MATHEMATICS ENCYCLOPEDIA

Definition of Pi: Pi is defined as the ratio of circles circumference ( C ) to the its diameter ( d ), i.e., π = C/d The ratio  π = C/d is constant for any size of circle. The symbol used to represent pi is the Greek letter π. π is irrational number. π is also transcendental, i.e. it is not the root of any non-zero polynomial. 22/7 is commonly used as an approximate value of π. π is also used in Euler's identity  e π i + 1 = 0

Two different numbers are such that the sum of proper divisors of each is equal to the other number.  Proper divisors of a given number are the numbers ( except the number itself ) that can divide the given  number Example: Proper divisors of 8 are 1, 2, 4.  The smallest pair of the amicable number is ( 220, 284 ) Proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110 and the sum of the divisors are 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 +  44 + 55 + 110 = 284 . Proper divisors of 284 are 1, 2, 4, 71, 142 and the sum of the divisors are 1 + 2 + 4 + 71 + 142 = 220. Other examples include ( 1184, 1210 ), ( 2620, 2924 ), ( 5020, 5564 ), ( 6232, 6368 ), ( 10744, 10856 ), ( 12285, 14595 ) etc.