Monday, May 14, 2018

The Mysteries of the Golden Ratio Explained by Math and Sunflowers | Popular Mechanics

 Photo: Jay Bennett
Jay Bennett, associate editor of PopularMechanics.com argues, "This number, approximately 1.62, has fascinated mathematicians and artists for centuries—but perhaps not for the reasons you think."

 Photo: YouTubeNumberphile The golden ratio is an almost mythical number that you may have heard of in various areas of architecture or design. For example, many claim the ancient Greek Parthenon has numerous examples of the golden ratio in its design. Others have said that the most beautiful people are those with features aligned according to the golden ratio. These claims are rough approximations of the golden ratio at best and pseudoscience at worst. The truth is much more awesome. The wonderful YouTube channel Numberphile recently spoke to Ben Sparks, a mathematician working at the University of Bath, to reveal the true nature of the golden ratio: 1 plus the square root of 5 over 2, or approximately 1.62, represented in mathematics by the Greek letter phi. In geometry, this number produces some fascinating patterns, such as a golden rectangle. (If you take the shorter length of a golden rectangle and make a square with that length, and then remove the area of that square from the golden rectangle, you are left with another, smaller golden rectangle.) As the video below explains, the golden ratio can also be considered the "most irrational" of all irrational numbers. An irrational number is one that cannot be expressed by a fraction of integers, or whole numbers. Pi, for example, is an irrational number. It is almost 22/7, but not quite.  A mathematical method for exploring irrational numbers is to play a kind of game. The idea is that you have a flower, and you are trying to place seeds on the face of the flower in such a way that you can fit as many as possible. If you place a seed, and then rotate the flower face a certain amount, and place another seed, and then repeat this process, what would be the ideal amount to rotate the flower face?  Source: Popular Mechanics and Numberphile Channel (YouTube)

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