My boy is in 2nd grade. His aramuseum.orgematics teacher offered the class a quiz, and also one question was this:

If a triangle has actually 3 sides, and a rectangle has 4 sides, how countless sides go a one have?

My first reaction was "0" or "undefined". Yet my kid wrote "$infty$" which i think is a reasonable answer. However, that was significant wrong v the comment, "the price is 1".

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Is over there an accepted correct prize in geometry?

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

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edited jan 20 "18 in ~ 17:34
asked Apr 8 "11 in ~ 19:26

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The answer relies on the an interpretation of the word "side." ns think this is a devastating question (edit: to put on a quiz) and also is the kind of point that will make youngsters hate "Side" is a term that must really be reserved for polygons.

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

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My third-grade child came residence a couple of weeks earlier with similar homework questions:

How numerous faces, edges and vertices do the following have?

cube cylinder cone ball

Like most aramuseum.orgematicians, my very first reaction was that forthe latter objects the question would require a precisedefinition that face, edge and vertex, and isn"t reallysensible without together definitions.

But ~ talking about the difficulty with numerous people, conducting a type of social/aramuseum.orgematical experiment, ns observed miscellaneous intriguing. What ns observed to be thatnone of my non-aramuseum.orgematical friends and acquaintances hadany trouble with making use of an intuitive geometric principle here,and they every agreed totally that the answers should 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 preferred by myson"s teacher (who is a truly outstanding teacher). Meanwhile, all of my aramuseum.orgematicalcolleagues hemmed and hawed about how we can"t reallyanswer, and also what go "face" typical in this context anyway,and therefore on; many of castle wanted at some point to say that asphere has infinitely plenty of faces and infinitely manyvertices and so on. Because that the homework, my child wrote an explanation offering the answers above, but likewise explaining the there was a sense in which few of the answers to be infinite, relying on what was meant.

At a party this past weekend complete ofaramuseum.orgematicians and also philosophers, it was a fun video game to firstask a aramuseum.orgematician the question, who invariably made miscellaneous objections and refusals and also and stated it made no sense and so on, and then thenon-aramuseum.orgematical spouse would certainly forthrightly offer a completely clearaccount. Over there were numerous friendly disputes around it the evening.

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So that seems, evidently, that our substantial aramuseum.orgematical cultivate hasinterfered v our capacity to grasp quickly what kids andnon-aramuseum.orgematicians discover to be a clear and also distinctgeometrical concept.

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