MATHEMATICS ENCYCLOPEDIA

A woman was travelling with her young son, a carton of cakes and a wolf She had to cross a river in a small boat large enough for herself and one of the three . The following problems arises: If she left her son alone with the cakes, he could eat them.  If she left the wolf alone with the boy, the wolf would eat him. The question is how could she make the crossing ? Puzzled! See the solution below. Solution: The woman takes the boy across, returns alone. She takes the carton of cakes across, returns with a boy. She takes wolf across, return alone. Then she takes the boy across.

In A.D. 1120, the king of England decreed that in his country, the yard will be used as the unit of length. It was the distance from the tip of the king's nose to the end of his outstretched arm. The original standard adopted by France was called a foot . It was equal to the royal foot of the king. In 1799, the kings foot was replaced by "meter". Then it was defined as one ten millionth distance from the equator to the north pole along a longitudinal line that passes through Paris . In 1889, 1 meter was defined as the distance between two lines on a specific platinum-iridium bar stored under controlled conditions. In 1960, meter was redefined as 1,650,763.73 wavelengths of a particular orange-red light emitted by atoms of Krypton-86 in a gas discharge tube . 1 meter = 100 cm The meter was redefined again in 1983, this time as the distance which light travel in a vacuum in 1/299,792,458 seconds. This remains the current definition. Note that in all these re...

Abacus - calculating device Abacus ( plural Abaci, or Abacuses ), calculating probably of Babylonian origin. It is the ancestor of modern calculating machines and computer. The earliest abacus was a board or slab on which Babylonian spread sand so he could trace letters for general writing purposes. The word abacus is probably is derived through its Greek form abacos . The abacus generally in the form of a large calculating board, was in universal use in Europe in the middle ages as well as in the Arab world and in Asia .It reached Japan in in the 16th century. The introduction of the Hindu-Arabic notation, with its place value and zero, gradually replaced the abacus.

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.

Pascal's triangle ( An extraordinary logical structure ) Pascal's triangle is one of the most interesting structure in mathematics, named after the French mathematician, inventor, physicist Blaise Pascal ( 1623 - 1662 ). The structure looks like a triangle with 1 at the top vertex and running down the two slanting sides. This array of numbers is known as Pascal's triangle. Also known as Meru Prastara, Tartaglia's triangle ( after Nicolo Tartaglia ). Many other mathematicians studied the Pascal's triangle centuries before him in China, India, Germany, Italy and Persia. Features of Pascal's triangle Expansion for the higher powers of binomial are possible by using Pascal's triangle. Example: The row for the index 5 in binomial expansion is 1   5   10   10   5   1 The sum of the numbers in each row is the power of 2. The numbers in each row is the power of eleven. Example: The first row is 11 to the power 0, 2nd row the number...

Topology ( Branch of mathematics ) Topology, branch of mathematics , sometime reffered to as "rubber sheet geometry" in which two ibjects are considered equivalent if they can be continuously deformed into one another through such motions in space as bending, twisting, stretching and shrinking while disallowing tearing apart or gluing together parts. The main topics of interest in topology are the properties that remain unchanged by such continuous deformations. Topology while similar to geometry differs from geometry in that geometrically equivalent objects often share numerically measured quantities, such as lengths, angles, while topologically equivalent objects resemble each other in a more qualitative sense. The area of topology dealing with abstract objects is referred to as general, or point set topology. General topology overlaps with another important area of topology called algebraic topology. These areas of specialization form the two major subdisciplines...