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Pythagorean Theorem

This guide covers essential mathematical formulas and conversions used in geometry, measurement, and basic algebra. It includes the Pythagorean theorem, formulas for nth numbers (triangular, pentagonal, hexagonal), diagonal calculations for squares and cubes, and the total angles in polygons. Additionally, it provides essential unit conversions such as miles to kilometers, quarts to gallons, and Fahrenheit to Celsius. This resource is ideal for students and anyone needing a quick reference for geometry and unit conversions.

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Pythagorean Theorem

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  1. Pythagorean Theorem a2 + b2 = c2

  2. Formula for: nth hexagonal number: n(4n - 2) 2

  3. Total radians in a circle 2

  4. ? = baker’s dozen 13

  5. ? km = 1 mile 1.61

  6. ? qts = 1 peck 8

  7. Formula for: 2 + 4 + 6 + 8 + . . . + n n(n+2) 4

  8. Diagonal of a square when given the side x x 2

  9. ? = 1 gross 144

  10. Number of Diagonals from one vertex n-3

  11. ? cu in = 1 cu ft 1728

  12. Total of all exterior angles in a polygon 360

  13. ? cu in = 1 gallon 231

  14. ? oz = 1 gal 128

  15. Internal diagonal of a cube when given the side x x 3

  16. ? acres = 1 sq mile 640

  17. Number of total diagonal in a polygon n(n-3) 2

  18. ? sq in = 1 sq ft 144

  19. Formula for: 1 + 2 + 3 + 4 + . . . + n n(n+1) 2

  20. Measure of each exterior angle in a regular polygon 360 n

  21. ? qt = 1 gal 4

  22. ? ft/sec = 15 mph 22

  23. ? pints = 1 qt 2

  24. ? mi = 1 km .621

  25. Degrees of each angle in a regular polygon 180(n-2) n

  26. ? lb = 1 ton 2000

  27. ? sq ft = 1 sq yd 9

  28. Formula for: nth triangular number: n(n+1) 2

  29. ? mph = 22 ft/sec 15

  30. Formula to chance Celsius to Fahrenheit 9 F = – C + 32 5

  31. Formula for: 1 + 3 + 5 + 7 + . . . + n 2 ( ) n+1 2

  32. ? ft = 1 mile 5280

  33. Total degrees in any polygon 180(n-2)

  34. Formula to chance Fahrenheit to Celsius 5 C = (F – 32) – 9

  35. Formula for: nth pentagonal number: n(3n-1) 2

  36. ? pecks = 1 bushel 4

  37. Area of any polygon Tan( )(4n) p2 180 n

  38. Total degrees in a circle 360°

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