For example—
A letter to the editor of the American Mathematical Monthly
from the June-July 1985 issue has—
|
… a "square-triangle" lemma:
(∀ t ∈ T , t is an n -replica )
[I.e., "Every triangle is an n -replica" |
For definitions, see the 1985 letter in Triangles Are Square.
(The 1984 lemma discussed there has now, in response to an article
in Wolfram MathWorld, been renamed the square-triangle theorem .)
A search today for related material yielded the following—
|
"Suppose that one side of a triangle has length n . Then it can be cut into n 2 congruent triangles which are similar to the original one and whose corresponding sides to the side of length n have lengths 1." |
This was supplied, without attribution, as part of the official solution
to Problem 3 in the 17th Asian Pacific Mathematics Olympiad
from March 2005. Apparently it seemed obvious to the composer
of the problem. As the 1985 letter notes, it may be not quite obvious.
At any rate, it served in Problem 3 as a lemma , in the sense
described above by Wikipedia. See related remarks by Doron Zeilberger.