My son is in second grade. His teacher provided the class a quiz, and also one inquiry was this:

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

My first reaction to be "0" or "undefined". But my boy wrote "$\infty$" which ns think is a reasonable answer. However, that was significant wrong through the comment, "the prize is 1".

You are watching: Does a circle have a face

Is over there an welcomed correct answer 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 understand that a sideways "8" method infinity.

geometry education and learning circles
edited january 20 "18 in ~ 17:34
inquiry Apr 8 "11 in ~ 19:26

11.1k66 gold badges3737 silver- badges6363 bronze title
| present 23 more comments

10 answers 10

energetic earliest Votes
The answer counts on the definition of words "side." ns think this is a terrible question (edit: to placed on a quiz) and is the sort of point that will make children hate "Side" is a ax that need to really be booked for polygons.

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

Qiaochu YuanQiaochu Yuan
350k3939 yellow badges738738 silver badges11151115 bronze badges
| present 9 more comments
My third-grade son came home a couple of weeks back with comparable homework questions:

How plenty of faces, edges and vertices carry out the adhering to have?

cube cylinder cone round

Like many rememberingsomer.comematicians, my very first reaction was the forthe last objects the inquiry would require a precisedefinition the face, edge and vertex, and also isn"t reallysensible without such definitions.

But after ~ talking around the problem with plenty of people, conducting a type of social/rememberingsomer.comematical experiment, i observed other intriguing. What ns observed to be thatnone of mine non-rememberingsomer.comematical friends and acquaintances hadany difficulty with using an intuitive geometric concept here,and they all agreed totally 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 likewise the answers wanted by myson"s teacher (who is a truly impressive teacher). Meanwhile, every one of my rememberingsomer.comematicalcolleagues hemmed and also hawed around how us can"t reallyanswer, and also what does "face" mean in this paper definition anyway,and therefore on; most of them wanted ultimately to say the asphere has infinitely numerous faces and also infinitely manyvertices and also so on. For the homework, my kid wrote one explanation offering the answer above, but also explaining the there was a sense in which few of the answers were infinite, depending upon what was meant.

At a party this past weekend complete ofrememberingsomer.comematicians and philosophers, it was a fun game to firstask a rememberingsomer.comematician the question, who invariably made miscellaneous objections and also refusals and and said it make no sense and so on, and then thenon-rememberingsomer.comematical spouse would certainly forthrightly provide a totally clearaccount. Over there were plenty of friendly disputes about it that evening.

See more: How Many Atoms Are In 141 G Of Calcium ? How Many Atoms Are In 141 G Of Calcium

So the seems, evidently, that our comprehensive rememberingsomer.comematical maintain hasinterfered with our ability to grasp easily what youngsters andnon-rememberingsomer.comematicians find to be a clear and also distinctgeometrical concept.

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