My boy is in 2nd grade. His teacher provided the course a quiz, and also one concern was this:

If a triangle has actually 3 sides, and a rectangle has actually 4 sides, how numerous sides walk a one have?

My an initial reaction to be "0" or "undefined". But my son wrote "$\infty$" which i think is a reasonable answer. However, that was significant wrong v the comment, "the prize is 1".

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Is there an embraced correct prize in geometry?

edit: i ran right into this teacher recently and mentioned this quiz problem. She said she assumed my son had written "8." She didn"t understand that a sideways "8" way infinity.

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edited january 20 "18 in ~ 17:34
inquiry Apr 8 "11 at 19:26

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The answer relies on the meaning of words "side." ns think this is a devastating question (edit: to placed on a quiz) and is the sort of thing that will make children hate "Side" is a ax that should really be reserved for polygons.

edited might 20 "11 in ~ 10:30
answer Apr 8 "11 at 19:30

Qiaochu YuanQiaochu Yuan
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My third-grade boy came house a few weeks earlier with similar homework questions:

How numerous faces, edges and also vertices perform the following have?

cube cylinder cone sphere

Like most bsci-ch.orgematicians, my very first reaction was that forthe last objects the question would need a precisedefinition of face, edge and also vertex, and isn"t reallysensible without such definitions.

But after ~ talking about the difficulty with countless people, conducting a sort of social/bsci-ch.orgematical experiment, i observed miscellaneous intriguing. What ns observed to be thatnone of mine non-bsci-ch.orgematical friends and acquaintances hadany trouble with using an intuitive geometric ide here,and they every agreed fully that the answers have to be

cube: 6 faces, 12 edges, 8 verticescylinder: 3 faces, 2 edges, 0 verticescone: 2 faces, 1 edge, 1 vertexsphere: 1 face, 0 edges, 0 vertices

Indeed, this were additionally the answers desired by myson"s teacher (who is a truly outstanding teacher). Meanwhile, every one of my bsci-ch.orgematicalcolleagues hemmed and also hawed around how we can"t reallyanswer, and also what go "face" mean in this paper definition anyway,and therefore on; most of them wanted eventually to say the asphere has actually infinitely countless faces and also infinitely manyvertices and so on. For the homework, my kid wrote one explanation offering the answers above, but likewise explaining the there was a sense in which some of the answers to be infinite, depending upon what to be meant.

At a party this previous weekend full ofbsci-ch.orgematicians and also philosophers, it was a fun game to firstask a bsci-ch.orgematician the question, who invariably made various objections and also refusals and and stated it make no sense and so on, and also then thenon-bsci-ch.orgematical spouse would forthrightly provide a fully clearaccount. There were numerous friendly disputes about it the evening.

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So the seems, evidently, the our extensive bsci-ch.orgematical cultivate hasinterfered with our capacity to grasp conveniently what youngsters andnon-bsci-ch.orgematicians find to it is in a clear and distinctgeometrical concept.

(My really view, however, is that it is our training that has actually taught us that the concepts are no so clear and also distinct, as observed by many borderline and also counterexample instances in the historic struggle to uncover the right meanings for the $V-E+F$ and other theorems.)