July 2020

HISTORY OF QUATERNIONS

The irish mathematician  William Rowan Hamilton discovered quaternions.

Now it is used in the areas related to 3d geometry like computer games, spaceship navigation etc.,

  • William always has the thought that numbers consists of three parts.(in the manner that complex number consists of 2 parts a+ib.
  • While he was walking along Royal canal in Dublin he felt that the number he was searching was 4 parts.
  • He was so happy with his discovery and he carved the basic formula on one of the bridges over the canal.
  • A quaternion is a number can be written as a+bi+cj+dk , where a, b , c, d are real. and i,j, k has the following properties.

Quaternions

Quaternions have the property that ‘x’ multiplied by ‘y’ is not equal to ‘y’ multiplied by ‘x’. These quaternions are used today in the areas related to 3 dimensional geometry.

we see its brief history in my next blog.

The Golden ratio Φ (phi)

Here the straight line AB is divided into AC and CB of  measure  ‘a’ and ‘b’ respectively.

we say that ‘a’ and ‘b’ are in the golden ratio, if

the ratio of the whole sum to the larger measure equals to the ratio of the larger measure to the smaller measure.

Φ=(a+b)/a =a/b

The value of  Φ is$ (1+√5)/2 =1.618…$