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

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

My very first reaction to be "0" or "undefined". Yet my son wrote "$infty$" which ns think is a reasonable answer. However, the was significant wrong with the comment, "the answer is 1".

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Is over there an accepted correct price in geometry?

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

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

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The answer depends on the definition of words "side." ns think this is a devastating question (edit: to put on a quiz) and also is the kind of point that will make children hate "Side" is a hatchet that have to really be reserved for polygons.

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

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

How many faces, edges and vertices execute the following have?

cube cylinder cone sphere

Like many civicpride-kusatsu.netematicians, my first reaction was the 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 problem with many people, conducting a type of social/civicpride-kusatsu.netematical experiment, i observed something intriguing. What ns observed was thatnone of my non-civicpride-kusatsu.netematical friends and also acquaintances hadany problem with utilizing an intuitive geometric ide here,and they every 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 additionally the answers wanted by myson"s teacher (who is a truly outstanding teacher). Meanwhile, every one of my civicpride-kusatsu.netematicalcolleagues hemmed and hawed around how we can"t reallyanswer, and also what go "face" average in this paper definition anyway,and for this reason on; most of castle wanted ultimately to say that asphere has actually infinitely numerous faces and also infinitely manyvertices and so on. For the homework, my child wrote one explanation offering the answers above, but likewise explaining the there was a feeling in which few of the answers were infinite, depending on what was meant.

At a party this past weekend full ofcivicpride-kusatsu.netematicians and philosophers, it was a fun game to firstask a civicpride-kusatsu.netematician the question, who invariably made miscellaneous objections and refusals and also and claimed it make no sense and so on, and then thenon-civicpride-kusatsu.netematical spouse would certainly forthrightly provide a totally clearaccount. There were numerous friendly disputes around it that evening.

See more: Is It Possible For A Triangle To Have Two Obtuse Angles ? Can A Triangle Have 2 Obtuse Angles

So that seems, evidently, that our comprehensive civicpride-kusatsu.netematical training hasinterfered v our ability to grasp easily what kids andnon-civicpride-kusatsu.netematicians uncover to be a clear and distinctgeometrical concept.

(My yes, really view, however, is that it is ours training that has actually taught united state that the principles are not so clear and distinct, as saw by many borderline and also counterexample situations in the historic struggle to discover the right definitions for the $V-E+F$ and also other theorems.)