# JClock VIII

2016-07-30, post № 135

**programming**, **Pygame**, **Python**, #clock, #complex number, #hour, #minute, #plane, #time

Interpreting the hour hand on a clock as a two-dimensional object on a plane, the hand’s tip can be seen as a complex number.

This clock converts the hour hand’s position into a complex number, sets the number’s length to the current minutes and displays it in the form .

The angle 𝜑 is determined by the hours passed () but has to be slightly modified because a complex number starts at the horizontal axis and turns anti-clockwise whilst an hour hand starts at the vertical axis and turns — as the name implies — clockwise. Thus, .

The complex number’s length is simply determined by the minutes passed. Because the length must not be equal to 𝟢, I simply add 𝟣: .

Lastly, to convert a complex number of the form into the form , I use the formula .