proofs

sonom, Ronan Downes, 2020年3月10日

目錄

  1. geometry
    1. the famous "1/7" triangle
    2. ptolemy's theorems
    3. pythagorean and galileo's law
    4. pythagorean theorem (proof)
    5. ratio of areas-1
    6. ratio of areas-2
    7. regular polygons-1
    8. sum of the interior angles of a n-gon
    9. secant-secant theorem
    10. square vs rhombus
    11. supplementary angles
    12. tangent-chord angle
    13. the famous "1/5" square
    14. Thales' theorem
    15. tangent-secant theorem
    16. the angle bisector theorems
    17. the lunes of Alhazen
    18. the lune of Hippocrates
    19. the outer Napoleon triangle
    20. triangle angle-sum theorem
    21. the three squares problem
    22. triangle midpoint theorem
    23. vivianni's theorem
    24. proof of pythagorean-5
    25. parallel chords theorem
    26. five squares
    27. Garfield's proof for pythagorean theorem
    28. median to the hypotenuse
    29. power of a point
    30. chord theorem
    31. cuboid
    32. diagonals of n-gons
    33. double reflection
    34. equal chords
    35. equilateral triangle (SAS)
    36. equal chords-1
    37. area of a triangle
    38. areas inside a trapezoid
    39. areas of similar triangles
    40. area of an equilateral triangle
    41. area of a triangle-2
    42. areas inside a parallelogram
    43. areas-3
    44. area of a trapezoid
    45. area of a quadrilateral
    46. area of a kite
    47. area of a rectangle
    48. archimedes' "salinon"
    49. area of a parallelogram
    50. area of a rectangle-1
    51. archimedes' arbelos
    52. a Reuleaux triangle
    53. a square in a square
    54. angle bisector as locus
    55. angle between secants
    56. Johnson's theorem
    57. geometric mean theorem
    58. frustum of a right cone
    59. proof of pythagorean-9
    60. euclid's proof of pythagorean
    61. circles of a regular n-gon
  2. calculus
    1. an extrema problem-2
    2. quadratic formula
    3. sierpinski triangles
    4. the center of an interval
    5. the locus of the intersection of two lines
    6. perpendicular lines
    7. law of cosines (proof)
    8. law of sines (proof)
    9. maximum area (angle)
    10. minimum area (line)
    11. maximum volume
    12. minimum perimeter
    13. minimum area
    14. collinear points-1
    15. area of an ellipse
    16. area of a triangle (sas)
    17. area of a circle
    18. an extrema problem-1

1.

geometry

  • 1. the famous "1/7" triangle
  • 2. ptolemy's theorems
  • 3. pythagorean and galileo's law
  • 4. pythagorean theorem (proof)
  • 5. ratio of areas-1
  • 6. ratio of areas-2
  • 7. regular polygons-1
  • 8. sum of the interior angles of a n-gon
  • 9. secant-secant theorem
  • 10. square vs rhombus
  • 11. supplementary angles
  • 12. tangent-chord angle
  • 13. the famous "1/5" square
  • 14. Thales' theorem
  • 15. tangent-secant theorem
  • 16. the angle bisector theorems
  • 17. the lunes of Alhazen
  • 18. the lune of Hippocrates
  • 19. the outer Napoleon triangle
  • 20. triangle angle-sum theorem
  • 21. the three squares problem
  • 22. triangle midpoint theorem
  • 23. vivianni's theorem
  • 24. proof of pythagorean-5
  • 25. parallel chords theorem
  • 26. five squares
  • 27. Garfield's proof for pythagorean theorem
  • 28. median to the hypotenuse
  • 29. power of a point
  • 30. chord theorem
  • 31. cuboid
  • 32. diagonals of n-gons
  • 33. double reflection
  • 34. equal chords
  • 35. equilateral triangle (SAS)
  • 36. equal chords-1
  • 37. area of a triangle
  • 38. areas inside a trapezoid
  • 39. areas of similar triangles
  • 40. area of an equilateral triangle
  • 41. area of a triangle-2
  • 42. areas inside a parallelogram
  • 43. areas-3
  • 44. area of a trapezoid
  • 45. area of a quadrilateral
  • 46. area of a kite
  • 47. area of a rectangle
  • 48. archimedes' "salinon"
  • 49. area of a parallelogram
  • 50. area of a rectangle-1
  • 51. archimedes' arbelos
  • 52. a Reuleaux triangle
  • 53. a square in a square
  • 54. angle bisector as locus
  • 55. angle between secants
  • 56. Johnson's theorem
  • 57. geometric mean theorem
  • 58. frustum of a right cone
  • 59. proof of pythagorean-9
  • 60. euclid's proof of pythagorean
  • 61. circles of a regular n-gon

1.1.

the famous "1/7" triangle

[url]http://www.futilitycloset.com/category/science-math/page/2/[/url]
the famous "1/7" triangle
– sonom

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2.

calculus

  • 1. an extrema problem-2
  • 2. quadratic formula
  • 3. sierpinski triangles
  • 4. the center of an interval
  • 5. the locus of the intersection of two lines
  • 6. perpendicular lines
  • 7. law of cosines (proof)
  • 8. law of sines (proof)
  • 9. maximum area (angle)
  • 10. minimum area (line)
  • 11. maximum volume
  • 12. minimum perimeter
  • 13. minimum area
  • 14. collinear points-1
  • 15. area of an ellipse
  • 16. area of a triangle (sas)
  • 17. area of a circle
  • 18. an extrema problem-1

2.1.

an extrema problem-2

an extrema problem-2
– sonom

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