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Monroe Eskew
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Why not some elementary theorems of Euclidan geometry? As I recall, the more general and fundamental theorems were just taken as given in my schooling, but I think many of them can be given accessible and beautiful proofs. Here are some good ones:

  1. The Pythagorean theorem. (many lovely proofs)

  2. Parallelograms having congruent bases and heights have the same area. (Euclid's proof is pretty.)

  3. Use 2 to derive that similar triangles have corresponding sides in common proportion.

  4. Two distinct circles have at most 2 points of intersection.

  5. Prove the formula for volume of a pyramid without using calculus.

Why not some elementary theorems of Euclidan geometry? As I recall, the more general and fundamental theorems were just taken as given in my schooling, but I think many of them can be given accessible and beautiful proofs. Here are some good ones:

  1. The Pythagorean theorem. (many lovely proofs)

  2. Parallelograms having congruent bases and heights have the same area. (Euclid's proof is pretty.)

  3. Use 2 to derive that similar triangles have corresponding sides in common proportion.

  4. Two distinct circles have at most 2 points of intersection.

Why not some elementary theorems of Euclidan geometry? As I recall, the more general and fundamental theorems were just taken as given in my schooling, but I think many of them can be given accessible and beautiful proofs. Here are some good ones:

  1. The Pythagorean theorem. (many lovely proofs)

  2. Parallelograms having congruent bases and heights have the same area. (Euclid's proof is pretty.)

  3. Use 2 to derive that similar triangles have corresponding sides in common proportion.

  4. Two distinct circles have at most 2 points of intersection.

  5. Prove the formula for volume of a pyramid without using calculus.

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Monroe Eskew
  • 18.6k
  • 5
  • 53
  • 114

Why not some elementary theorems of Euclidan geometry? As I recall, the more general and fundamental theorems were just taken as given in my schooling, but I think many of them can be given accessible and beautiful proofs. Here are some good ones:

  1. The Pythagorean theorem. (many lovely proofs)

  2. Parallelograms having congruent bases and heights have the same area. (Euclid's proof is pretty.)

  3. Use 2 to derive that similar triangles have corresponding sides in common proportion.

  4. Two distinct circles have at most 2 points of intersection.