If a triangle has actually 3 sides, and a rectangle has actually 4 sides, how numerous sides go a circle have?

My first reaction was "0" or "undefined". But my kid wrote "$\infty$" which ns think is a reasonable answer. However, the was marked wrong v the comment, "the prize is 1".

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Is over 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 actually written "8." She didn"t recognize that a party "8" means infinity.

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edited jan 20 "18 in ~ 17:34

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inquiry Apr 8 "11 in ~ 19:26

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The answer depends on the meaning of words "side." i think this is a destructive question (edit:

*to put on a quiz*) and is the kind of point that will make children hate centregalilee.com. "Side" is a ax that need to really be scheduled for polygons.

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edited might 20 "11 at 10:30

answered Apr 8 "11 in ~ 19:30

Qiaochu YuanQiaochu Yuan

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My third-grade son came home a few weeks earlier with comparable homework questions:

How numerous faces, edges and also vertices execute the adhering to have?

cube cylinder cone roundLike many centregalilee.comematicians, my first reaction was the forthe latter objects the question would require a precisedefinition of face, edge and vertex, and also isn"t reallysensible without such definitions.

But after ~ talking around the difficulty with countless people, conducting a sort of social/centregalilee.comematical experiment, ns observed something intriguing. What ns observed to be thatnone of mine non-centregalilee.comematical friends and also acquaintances hadany problem with making use of an intuitive geometric principle here,and they every agreed totally that the answers must 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 verticesIndeed, this were also the answers preferred by myson"s teacher (who is a truly superior teacher). Meanwhile, all of my centregalilee.comematicalcolleagues hemmed and also hawed around how us can"t reallyanswer, and also what walk "face" average in this paper definition anyway,and for this reason on; many of lock wanted eventually to say the asphere has infinitely countless faces and also infinitely manyvertices and also so on. For the homework, my son wrote one explanation giving the answer above, but additionally explaining the there to be a sense in which several of the answers were infinite, depending upon what to be meant.

At a party this past weekend full ofcentregalilee.comematicians and philosophers, it was a fun game to firstask a centregalilee.comematician the question, who invariably made assorted objections and refusals and also and claimed it make no sense and so on, and then thenon-centregalilee.comematical spouse would forthrightly offer a totally clearaccount. There were plenty of friendly disputes about it that evening.

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So that seems, evidently, the our considerable centregalilee.comematical maintain hasinterfered with our ability to grasp quickly what youngsters andnon-centregalilee.comematicians discover to it is in a clear and also distinctgeometrical concept.

(My actual view, however, is that it is our training that has taught united state that the ideas are no so clear and distinct, as experienced by plenty of borderline and also counterexample situations in the historical struggle to discover the right definitions for the $V-E+F$ and other theorems.)