Which regular polygon has a minimum rotation of 45degree to carry the polygon onto itself?

1 Answer
Jan 3, 2017

Everything up to an octagon.


Imagine a circumscibed circle around the polygon as a wheel, the spokes being the lines connecting the corners of the polygon to the centre of the circle.
Now if we turn the wheel, every time a spoke comes to the position of the previous spoke, we 'carry the polygon onto itself'.

A triangle or 3-gon has three 'spokes' so in a full turn this happens three times, or every 1/3 of a turn of 360 degrees = every 120 degrees.

This goes for all n-gons, so the required rotation is #360^o/n#

Now we have to find out for which #n# the rotation is#>=45^o#: