why do they call the two short sides of a right triangle the "legs"?

Question

In the Pythagorean theorem why do they refer to the sides of the right angle as the legs of the triangle? Who or where does this terminology come from?

Answer 1

I bet it's because most of the Western World learned their geometry from the Greeks first, who used the compass and straightedge for their geometry.  To make right triangles with a compass, you could set it to a "L" shape...and stand it on it's "legs."

I don't think Pythagoras invented it because everyone from the Chinese to the Mayans had been using it forever.  Perhaps he first proved it?

The Japanese learned their geometry with origami, so perhaps someone who knows Japanese will think of some other explanation...

Answer 2

Interesting question, Mary!

I found this reference:

From Steven Schwartzman's _The Words of Mathematics, An Etymological Dictionary of Mathematical Terms used in English_ (Mathematical Association of America):

leg
from Old Norse leggr "leg," of unknown prior origin. In a right triangle, the two sides that aren't the hypotenuse are known as legs. Because there are two of them, (as opposed to the three sides of a non-right triangle) they are named by analogy with the two legs of the human body.

- Doctor Sarah, The Math Forum

Hope this helps!

Answer 3

Hello Mary!

They refer to the shorter sides of the triangle as legs to show that they are different from the longest side of the triangle, known as the hypotenuse. It is possible that they are known as legs because there are two of them supporting the hypotenuse. The use of this terminology dates back to Pythagoras, who is credited with developing this theorem.

Hope this helps!

Andrew