Geometry -------- The branch of mathematics concerned with the properties and relationships of points, lines and angles. Geometry may thought to be the science of space. Interior angles of a polygon A polygon of sides N has (180 * (N-2)) degrees for total interior angles N = 3, triangle, interior angles = 60 * 3 degrees N = 4, square, interior angles = 90 * 4 degrees N = 5, pentagon, interior angles = 108 * 5 degrees Series & Sequences ------------------ Sum of the first N integers { 1, 2, 3, 4, 5 ... } N ( N + 1 ) /2 e.g. N = 10 evaluates to 55 Sum of the first N^2 integers { 1, 4, 9, 16, 25 ...} 1/3N^3 + 1/2N^2 + 1/6N e.g. N = 10 evaluates to 385 Fibonacci Series { 1, 1, 2, 3, 5, 8, 13 ...} Combinations and Permutations ----------------------------- N choose R / \ nCr = | N | = N! | R | --------- \ / (N-R)! R! e.g. 6 distinct objects choose 3 = 6! / (6-3)! 3! = 20 combinations nPr = N! ------ (N-R)! e.g. 6 distinct objects choose 5 = 6! / (6-5)! = 720 permutations The number of N-arrangements of N objects, if N1 are alike of one kind, N2 alike of a second , ... Nr alike of an rth kind is N! ----------------- N1! * N2! ... Nr!