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

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

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

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Is there an accepted correct answer in geometry?

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

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edited january 20 "18 at 17:34
asked Apr 8 "11 at 19:26

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The answer counts on the definition of words "side." ns think this is a destructive question (edit: to put on a quiz) and is the type of point that will certainly make kids hate "Side" is a term that have to really be booked for polygons.

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

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

How plenty of faces, edges and vertices perform the complying with have?

cube cylinder cone ball

Like many invernessgangshow.netematicians, my an initial reaction was that forthe latter objects the concern would require a precisedefinition the face, edge and also vertex, and also isn"t reallysensible without together definitions.

But after talking around the trouble with plenty of people, conducting a kind of social/invernessgangshow.netematical experiment, i observed something intriguing. What ns observed to be thatnone of my non-invernessgangshow.netematical friends and acquaintances hadany trouble with utilizing an intuitive geometric ide 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 likewise the answers desired by myson"s teacher (who is a truly superior teacher). Meanwhile, every one of my invernessgangshow.netematicalcolleagues hemmed and hawed about how us can"t reallyanswer, and what does "face" average in this paper definition anyway,and for this reason on; many of lock wanted at some point to say that asphere has infinitely numerous faces and also infinitely manyvertices and also so on. For the homework, my boy wrote one explanation giving the answers above, but also explaining that there was a feeling in which several of the answers were infinite, depending on what to be meant.

At a party this past weekend complete ofinvernessgangshow.netematicians and philosophers, it to be a fun game to firstask a invernessgangshow.netematician the question, who invariably made miscellaneous objections and also refusals and also and stated it do no sense and so on, and then thenon-invernessgangshow.netematical spouse would forthrightly provide a completely clearaccount. Over there were many friendly disputes about it the evening.

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So it seems, evidently, the our extensive invernessgangshow.netematical maintain hasinterfered with our capacity to grasp quickly what children andnon-invernessgangshow.netematicians discover to it is in a clear and also distinctgeometrical concept.

(My really view, however, is the it is our training that has taught united state that the principles are not so clear and distinct, as witnessed by many borderline and also counterexample cases in the historic struggle to find the right meanings for the $V-E+F$ and also other theorems.)