# Geometry - Pythagorean Theorem

For a right triangle with side-lengths a, b, c, where c is the length of the hypotenuse,

$$a^2+b^2 = c^2$$

## Documentation / Reference

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Linear Algebra - Orthogonality (Perpendicular)

Orthogonal is linear-algebra-ese for perpendicular. The squared length of the “hypotenuse” (the vector u + v) is Thus following the Pythagorean Theorem u and v are orthogonal when then:...
Linear Algebra - Closest Point on a Line

How to find the closest point on a line from a point ? How to find the vector on the line that best approximates the given vector b (the closest point on the line) Letb be a vector Leta be a...
Linear Algebra - Norm (Length)

The norm of a vector v is written The norm of a vector v is defined by: where: is the inner product of v. In Euclidean space, the inner product is the . For a 2-vector: as the Pythagorean...
Linear Algebra - Pythagorean Theorem

Following the definition of orthogonality, the Pythagorean Theorem for vectors becomes: