Euclid’s masterpiece textbook, The Elements, was once written twenty-three hundred years in the past. it truly is essentially approximately geometry and includes dozens of figures. 5 of those are developed utilizing a line that “is reduce in severe and suggest ratio.” this day this can be known as the golden ratio and is frequently mentioned via the emblem Φ.
Many myths have grown up round this ratio. This publication used to be written to profit approximately them. They come up from the pyramids, the Pythagorean Brotherhood, the platonic solids, the Fibonacci numbers, sea shells, and others. there's a universal thread between those myths. Φ is an irrational quantity (a quantity whose digits after the decimal aspect move on eternally and not shape a repeating pattern). Φ can be utilized to attract entertaining figures. yet its numerical worth can't be written down utilizing integers and fractions, that have been the single numbers utilized in Euclid’s time.
Mathematicians earlier than Euclid knew that irrational numbers existed. yet to many of us, a bunch that can’t be written down used to be absurd. for hundreds of years, many scientists and engineers believed that Φ was once godlike.
This ebook discusses the myths from an engineering standpoint. The final bankruptcy of the e-book indicates how Euclid dealt with irrational numbers; how Euclid did algebra utilizing geometry; and an easy visible facts of why there are just 5 platonic solids.
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