What is the Golden Section?. Presented by : Kamile Perskaudaite , Nicole Maetta , Keith Newman, and Rawan Abouzeid. Also known as the Golden Ratio An irrational number, approximately 1.618, with special properties

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Aim: What is the Golden Section?

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  1. Aim: What is the Golden Section? Presented by : KamilePerskaudaite, Nicole Maetta, Keith Newman, and RawanAbouzeid

  2. Also known as the Golden Ratio • An irrational number, approximately 1.618, with special properties • Interesting property: The reciprocal of the Golden Ratio has the same decimal integers (1/1.618 = 0.618) • Found in nature, art, and architecture, it also used in geometry when finding ratios of distances in simple figures • Things with the Golden Ratio are visually appealing

  3. Fibonacci Sequence and the Golden Ratio Related not in numbers, but ratios between numbers Whenever you divide a number in the sequence by the previous number, you obtain the Golden Ratio As you continue, the number gets closer to the ratio 1,1,2,3,5,8,13,21,34,55 …

  4. The equation most commonly used to find the value of phi • Basic property: • Simplify like a normal quadratic function: • Substitute into quadratic formula:

  5. The most common way of depicting the Golden Ratio: • Known as the Golden Section • a/b = b/c = phi

  6. Constructing a Golden Rectangle 1,1,2,3,5,8,13 … It’s the Fibonacci sequence!

  7. Constructing a Golden Spiral

  8. Where else does the Golden Ratio exist?

  9. Also applies to humans! • Dr. Stephen Marquardt developed the Marquardt beauty mask using the Golden Ratio • Can be applied to both genders and all races

  10. Bibliography • http://cuip.uchicago.edu/~dlnarain/golden/activity8.htm • http://www.goldennumber.net/goldsect.htm • http://www.geom.uiuc.edu/~demo5337/s97b/figures.htm • http://mathworld.wolfram.com/GoldenRatio.html • http://library.thinkquest.org/C005449/

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