Math 2.0

Learn Year 1

Geometry

100 ideas in teaching order. Each idea comes after the ideas that it builds on. 98 of them have a page so far; the others are on the list in grey.

Start with Euclidean plane →

  1. Euclidean plane object
  2. Euclidean space object
  3. Cartesian coordinate system concept
  4. Euclidean vector definition
  5. Length of a vector definition
  6. Euclidean distance definition
  7. Angle between two vectors definition
  8. Geometric formula for the dot product statement
  9. vectors are perpendicular iff their dot product is zero statement
  10. Vector projection definition
  11. Cross product definition
  12. The cross product is perpendicular to its factors statement
  13. Anticommutativity of the cross product statement
  14. Scalar triple product statement
  15. Vector triple product statement
  16. Parallelepiped definition
  17. Line definition
  18. Parametric equation of a line concept
  19. Plane definition
  20. Equation of a plane concept
  21. Normal vector definition
  22. Distance from a point to a line statement
  23. Distance from a point to a plane statement
  24. Dihedral angle definition
  25. Affine space definition
  26. Affine subspace definition
  27. Affine span definition
  28. Affine combination definition
  29. Midpoint definition
  30. Collinear points definition
  31. Affine map definition
  32. Homothety definition
  33. Angle at a point definition
  34. Oriented angle definition
  35. Triangle definition
  36. Angle sum of a triangle statement
  37. Exterior angle theorem statement
  38. Isosceles triangle theorem statement
  39. Congruent triangles definition
  40. Side-side-side congruence statement
  41. Similar triangles definition
  42. Angle-angle similarity statement
  43. Intercept theorem statement
  44. Pythagorean theorem statement
  45. Law of cosines statement
  46. Law of sines statement
  47. Area of a triangle concept
  48. Heron's formula statement
  49. Median of a triangle definition
  50. Apollonius's theorem statement
  51. centroid definition
  52. The medians meet at the centroid statement
  53. Perpendicular bisector definition
  54. Circumcentre definition
  55. Circumcircle definition
  56. Angle bisector theorem statement
  57. Incentre definition
  58. Incircle definition
  59. Altitude of a triangle definition
  60. Orthocentre definition
  61. Euler line statement
  62. Nine-point circle definition
  63. Ceva's theorem statement
  64. Menelaus's theorem statement
  65. Circle definition
  66. Concyclic points definition
  67. Thales's theorem statement
  68. Inscribed angle theorem statement
  69. Angles in the same segment are equal statement
  70. Cyclic quadrilateral definition
  71. Ptolemy's theorem statement
  72. Tangent line to a circle definition
  73. A tangent is perpendicular to the radius statement
  74. Power of a point definition
  75. Intersecting chords theorem statement
  76. Intersecting secants theorem statement
  77. Tangent–secant theorem statement
  78. Conic section definition
  79. Ellipse definition
  80. Parabola definition
  81. Hyperbola definition
  82. Focus of a conic definition
  83. Directrix definition
  84. Eccentricity definition
  85. Classification of conics by the discriminant statement
  86. Euclidean isometry definition
  87. Euclidean group object
  88. Translation definition
  89. Rotation definition
  90. Reflection in a line or plane definition
  91. Glide reflection definition
  92. Classification of isometries of the plane statement
  93. Convex set definition
  94. Convex hull definition
  95. Carathéodory's theorem statement
  96. Regular polygon definition
  97. Polyhedron definition
  98. Euler's polyhedron formula statement
  99. Platonic solid definition
  100. Classification of the Platonic solids statement