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Sharing a Pizza in 6 with trigonometry!

Sharing a Pizza in 6 with trigonometry!

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!

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