### Important Mathematical Constants

Important Mathematical Constants

Mathematical constants are those numbers that are special and interesting because they come up in the various fields of mathematics like geometry, calculus etc. These mathematical constants are usually named after the person who discovered it and they are represented by a symbol that is usually picked up from the Greek alphabet. Mathematical constants are by definition very important. In this article we will take a look at certain mathematical constants that are more commonplace than others.

### 1.     π (pi) or Archimedes constant (~3.14159):

π is defined as the ratio of the circumference of a circle to its diameter. This is probably the most popular mathematical constant. So π is the circumference of the circle whose diameter is 1 unit. You might have seen it popping up when calculating the area of a circle (πr2) or the circumference of a circle (2πr). It has many uses throughout mathematics from calculating the area of certain shapes to the Gaussian integral in complex analysis. π is irrational and is represented by the small letter π in the Greek alphabet.

### √2 is a very well known mathematical constant. It is the ratio between the diagonal and side of a square. √2 is calculated by square rooting 2. It is based around the Pythagoras’ Theorem.

Let us assume x represents length of one side of a square. Let y assume the length of the side adjacent to it. x = y. Let z represent length of diagonal. x2 +  y2 = z2. This simplifies into 2x2 = z2. Therefore z = √2x. So the ratio z : x becomes √2x : x, which leaves you with √2.

Therefore √2 can be very easily proved geometrically. It is also a number whose infinite tetrate is equal to its square. This means:

√2 raised to the power to √2 raised to the power of √2 raised to the po……. infinitely = 2 or √22.

To be continued in part two…