You may share a pizza in 6 equal portions with the help of trigonometry laws!
The method is so:
- share the pizza in 2
- share the diameter in 2 radius
- share one radius in 2
- elevate the perpendicular to the radius up the the circle
- cut from the center to the obtained point.
You obtain a portion that is exactly the 6th of the pizza!
Why is it so?
It is because of trigonometry!
Indeed, if you cut a circle into 6 equal portions from the center, the angles of the portions are 60° each. And the cosine of 60° is 1/2. Thus the adjacent side of the rectangle triangle shown on the picture is 1/2 of the hypothenus. As the hypothenu is equal to the radius, then the adjacent side shares the other radius in 2 halfs.
The methos explained above applies the reversal geometric construction.
That is why it works!