7
$\begingroup$

I was watching the Turkish version of Who Wants to Be a Millionaire? and they asked this question:

What field is the Donkey Case (or I guess it can be translated as Donkey Theorem) related to?

The correct answer was Mathematics. I've never heard of it. What is it?

  • 0
    Do Turkish geometry texts really include English puns? I think Dilip's guess is probably more likely. Is perhaps the turkish word translated here as "Case" also "Bridge"?2013-04-15

3 Answers 3

2

The donkey theorem is also known as the triangle inequality theorem. It states that in a triangle ABC: a < b + c.

The name comes from the idea that if you have a donkey standing at side A, and a hay stack at side C, it will ALWAYS be a shorter path for the donkey to go straight from A to C instead of from A to B to C.

This theorem comes in handy when you're trying to find if it's possible to have a triangle with side lengths 44, 32, and 19, for example.

  • 4
    Welcome to Math.SE! I'm afraid your proposed Answer to this older question is not very well written. By A,B,C do you mean the vertices or the sides of the triangle? It would make more sense for these to be vertices ("if you have a donkey standing at _vertex_ A"), and for the lowercase **a,b,c** to denote the side lengths.2013-04-07
2

Alternate interpretation of the case (historical novelty): There is no loop path involving a specific set of 3 land masses and five bridges crossing each bridge only once. (I don't have the link but the original question included a map of a real city on an island).

0

The Donkey Theorem is a humorous name for the theorem that triangles can't be proven congruent through ASS (angle, side, side). SSS, ASA, SAS, and AAS can be used to prove congruency because they are static shapes. There are two possible triangles to be made with angle, side, side congruency as shown by the swinging door. / \ /| /___\ = /_|