Proof without word

Daniel Mentrard, 2021. 4. 17.


  • 1. Proof without word: Area of an Arbelos
  • 2. Proof without word: Area of a regular dodecagon
  • 3. Lunes aorund a square (2)
  • 4. Proof without word: r +r(1-r) + r(1-r)² +.....=?
  • 5. Proof without word: serie of1/2
  • 6. Proof without word : Pythagore
  • 7. Path on half circle or on n half circles?
  • 8. Proof without words: 1/4 +(1/4)² +.... = ?
  • 9. Proof without words: 1/x and ln
  • 10. Pythagora's puzzle
  • 11. cos²x +sin²x =1 (Pythagora in the unit Circle)
  • 12. Area of the parallelogram
  • 13. Pythagora by water
  • 14. Proof without words: Integral of sin(x) between 0 and pi/2
  • 15. Cosine and sine subtraction formulas
  • 16. Cosine and sine addition formulas
  • 17. Haga's Theorem
  • 18. Sum of interior angles of a polygon
  • 19. Arithmetic mean vs geometric mean (proof without word)
  • 20. sin(a+b)= sina cosb+ sinb cosa (addition formula)
  • 21. Sum of 7 consecutive intergers
  • 22. The derivative of ln(x) is ........
  • 23. Sine and cosine are out of phase by 90 °
  • 24. Proof without words: Mid segments in a triangle
  • 25. Proof without words : relationship two between arctan
  • 26. Proof without words: Relationship between arctan
  • 27. Proof without words : Steiner'ellipse of a triangle
  • 28. Proof without words: Median to hypotenuse
  • 29. Proof without words : the derivative of sinus function
  • 30. Area of the circle by the triangle or the rectangle
  • 31. Proof without words : Metric relations (2)
  • 32. Proof wihout words : metric relation (1)
  • 33. Proof without words : Area of a parallelogramm
  • 34. Proof without words : Sum of the first n integer numbers
  • 35. Proof without words : Sum of alternate squares
  • 36. Proof without word : x²+ax= (x+a/2)²-(a/2)²
  • 37. Proof without word 4ab = (a+b)²-(a-b)²
  • 38. Relation between pentagonal and triangular numbers
  • 39. Proof without word : Sum of the odd numbers
  • 40. Catenary vs Parabola
  • 41. Proof without words: Odd number and squared numbres
  • 42. Proof without words: Intersecting chords theorem
  • 43. Proof without words: Law of cosinus
  • 44. Proof without words: Tangent theoreme
  • 45. Proof in a few words: metric relationships
  • 46. The sum of the angles of a quadrilateral
  • 47. Proof without words : Sum of external angles of a polygon
  • 48. Law of cosine in visual
  • 49. Pythagore with regular polygons
  • 50. Proof without words with Fibonacci numbers
  • 51. Proof without words: Viviani theorem by the areas of the triangle
  • 52. Proof without words (or very few words): volume of the sphere
  • 53. Proof without words : 1/2 + 1/4 + 1/8 +..... = 1
  • 54. Proof without words : Area of a parallelogram
  • 55. Proof without words : Area of the triangle
  • 56. Proof without words : Sum of the square
  • 57. Proof without words: The third power sum
  • 58. Area of regular polygons
  • 59. Proof without words : difference a^3 - b^3
  • 60. Proof without words: volume of a pyramide
  • 61. Proof without words :Sum of the cube
  • 62. Proof without word: arithmetic sequences
  • 63. (a + b +c )²=a²+b²+c²+2ab+2ac+2bc
  • 64. (a +b) (a -b)
  • 65. (a - b)²
  • 66. (a+b)²=a²+2ab+b²
  • 67. Distributivity
  • 68. Smilog: properties of the logarithms (1)
  • 69. Area of a triangle (acute or obtuse)
  • 70. Puzzle for the unit cube
  • 71. Law of cosine : proof without words
  • 72. Unwinding the Theodorus spiral
  • 73. Area of the cycloid by Mamikon
  • 74. Area and perimeter of a triangle
  • 75. Serie of cubes
  • 76. Pythagore: a²+=b²+c² (proofs serie 1)
  • 77. Pythagora theorem (proofs serie 2)

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Proof without word: Area of an Arbelos

Animation by the slider
– Daniel Mentrard

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