Similar spurious patterns are also observed in the solar system (which also has lots of different ratios that you can choose from). Indeed most numbers between 1 and 2 will have two parts of the body approximating them in ratio. If you look hard enough you will also find proportions in the human body close to 1.6, 5/3, 3/2, the square root of 2, 42/26, etc, etc. This is especially true if the things that you are measuring are not particularly well-defined (as in the picture on the left) and it is possible to vary the definition in such a way as to get the proportions that you want to find. If you consider enough of them then you are bound to get numbers close to the value of the golden ratio (around 1.618). The body has many possible ratios, lots of which lie somewhere between 1 and 2. However, none of this is true, not even remotely. You can superimpose all sorts of rectangles on a beautiful face and then claim that beauty derives from the proportions of the rectangle. You'd like to divide it in such a way that the ratio between the whole segment and the longer of the two pieces is the same as the ratio between the longer of the two pieces and the shorter one. Imagine you have a line segment which you would like to divide into two pieces. It was defined by the ancient Greek mathematician Euclid as follows. Let's start by quickly recalling what the golden ratio actually is. Yes, twice! So are any of these great claims made for the golden ratio true? What's the golden ratio again? Yet in my whole career of applying mathematics to the real world I have come across the golden ratio exactly twice. It has also been claimed that the golden ratio appears in the human body, for example as the ratio of the height of an adult to the height of their navel, or of the length of the forearm to that of the hand. For example it is claimed that both the Parthenon and the pyramids are in this proportion. It is claimed that much of art and architecture contains features in proportions given by the golden ratio. It has been described by many authors (including the writer of the da Vinci Code) as the basis of all of the beautiful patterns in nature and it is sometimes referred to as the divine proportion. It appears, for example, in the book/film The da Vinci Code and in many articles, books, and school projects, which aim to show how mathematics is important in the real world. Most of you will have heard about the number called the golden ratio. That has saved us all a lot of trouble! Thank you Leonardo.įibonacci Day is November 23rd, as it has the digits "1, 1, 2, 3" which is part of the sequence.This article is based on a talk in an ongoing GreshamĬollege lecture series. "Fibonacci" was his nickname, which roughly means "Son of Bonacci".Īs well as being famous for the Fibonacci Sequence, he helped spread Hindu-Arabic Numerals (like our present numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) through Europe in place of Roman Numerals (I, II, III, IV, V, etc). His real name was Leonardo Pisano Bogollo, and he lived between 11 in Italy. Historyįibonacci was not the first to know about the sequence, it was known in India hundreds of years before! Which says that term "−n" is equal to (−1) n+1 times term "n", and the value (−1) n+1 neatly makes the correct +1, −1, +1, −1. In fact the sequence below zero has the same numbers as the sequence above zero, except they follow a +-+. (Prove to yourself that each number is found by adding up the two numbers before it!)
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