Allen Klinger, © 12/20/2016

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Math changes: new questions are asked and answered.

Facts that are discovered might be expressed by an

Arthur, Betty, Carmen, and David are thinking about an event. If Arthur goes, Betty will go. If Betty goes, Carmen will go. If Carmen goes, David will go. Two of these four went. What are their names?

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Also note: "It has been observed that for a circle, the maximum number of pieces that can be produced by n cuts is {[(n

For n = 1, 2, 3 the values of {[n(n+1)/2]+1} are 2, 4, 7. It is easy to see the first two; the value 7 comes when the 3rd cut intersects three sectors (e.g., 3 of the 4 areas that reults from quartering a circle).

For n = 1, 2, 3 the values of {[n(n+3)/2]+1} are 3, 6, 10. It is easy to see the first - a crescent is divided 3 by a single cut. Only 5 areas result from 2 cuts unless the parts are moved.

The table summarizes the known situation for the first few n when no motion of parts is allowed. However, it seems clear that

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CV,.......... Caltech Site,......... MamiChess

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**Gardner, Martin,

Nahin, Paul

12/20/2016 Version |
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