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  1. If a and b have the same sign, then a*b >= 0
  2. In general, A – B ≤ | A – B |
  3. | A – B | ≤ | A | – | B |. This is called the triangle inequality.
  4. | | A | – | B | | ≤ | A – B |. This is an extension of the triangle inequality.
  5. The quotient a / b will end up being a terminating decimal number only if b can be written as the product of 2’s and 5’s when broken down into its prime factors. Stated another way, if you can write b = 2x5y, x ≥ 0, y ≥ 0, then the quotient a / b will be a terminating decimal value when it is calculated (e.g. 3 / 8 = 3 / 23 = 0.375)
  6. Two lines the Cartesian plane are perpendicular if m1m2 = -1
  7. The angle between 2 lines on the cartesian plane is given by:

    tan( a ) = | (m2 – m1) / (1 + m1m2) |

    Notice that if the lines are perpendicular, then the RHS becomes infinity.

  8. The sum of angles in any polygon is (V-2)*180, where V is the number of vertices in the shape. See (V-2) triangles to make any shape
  9. If you’re not sure how to solve a complex problem, try using the principle of superposition ;)
  10. Interesting, but not very useful fact when it comes to programming with math:
    max( a, b ) = 1/2( a + b + | a – b | )

    min( a, b ) = 1/2( a + b – | a – b | )

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