# What is the most fascinating number

## Circle number: It doesn't work without pi

Numbers play less of a role in mathematics than is commonly thought. But you can't do without them completely. Especially not without constants - and as far as they are concerned, no number is as important and popular as π at the same time.

For me, the fascination of this number lies in its connection between simplicity and complexity. Defining π couldn't be easier, the corresponding formula is:

#### This article is included in Spectrum - The Week, 28/2016

π = U / d

The circumference U of a circle is divided by its diameter d, and the result is always the same. However, it cannot be written down; at least not completely. The number π is irrational, which means that it cannot be represented by an integer or the ratio of two integers. The ratio of the circumference to the diameter of a circle is always a little larger than the number 3. But how much this "a little larger" is exactly cannot be written down. In the decimal notation, the decimal point is followed by an infinite number of places without periodicity and order.

It is amazing enough that something that seems as neat and simple to us humans as a circle is defined by such a complex and "messy" number. Even more astonishing is the multitude of scientific phenomena that can be described with the help of these seemingly simple constants. It appears in the field equations of Albert Einstein's general theory of relativity as well as in the Schrödinger equation of quantum mechanics and in countless other mathematical and scientific formulas. Whether the beginning and the end of the universe or the behavior of elementary particles: It doesn't work without π!

The many interesting and curious properties of the circle number are also wonderfully suitable for getting people excited about mathematics. This is one of the reasons why I became a member of the "Association of Friends of the Number Pi" during my studies. It was founded in 1995 by a couple of astronomers from Vienna, and in addition to dealing with the district number itself, the task is to spread mathematical knowledge. In order to become a member, you have to learn the first 100 decimal places of π by heart and recite them in a creative or spectacular way. I repeated the 100 passages and juggled at the same time; others were a little more daring and took their entrance exams, for example in free fall during a parachute jump.

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