Question 4 - Curve

A cardioid is the curve described by a fixed point on the perimeter of a circle rolling around another circle of the same radius.

The cardioid can be obtained also as the envelope of lines. Imagine having a circle with evenly spaced points on it (let’s say, you have 29 points, numbered from 0 to 28). From every point, you trace a line till the point being the double of it divided by 29.

For example: from point 1 you trace a line till point numbered 2, from point 15 you would trace a line till point remainder of 15x2 divided by 29, that is 1.

Basically, you need to draw a set of lines based on the above rule: point number k is connected with the point having the number equal to remainder of 2·k when divided by n, where n is the number of points. The points are numbered from 0 to n - 1.

More examples, here: http://mathgifs.blogspot.com/2013/12/mathematical-envelopes.html (many more on Internet).

Your task is to create an animated version of this type of curves. Start with 151 points, evenly spaced on a unit circle. The animation is based on the value of the parameter a representing the factor with which we multiply. So, point number k is connected with the point having the number equal to remainder of a·k when divided by 151, where 151 is the number of points. Make a take values from 2 to 30.

Your animated image should look something like the one shown at the end of this video: https://www.youtube.com/watch?v=qhbuKbxJsk8 (minute 12:22 on)