Mathematics is the base of human civilization. From cutting vegetables to arranging books on the shelves, from tailoring clothes to motion of Planets - Mathematics applies everywhere.
While dealing with natural numbers and whole numbers, it is not always possible to subtract a number from another. For example, (2 – 3), (3 – 7), and (9 – 20) are all not possible in the system of natural numbers and whole numbers. Thus, it needed another extension of numbers which allow such subtractions.
The term ‘Geometry’ is the English equivalent of the Greek word ‘Geometron’. ‘Geo’ means Earth and ‘metron’ means Measurement. According to historians, the geometrical ideas shaped up in ancient times, probably due to the need in art, architecture and measurement. These include occasions when the boundaries of cultivated lands had to be marked without giving room for complaints.
The Lowest Common Multiple (LCM) of two or more given numbers is the lowest (or smallest or least) of their common multiples. For example, the common multiples of 4 and 6 are 12, 24, 36, ... . The lowest of these is 12. So, the lowest common multiple of 4 and 6 is 12.
Given any natural number, you can add 1 to that number and get the next number i.e. you get its successor. The successor of 16 is 16 + 1 = 17, that of 19 is 19 +1 = 20 and so on. The number 16 comes before 17, we say that the predecessor of 17 is 17 – 1 = 16, the predecessor of 20 is 20 – 1 = 19, and so on. Does 1 have both a successor and a predecessor?
A geometric progression (GP) is a sequence of numbers in which the first term is non-zero and each term, except the first, is obtained by multiplying the term immediately preceding it by a fixed non-zero number. This fixed number is called the common ratio and it is denoted by r.
Triangle Law of Addition of vectors states that, if two vectors are represented in magnitude and direction by the two sides of a triangle taken in the same order, then their sum is represented by the third side taken in the reverse order.
θ = nπ + (−1)nα, where n ∈ Z
The general solution of sin θ = 0 is given by
θ = nπ, n ∈ Z where Z is the set of all integers.
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