My boy is in second grade. His keolistravelservices.comematics teacher provided the course a quiz, and one inquiry was this:

If a triangle has actually 3 sides, and a rectangle has 4 sides, how many sides walk a circle have?

My an initial reaction to be "0" or "undefined". But my kid wrote "$infty$" which ns think is a reasonable answer. However, it was significant wrong with the comment, "the answer is 1".

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Is over there an welcomed correct price in geometry?

edit: ns ran right into this teacher recently and mentioned this quiz problem. She stated she believed my son had written "8." She didn"t recognize that a sideways "8" method infinity.

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

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The answer depends on the definition of the word "side." i think this is a damaging question (edit: to placed on a quiz) and also is the sort of thing that will certainly make kids hate "Side" is a term that have to really be scheduled for polygons.

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

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

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

cube cylinder cone ball

Like most keolistravelservices.comematicians, my first reaction was the forthe last objects the question would need a precisedefinition of face, edge and vertex, and isn"t reallysensible without such definitions.

But after talking about the trouble with many people, conducting a sort of social/keolistravelservices.comematical experiment, i observed miscellaneous intriguing. What i observed was thatnone of my non-keolistravelservices.comematical friends and acquaintances hadany difficulty with utilizing an intuitive geometric ide here,and they every agreed fully 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, these were also the answers preferred by myson"s teacher (who is a truly exceptional teacher). Meanwhile, all of my keolistravelservices.comematicalcolleagues hemmed and hawed around how we can"t reallyanswer, and what walk "face" average in this paper definition anyway,and so on; many of castle wanted ultimately to say the asphere has actually infinitely countless faces and infinitely manyvertices and also so on. For the homework, my boy wrote an explanation providing the answers above, but also explaining the there to be a sense in which few of the answers were infinite, relying on what to be meant.

At a party this past weekend complete ofkeolistravelservices.comematicians and also philosophers, it was a fun game to firstask a keolistravelservices.comematician the question, who invariably made various objections and refusals and also and stated it do no sense and also so on, and then thenon-keolistravelservices.comematical spouse would certainly forthrightly offer a fully clearaccount. There were many friendly disputes around it the evening.

See more: One Million Is Equal To How Many Thousands Make 1Million? Millions To Thousands Conversion

So the seems, evidently, that our extensive keolistravelservices.comematical training hasinterfered with our ability to grasp easily what kids andnon-keolistravelservices.comematicians uncover to be a clear and distinctgeometrical concept.

(My really view, however, is the it is our training that has taught us that the concepts are no so clear and also distinct, as saw by countless borderline and also counterexample cases in the historical struggle to find the right interpretations for the $V-E+F$ and other theorems.)