math

Pythagorean Theorem

A fundamental relation in geometry: the square of the hypotenuse equals the sum of squares of the other two sides.

The Pythagorean theorem states that in a right triangle: aΒ² + bΒ² = cΒ², where c is the hypotenuse (the longest side, opposite the right angle) and a and b are the other two sides.

Example

A right triangle has legs of 3 and 4. Hypotenuse = √(3² + 4²) = √(9 + 16) = √25 = 5.

Applications

  • Measuring diagonal distances
  • Construction and carpentry (the 3-4-5 rule for square corners)
  • Navigation and GPS calculations
  • Computer graphics and game development

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