1.61803398…

In order to declutter my website at school I decided to move all explanatory content over to this blog. I decided to start with an interesting number I have been using in some of my programming assignments. This magic number is the numeric result of a simple problem found by Euclid about 300 BC.

Imagine a line which is described by two line segments a and b.

Euclid’s assignment is to position the point in a way that a/b is equal to (a+b)/a. In plain English. What is the ratio when a over b is the same at total length over a.

Any high school student should be able to solve the problem, because it just involves solving a quadratic equation. (In case you didn’t like math back in high school, here’s how it works 😉

Since negative lengths (probably) do not exist in real life, we may focus on the positive solution which is … tadaa … 1.61803398

So why is this number so damn awesome? Well, the are plenty of reasons.

One reason is that there are a lot of different algorithms that lead exactly to this number. For instance, consider the following sequence of numbers:

1, 1, 2, 3, 5, 8, 13, 21, 34, …

This series is called the “Fibonacci Series”. You might have noticed that each new number is determined by adding the two previous numbers.

So what happens if you choose a random number out of this series and divide it by its predecessor? Let us choose “34”: 34 devided by 21 equals 1.61905 — a number that comes very close to the above solution. If we choose higher numbers from the series we get closer and closer to what is called the “Golden Ratio“.

Ok, I must admit that there are many more other mathematical constants that can  be determined by different seemingly independent algorithms, but here are the really interesting facts about the Golden Ratio:

  • You will find rectangular shaped things (e.g. TV screens, swimming pools) more appealing, if their width/height ratio is about 1.618.
  • The Golden Ratio defines the dimensions of the human profile and even those of our teeth.
  • Many artists (most of them unconsciously) rely on the Golden Ratio to make their pictures look appealing.
  • The shell of certain snails reveal the Golden Ratio (most famous among them is the nautilus pompilius)
  • You will find the Golden Ratio in the growth pattern of certain ferns
  • … and more

Well, so if you meet an ugly person don’t call him or her ugly. Say “Your face seems to have missed the Golden Ratio by a mile.” instead.

Cheers,

— Andre M. Maier

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About bitjunkie

Teacher, Lecturer, and BITJUNKIE ...
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