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2. Pythagorean theorem - Wikipedia

   en.wikipedia.org/wiki/Pythagorean_theorem

   In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

3. Garfield's proof of the Pythagorean theorem - Wikipedia

   en.wikipedia.org/wiki/Garfield's_proof_of_the...

   Garfield in 1881. Garfield's proof of the Pythagorean theorem is an original proof the Pythagorean theorem invented by James A. Garfield (November 19, 1831 – September 19, 1881), the 20th president of the United States. The proof appeared in print in the New-England Journal of Education (Vol. 3, No.14, April 1, 1876). [1][2] At the time of ...

4. Pick's theorem - Wikipedia

   en.wikipedia.org/wiki/Pick's_theorem

   In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points within it and on its boundary. The result was first described by Georg Alexander Pick in 1899. [2] It was popularized in English by Hugo Steinhaus in the 1950 edition of his book Mathematical ...

5. Proofs of trigonometric identities - Wikipedia

   en.wikipedia.org/wiki/Proofs_of_trigonometric...

   Pythagorean identities. Identity 1: The following two results follow from this and the ratio identities. To obtain the first, divide both sides of by ; for the second, divide by . Similarly. Identity 2: The following accounts for all three reciprocal functions. Proof 2: Refer to the triangle diagram above.

6. Hilbert's third problem - Wikipedia

   en.wikipedia.org/wiki/Hilbert's_third_problem

   Hilbert's third problem. Two polyhedra of equal volume, cut into two pieces which can be reassembled into either polyhedron. The third of Hilbert's list of mathematical problems, presented in 1900, was the first to be solved. The problem is related to the following question: given any two polyhedra of equal volume, is it always possible to cut ...

7. Wiles's proof of Fermat's Last Theorem - Wikipedia

   en.wikipedia.org/wiki/Wiles's_proof_of_Fermat's...

   Sir Andrew John Wiles. Wiles's proof of Fermat's Last Theorem is a proof by British mathematician Sir Andrew Wiles of a special case of the modularity theorem for elliptic curves. Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be impossible to ...