My child is in 2nd grade. His teacher gave the class a quiz, and also one inquiry was this:

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

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

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Is over there an embraced correct prize in geometry?

edit: i ran into this teacher recently and mentioned this quiz problem. She stated she thought my son had written "8." She didn"t understand that a sideways "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 counts on the definition of the word "side." ns think this is a destructive question (edit: to put on a quiz) and is the kind of thing that will certainly make children hate "Side" is a ax that must really be reserved for polygons.

edited might 20 "11 at 10:30
answered Apr 8 "11 at 19:30

Qiaochu YuanQiaochu Yuan
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My third-grade son came house a couple of weeks back with comparable homework questions:

How plenty of faces, edges and also vertices perform the adhering to have?

cube cylinder cone round

Like many barisalcity.orgematicians, my first reaction was the forthe latter objects the concern would need a precisedefinition that face, edge and also vertex, and isn"t reallysensible without together definitions.

But after talking around the problem with many people, conducting a type of social/barisalcity.orgematical experiment, ns observed something intriguing. What ns observed to be thatnone of mine non-barisalcity.orgematical friends and acquaintances hadany problem with making use of an intuitive geometric ide here,and they every agreed fully 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, these were additionally the answers desired by myson"s teacher (who is a truly exceptional teacher). Meanwhile, every one of my barisalcity.orgematicalcolleagues hemmed and also hawed about how us can"t reallyanswer, and what go "face" average in this context anyway,and so on; most of castle wanted at some point to say that asphere has actually infinitely countless faces and also infinitely manyvertices and also so on. For the homework, my boy wrote an explanation providing the answer above, but likewise explaining the there was a sense in which some of the answers to be infinite, relying on what was meant.

At a party this previous weekend full ofbarisalcity.orgematicians and philosophers, it to be a fun video game to firstask a barisalcity.orgematician the question, who invariably made various objections and refusals and and claimed it make no sense and so on, and also then thenon-barisalcity.orgematical spouse would forthrightly offer a fully clearaccount. Over there were many friendly disputes about it that evening.

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So that seems, evidently, the our extensive barisalcity.orgematical training hasinterfered with our ability to grasp easily what children andnon-barisalcity.orgematicians discover to it is in a clear and distinctgeometrical concept.

(My really view, however, is that it is ours training that has taught us that the principles are not so clear and distinct, as experienced by many borderline and also counterexample instances in the historical struggle to discover the right interpretations for the $V-E+F$ and other theorems.)