My boy is in second grade. His teacher provided the class a quiz, and one question was this:

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

My very first reaction to be "0" or "undefined". Yet my boy wrote "$\infty$" which i think is a reasonable answer. However, that was marked wrong with the comment, "the prize is 1".

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Is over there an welcomed correct prize in geometry?

edit: ns ran into this teacher recently and also mentioned this quiz problem. She stated she assumed my son had actually written "8." She didn"t know that a sideways "8" method infinity.

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edited jan 20 "18 at 17:34
request Apr 8 "11 at 19:26

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The answer relies on the an interpretation of words "side." i think this is a destructive question (edit: to placed on a quiz) and is the kind of thing that will make youngsters hate "Side" is a term that should really be reserved for polygons.

edited may 20 "11 at 10:30
reply Apr 8 "11 at 19:30

Qiaochu YuanQiaochu Yuan
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My third-grade son came residence a few weeks ago with comparable homework questions:

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

cube cylinder cone round

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

But after ~ talking around the difficulty with numerous people, conducting a sort of social/bsci-ch.orgematical experiment, i observed something intriguing. What i observed to be thatnone of my non-bsci-ch.orgematical friends and acquaintances hadany difficulty with making use of an intuitive geometric concept here,and they all agreed completely that the answers need 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 likewise the answers desired by myson"s teacher (who is a truly outstanding teacher). Meanwhile, all of my bsci-ch.orgematicalcolleagues hemmed and also hawed about how we can"t reallyanswer, and also what walk "face" mean in this context anyway,and therefore on; many of castle wanted at some point to say that asphere has actually infinitely many faces and also infinitely manyvertices and so on. For the homework, my child wrote an explanation providing the answers above, but likewise explaining that there to be a feeling in which several of the answers to be infinite, relying on what to be meant.

At a party this previous weekend full ofbsci-ch.orgematicians and also philosophers, it to be a fun video game to firstask a bsci-ch.orgematician the question, that invariably made miscellaneous objections and also refusals and also and claimed it make no sense and also so on, and then thenon-bsci-ch.orgematical spouse would forthrightly provide a completely clearaccount. There were plenty of friendly disputes about it that evening.

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So it seems, evidently, the our considerable bsci-ch.orgematical training hasinterfered through our capacity to grasp quickly what kids andnon-bsci-ch.orgematicians discover to be a clear and distinctgeometrical concept.

(My yes, really view, however, is that it is our training that has taught us that the ideas are not so clear and distinct, as experienced by numerous borderline and also counterexample situations in the historical struggle to uncover the right interpretations for the $V-E+F$ and also other theorems.)