Geometry: An Interactive Journey to Mastery



x DOOYROXPHVFKDQJHE\DIDFWRUk^3.

x all angles remain unchanged.

Fractal Dimension
If a fractal is composed of N parts, each a scaled copy of the original fractal with scale factor k, then its

IUDFWDOGLPHQVLRQLVWKHQXPEHUd so that kd (^) N^1.
Geometric Series Formula
NN11 1 NN^23 "^1  1 IRUZKROHQXPEHUV1t 2.
Figurate Number Formulas
123    "" NNN 1 1 321 N^2.
7KHVXPRIWKH¿UVWNRGGQXPEHUVLVN^2.
7KHVXPRIWKH¿UVWNHYHQQXPEHUVLVNͼ௘N௘ͽ
7KHVXPRIWKH¿UVWNFRXQWLQJQXPEHUVLV 123   " N NN^2 ^1.
The N thVTXDUHQXPEHULVSͼ௘N௘ͽ = N^2.
The N thWULDQJXODUQXPEHULVTN NN^2 ^1.
Spherical Triangles
The area of a spherical triangle with interior angles of measures xƒyƒDQGzƒLV
xyz^180 utotal surface area of the sphere.