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Quadrilaterals

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GuyBarry
1304949.  Wed Nov 28, 2018 11:52 am Reply with quote

There was some confusion over the meaning of the word "trapezoid" in a recent thread, where it was mistakenly taken to be a three-dimensional figure. It's actually a quadrilateral - a four-sided plane figure. Here's a neat diagram from Wikipedia illustrating the different types of quadrilateral, and how the definitions overlap:

https://en.wikipedia.org/wiki/Quadrilateral#/media/File:Euler_diagram_of_quadrilateral_types.svg

"Trapezium" and "trapezoid" are, confusingly, different ways round in British and American usage. In British usage, a trapezium is a quadrilateral with two parallel sides, and a trapezoid is a quadrilateral with no parallel sides. In American usage it's the other way round. In practice the word "trapezoid" is generally avoided in British geometrical texts and the term "irregular quadrilateral" is used.

According to the Oxford English Dictionary, the confusion of "trapezium" and "trapezoid" between the United States and Great Britain dates back to an error in Hutton's Mathematical Dictionary in 1795, the first work of its kind in the United States, which directly reversed the accepted meanings.

 
suze
1304951.  Wed Nov 28, 2018 12:05 pm Reply with quote

Guy, you might be the man for this.

A solid figure made of six squares is called a cube, and one made of six rectangles is called a cuboid. One made of six parallelograms is called a parallelepiped, and that's as far as I ever went in school geometry.

What's more, my Math teacher wasn't quite sure how to pronounce that last one. Sometimes it was piped as in "did pipe", and sometimes it was epiped like "epi pen", the device for treating anaphylactic shock.

But what is the word for a six sided solid whose sides are trapez***s? If we ignore the rounded corners, a corned beef can, for instance. The good husband wanted that to be a trapezohedron, but we don't think it is.

 
GuyBarry
1304955.  Wed Nov 28, 2018 12:30 pm Reply with quote

suze wrote:

A solid figure made of six squares is called a cube, and one made of six rectangles is called a cuboid. One made of six parallelograms is called a parallelepiped, and that's as far as I ever went in school geometry.

What's more, my Math teacher wasn't quite sure how to pronounce that last one. Sometimes it was piped as in "did pipe", and sometimes it was epiped like "epi pen", the device for treating anaphylactic shock.


It's certainly six syllables, as the etymology is from Greek επίπεδον ("plane"). I pronounce it as "parallel-e-PIE-ped", but "parallel-e-PIP-ed" and "parallel-EP-i-ped" are given as alternatives.

Quote:
But what is the word for a six sided solid whose sides are trapez***s? If we ignore the rounded corners, a corned beef can, for instance. The good husband wanted that to be a trapezohedron, but we don't think it is.


I'm not sure what shape you mean here - a pyramidal frustum maybe?

 
suze
1304961.  Wed Nov 28, 2018 12:53 pm Reply with quote

Yes, that's the thing!

Here is a very old corned beef can, and that product still comes in cans of more or less that shape.

I hadn't actually realized that it's a rectangular pyramid with the top chopped off, but that is of course precisely what it is.

 

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