Pythagoras' Theorem and Vectors

Pythagoras' Theorem

Definition

• In any triangle where two sides are perpendicular to each other, the length of the hypotenuse c is the square root of the sum of the squares of the other two sides, a and b.
• Pythagoras' theorem states the following two equations:
  • a^2 = b^2 + c^2
  • a = √(b^2 + c^2)

Vector

Definition

• A physical quantity characterized by velocity (length) and direction

  • It does not have a starting point

• You can use the Pythagorean theorem to find the length of a vector.

Notation

• If you add the arrow at the top of the image, it will display only the vectors.

Subtraction

Normalize

• Setting the length to 1 indicates a pure direction

  

• In Unity, you can normalize a vector using Vector3.normalized

References

• Game Math for Math-Phobes #02 - A Clear Understanding of the Pythagorean Theorem
• Game Math for Math Phobics #04 - Vectors #1: Vector Man Is a Total Geek!