I came across the following question
"A person plays the following game with a cake. He cuts a piece forming a circular sector of x degrees and flips the piece upside down, with the icing on the bottom. He then rotates the cake by x degrees counterclockwise, cuts an adjacent x degree piece and flips it upside down. He keeps repeating this, until after a total of N steps, all the icing is back on top. Amazingly, this works for any piece size, even if the cutting angle is an irrational number: all the icing will be back on top after a finite number of steps"
I understand why this must be true for any x being any rational number(https://simomaths.wordpress.com/2013/02/08/thoughts-on-a-problem-iii/) but can someone explain how this can be achieved for x being irrational ?
for example if x = 360/sqrt(60) how can N.x be a multiple of 360 degrees