{"id":180,"date":"2019-06-26T22:55:39","date_gmt":"2019-06-26T22:55:39","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=180"},"modified":"2019-12-11T17:01:56","modified_gmt":"2019-12-11T17:01:56","slug":"pizza-slices","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/pizza-slices\/","title":{"rendered":"Pizza Slices"},"content":{"rendered":"\n
\"\"<\/figure><\/div>\n\n\n\n

Take a pizza and pick an arbitrary point in it. Suppose you cut the pizza into 8 slices by cutting at 45 degree angles through that point, and color the alternate pieces red and green.<\/p>\n\n\n\n

Surprising theorem: the total area of the red slices and the total area of the green slices will always be the same!<\/p>\n\n\n\n

In fact, this theorem is true if the number of slices is any multiple of 4 except for 4, and the slices are cut by using equal angles through a fixed arbitrary point in the pizza.<\/p>\n\n\n\n

Alternatively, if instead of equal angles, you use equal-length arcs on the circumference and slice from a fixed arbitrary point in the pizza, the conclusion still holds if the number of slices is even and greater than 2.<\/p>\n\n\n\n

Presentation Suggestions:<\/strong>
Draw a few pictures to illustrate some special cases.<\/p>\n\n\n\n

The\u00a0Math\u00a0Behind\u00a0the\u00a0Fact:<\/strong>
The theorem can be proved by using\u00a0calculus\u00a0and\u00a0polar coordinates. The reference gives background and generalizations.<\/p>\n\n\n\n

How to Cite this Page:<\/strong> 
Su, Francis E., et al. “Pizza Slices.” Math Fun Facts<\/em>. <http:\/\/www.math.hmc.edu\/funfacts>.<\/p>\n\n\n\n

References:<\/strong>
J. Konhauser, D. Velleman, S. Wagon, Which way did the bicycle go?<\/a><\/em>, pp. 20, 117-122.<\/p>\n\n\n\n

Fun Fact suggested by: <\/strong>
Francis Su<\/p>\n","protected":false},"excerpt":{"rendered":"

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