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Vedic Mathematics
Vedic Mathematics is a collection of Techniques/Sutras to solve mathematical arithmetics in easy and faster way. It consists of 16 Sutras (Formulae) and 13 sub-sutras (Sub Formulae) which can be used for problems involved in arithmetic, algebra, geometry, calculus, conics.
Some Vedic Maths trics
Multiply a number by 9
Multiply a number by 11
Shift the number by one unit and add to same number
vinculam and its application
A vinculum is a horizontal line used in mathematical notation for a specific purpose. It may be placed as an overline (or underline) over (or under) a mathematical expression to indicate that the expression is to be considered grouped together. Historically, vincula were extensively used to group items together, especially in written mathematics, but in modern mathematics this function has almost entirely been replaced by the use of parentheses.Today, however, the common usage of a vinculum to indicate the repetend of a repeating decimal is a significant exception and reflects the original usage.
A vinculum can indicate a line segment where A and B are the endpoints:
A vinculum can indicate the repetend of a repeating decimal value:
- 1⁄7 = 0.142857 = 0.1428571428571428571…
Similarly, it is used to show the repeating terms in a periodic continued fraction. Quadratic irrational numbers are the only numbers that have these.
Its main use was as a notation to indicate a group (a bracketing device serving the same function as parentheses):
meaning to add b and c first and then subtract the result from a, which would be written more commonly today as a − (b + c). Parentheses, used for grouping, are only rarely found in the mathematical literature before the eighteenth century. The vinculum was used extensively, usually as an overline, but Chuquet in 1484 used the underline version.
The vinculum is used as part of the notation of a radical to indicate the radicand whose root is being indicated. In the following, the quantity is the whole radicand, and thus has a vinculum over it:
In 1637 Descartes was the first to unite the German radical sign √ with the vinculum to create the radical symbol in common use today.
The symbol used to indicate a vinculum need not be a line segment (overline or underline); sometimes braces can be used (pointing either up or down).
Other notations
There are several mathematical notations which use an overbar that can easily be mistaken for a vinculum. Among these are:
It can be used in signed-digit representation to represent negative digits, such as the following example in balanced ternary:
or the bar notation in common logarithms, such as
The overbar is sometimes used in Boolean algebra, where it serves to indicate a group of expressions whose logical result is to be negated, as in:
In electronics, the overbar is used to notate complementary binary signals. For example, READY pronounced “not ready”, would be the same signal as READY but with the opposite polarity. This usage is closely related to the usage in Boolean algebra.
It is also used to refer to the conjugate of a complex number:
In statistics the overbar can be used to indicate the mean of series of values.
In particle physics, the overline is used to indicate antiparticles. For example, p and p are the symbols for proton and antiproton, respectively.