Geometry
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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
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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
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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!
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(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!
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N1! * N2! ... Nr!