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2. Identity (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Identity_(mathematics)

   Visual proof of the Pythagorean identity: for any angle , the point (,) = (⁡, ⁡) lies on the unit circle, which satisfies the equation + =.Thus, ⁡ + ⁡ =. In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables ...

3. Sophie Germain's identity - Wikipedia

   en.wikipedia.org/wiki/Sophie_Germain's_identity

   Sophie Germain's identity. In mathematics, Sophie Germain's identity is a polynomial factorization named after Sophie Germain stating that Beyond its use in elementary algebra, it can also be used in number theory to factorize integers of the special form , and it frequently forms the basis of problems in mathematics competitions. [1][2][3]

4. Lagrange's identity - Wikipedia

   en.wikipedia.org/wiki/Lagrange's_identity

   In algebra, Lagrange's identity, named after Joseph Louis Lagrange, is: [1][2] which applies to any two sets {a1, a2, ..., an} and {b1, b2, ..., bn} of real or complex numbers (or more generally, elements of a commutative ring). This identity is a generalisation of the Brahmagupta–Fibonacci identity and a special form of the Binet–Cauchy ...

5. List of mathematical identities - Wikipedia

   en.wikipedia.org/.../List_of_mathematical_identities

   List of logarithmic identities. MacWilliams identity. Matrix determinant lemma. Newton's identity. Parseval's identity. Pfister's sixteen-square identity. Sherman–Morrison formula. Sophie Germain identity. Sun's curious identity.

6. 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.

7. Pascal's rule - Wikipedia

   en.wikipedia.org/wiki/Pascal's_rule

   In mathematics, Pascal's rule (or Pascal's formula) is a combinatorial identity about binomial coefficients. It states that for positive natural numbers n and k, where is a binomial coefficient; one interpretation of the coefficient of the xk term in the expansion of (1 + x)n. There is no restriction on the relative sizes of n and k, [1] since ...