02.28.2017. Tuesday
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 Geometry
Two-dimensional geometric shapes
⦿ Rhombus
⦿ Parallelogram
⦿ Trapezoid
⦿ Kite
⦿ Circle
⦿ Circular sector
⦿ Circular segment
⦿ Area of a Triangle
⦿ Squere
⦿ Rectangle
Three-dimensional geometric shapes
⦿ Cube
⦿ Sphere
⦿ Cylinder
⦿ Cone
⦿ Prism
⦿ Pyramide
⦿ Platonic solids
Trigonometry
⦿ Law of Sines
⦿ Law of Cosines
⦿ Trygonometry Identities of same angle
⦿ Identities for the sum and difference of two angles
⦿ Trigonometric identities of double angles
⦿ Trigonometric identities of half angles
⦿ Sum and difference of trigonometric functions
⦿ Trigonometry of right triangles
Vectors
⦿ Scalar Product of Vectors
⦿ Vector Product of Vectors
Analytical Geometry 2D
⦿ Distance between two points
⦿ Circle
⦿ Linear equation
⦿ Ellipse


Three-dimensional geometric shapes

Platonic solids

Name Tetrahedron Hexahedron
(Cube)
Octahedron Dodecahedron Icosahedron
Picture Tetrahedron Hexahedron (Cube) Octahedron Dodecahedron Icosahedron
Net Tetrahedron net Hexahedron (Cube) net Octahedron net Dodecahedron net Icosahedron net
Faces 4 6 8 12 20
Face type
equilateral triangle square equilateral triangle equilateral pentagon equilateral triangle
Duality tetrahedron octahedron hexahedron icosahedron dodecahedron
Edges 6 12 12 30 30
Vertices 4 8 6 20 12
Edges from vertex 3 3 4 3 5
Number of diagonals 0 4 3 100 36
Dihedral angle ≈70°31'43,61'' 90° ≈109°28'16,39'' ≈116°33'55,84'' ≈138°11'22,87''
Surface area 3 a 2 6 a 2 2 3 a 2 3 25 + 10 5 a 2 5 3 a 2
Volume 2 a 3 12 a 3 2 a 3 3 ( 15 + 7 5 ) a 3 4 ( 15 + 5 5 ) a 3 12
Circumradiu 6 a 4 3 a 2 3 a 2 3 ( 1 + 5 ) a 4 10 + 2 5 a 4
Inradiu 6 a 12 a 2 6 a 6 1 2 25 + 11 5 10 a 42 + 18 5 12 a
Midradius 2 a 4 2 a 2 a 2 ( 5 + 3 ) a 4 ( 1 + 5 ) a 4