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3 votes

Multiple proofs for the same problem

It just crossed my mind that I can offer you some option you haven't probably considered yourself. Once I experimented in my calculus course (which also involved some elements of analytic geometry and ...
  • 2,424
1 vote

Multiple proofs for the same problem

At the college level, see here, here, here, here, and here. Only the first link is suitable for high school courses.
  • 2,888
2 votes

Geometrical approaches in algebra

Here's a well-known one: $$\sum_{n=1}^{\infty} \frac{1}{2^n} = 1$$
  • 1,252
7 votes

Geometrical approaches in algebra

I offer this (community wiki) only to illustrate the OP's 2nd example. From the Archimedes Lab Project: Quite beautiful!
4 votes

Geometrical approaches in algebra

This may not be what you have in mind, but your question reminds me of “proofs without words” aka visual proofs. The three examples you gave have relatively famous visual proofs. There’s some ...

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