paula (npub1er6…h92c) This is a very interesting question!
First the practical solution: buy a pizza cutting board that’s marked with circles of all sizes. Center the outside of the pizza with the nearest matching circle. You’re good to go.
To do it perfectly mathematically though: you want to find the center of the circle. Draw any line which cuts the circle in a line segment. Using ruler and compass, you can draw the perpendicular bisector of that line segment (the line which cuts it in half at a 90 degree angle). By symmetry, this line goes through the center. Now do this process again and you have two lines which intersect at the center.
To find the angle for cutting into 8 slices: using ruler and compass, you can draw two perpendicular lines through the center. You can also bisect this right angle to get the 45 degree lines you want. You can keep bisecting to get any power of two number of slices.
For cutting into any number of equal slices: it’s not always possible using ruler and compass. You can read more here: https://en.m.wikipedia.org/wiki/Constructible_polygon
I’m not sure how to do it if the pizza is an ellipse. Could be interesting
Happy to explain more, just ask
⚗️alchemist⚗️ /
npub1pt…r6mf6
2023-11-22 18:31:16
in reply to nevent1q…g6cz
Author Public Key
npub1pt6l3a97fvywrxdlr7j0q8j2klwntng35c40cuhj2xmsxmz696uqfr6mf6Published at
2023-11-22 18:31:16Event JSON
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"content": "nostr:npub1er6yqxdkvc35gjpvvzskf6s2r2e8q7grv8h0njkjceqmleg2kcgq9wh92c This is a very interesting question! \n\nFirst the practical solution: buy a pizza cutting board that’s marked with circles of all sizes. Center the outside of the pizza with the nearest matching circle. You’re good to go. \n\nTo do it perfectly mathematically though: you want to find the center of the circle. Draw any line which cuts the circle in a line segment. Using ruler and compass, you can draw the perpendicular bisector of that line segment (the line which cuts it in half at a 90 degree angle). By symmetry, this line goes through the center. Now do this process again and you have two lines which intersect at the center. \n\nTo find the angle for cutting into 8 slices: using ruler and compass, you can draw two perpendicular lines through the center. You can also bisect this right angle to get the 45 degree lines you want. You can keep bisecting to get any power of two number of slices. \n\nFor cutting into any number of equal slices: it’s not always possible using ruler and compass. You can read more here: https://en.m.wikipedia.org/wiki/Constructible_polygon\n\nI’m not sure how to do it if the pizza is an ellipse. Could be interesting \n\nHappy to explain more, just ask",
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