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My daughter, who is in the second grade, brought home a math worksheet in which one of the questions was the following:

Which shape am I? If you looked at me from the side, you would see a rectangle. (pictures of a rectangular parallelepiped, a sphere, and a cylinder are given)

From the context of the worksheet, there is one and only one correct answer for each question. Evidently, the intended correct answer for this question is the rectangular parallelepiped. However, I believe that the side view of a cylinder is also a rectangle, but I wanted to check this with the mathematics community before complaining to the teacher about it.

So, what is the verdict?

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  • $\begingroup$ Real cylinders have light shining on them though, so you would be having a row about idealized cylinders versus real world cylinders. I would save your fire till they start teaching algebra... $\endgroup$ – Paul Apr 14 '15 at 14:51
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The only way a disc comes to look like a straight line is if your eye is in the same plane as that disc. Since your eye cannot lie in the same plane as both end discs, one of them will have to look a bit ellipsoid.

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I don't disagree with your complaint, just sounds like a bad question. Perhaps if it had said "If you look at me from any side" instead it could be more clear (especially for a 2nd grade assignment).

This is most likely a case of the student being expected to pick the "best" answer, since more sides of the rectangular parallelpiped could be seen as a rectangle, whereas the cylinder could be seen as a circle, depending on the side.

MY verdict (most likely not THE verdict): I agree a side of a cylinder can look like a rectangle, but seeing as it is a 2nd grade assignment, the "best" answer would be the parallelpiped. If I were the teacher I'd give credit for both answers if the student could justify the cylinder as you did.

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  • $\begingroup$ As I point out in my answer, the parallelpiped cannot look like the cylinder from any side from a the viewpoint of Euclidean geometry. $\endgroup$ – String Apr 14 '15 at 15:29

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