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$Vedic Maths$

What is Vedic Maths?

Vedic maths is a system of mathematics that was rediscovered by Swami Bharati Krishna Tirthaji in the early 20th century.

He claimed that he found 16 sutras (formulas) and 13 sub-sutras (sub-formulas) in the Vedas that can be used to solve any mathematical problem.

Vedic maths is not only about arithmetic, but also covers algebra, geometry, trigonometry, calculus, and more. Vedic maths is based on the principle of unity, which means that everything is connected and can be simplified to a single entity.

History of Vedic Maths

The Vedas, which date back more than 5,000 years, are the most honored and ancient texts in Hinduism. The word “Veda” in Sanskrit means “knowledge” or “wisdom.” The Rigveda, Yajurveda, Samaveda and Atharvaveda are the four divisions of the Vedas. The Brahmana (rituals),the Samhita (hymns), the Upanishad (philosophy) and the Aranyaka (forest literature) make up each of the four sections.

The Sulba Sutras, which are part of the Kalpa Sutras (ritual manuals), contain the majority of the Vedic mathematical knowledge. The Sulba Sutras are concerned with the building of altars and geometric shapes for sacrifice rites. They also include early instances of algebraic equations, the Pythagorean theorem, irrational numbers, square roots, and pi.

Vedic Mathematics was rediscovered by Indian mathematician Jagadguru Shri Bharati Krishna Tirthaji between 1911 and 1918. He was a Sanskrit, math, history, and philosophy expert. From 1925 until 1960, he was also the Shankaracharya (spiritual head) of Puri. He spent several years researching the Vedas and other ancient manuscripts, claiming to have discovered a cohesive mathematical system concealed within them.

These formulae were later published in a book called Vedic Mathematics in 1965. The system is based on 16 sutras (formulae) and 13 sub sutras.

Shri Bharati Krishna Tirthaji

Benefits of Vedic Maths

• It is basic and straightforward to learn and remember.

• It is quick and accurate, reducing the possibility of mistakes.

• It’s entertaining and pleasant, and it encourages innovation and lateral thinking.

• It is adaptable and versatile, and it can be used in any discipline of mathematics.

• It is comprehensive and global, promoting mental and spiritual growth.

Interesting Facts & Formulae :

Vertically and Crosswise Multiplication (Urdhva Tiryagbhyam) :

This technique allows for rapid multiplication of numbers. It's particularly useful when multiplying numbers with multiple digits.

Formula: Let's say you want to multiply two numbers, ab and cd.

The product is given by: (10a+b) x (10c+d)

To find the product: Multiply the digits in the vertical and crosswise direction. Add the results to get the final product.

Squaring Numbers Ending in 5 (Ekadhikena Purvena):

Squaring numbers ending in 5 becomes extremely simple with this technique.

Formula: To square a number ending in 5, let's say N5 follow these steps: Multiply the digit before 5 by itself plus 1 to get the first part of the result. Append 25 to the result.

Example: To square 35, 3 x (3+1) gives 12, and appending 25 gives 1225.

Digital Roots and Casting Out Nines:

Vedic maths includes techniques for quickly checking the accuracy of calculations through digital roots.

Digital Root: The digital root of a number is the sum of its digits, and if the result is a two-digit number, its digits are summed again.

Casting Out Nines: This is a method for checking the correctness of arithmetic operations. The idea is that if the sum of the digits of the result is the same as the sum of the digits of the operands, then the operation is likely correct.

Example: If you add 123 and 456, the sum is 579. The digital root of 123 is 6, the digital root of 456 is 6, and the digital root of 579 is 3. Since 6 + 6 ≠ 3, an error may be present in the calculation.

SUTRAS

The sixteen sutras (word-formulas), and thirteen sub-sutras that constitute the foundation of Vedic mathematics each offer precise solutions for a variety of mathematical problems.These approaches are applicable to addition, subtraction, multiplication, and division, as well as other mathematical operations.

Sutra	Meaning	Uses
Ekadhikena Purvena	By one more than the one before	This Sutra simplifies squaring numbers close to base values
Nikhilam Navatashcaramam Dashatah	All from 9 and the last from 10.	A powerful technique for subtraction, especially useful when dealing with numbers close to multiples of 10.
Urdhva Tiryak	Vertically and Crosswise.	This Sutra streamlines multiplication, especially useful for multiplying large numbers.
Paraavartya Yojayet	Transpose and adjust	This technique aids in simplifying complex mathematical problems involving equations and variables.
Shunyam Saamyasamuccaye	When the sum is the same, that sum is zero.	An effective approach for solving algebraic equations with equal sums on both sides.
Anurupye Shunyamanyat	If one is in ratio, the other is zero	This Sutra is indispensable for solving proportionality problems.
Yavadunam Tavadunikritya Varga Samam	Whatever the extent of its deficiency, lessen that deficiency to form a square	Simplifies division and finding square roots.
Vilokanam	By mere observation	A technique that encourages quick, intuitive solutions based on patterns and observations.
Sankalana-vyavakalanabhyam	By addition and by subtraction	This Sutra offers techniques for both addition and subtraction, enabling quick calculations
Puranapuranabhyam	By the completion or non-completion.	This Sutra aids in finding fractions and complements, simplifying various mathematical operations.
Chalana-kalanabyham	Differences and Similarities	Useful for problems involving ratios and proportions
Yaavadunam	Partial Products	This Sutra facilitates the multiplication of large numbers by breaking them down into smaller, more manageable parts
Vestanam	Specific and General	This Sutra helps in solving problems where a specific value is derived from a general one
Yavadvividham Vyashtih	Separately the particular from the general	This Sutra is handy for finding individual components from a group
Samuccaye	Collective addition.	Useful for quick summations, especially when dealing with a series of numbers
Ekanyunena Purvena	By one less than the previous one	This Sutra provides a technique for division and helps in finding quotients efficiently

SUBSUTRAS

Vedic maths tricks are also known as sub-sutras or corollaries. They are derived from the main sutras and provide additional methods or shortcuts to solve problems faster and easier. There are 13 sub sutras. These sub sutras are discussed below in the table.

Sub-Sutra	Meaning	Uses
Antyayordashakepi	The last digit remains the same	This sub-Sutra aids in quickly determining the last digit of a product.
Sopantyadvayamantyam	The last two of the last	Useful for solving problems where the last two digits are required.
Ekaadhikena Purvena	One more than the previous	This sub-Sutra extends the “Ekadhikena Purvena” technique for squaring numbers closer to the base.
Paravartya Sutra	Transposition and adjustment	Helps in solving linear equations and balance problems.
Calana-Kalanabhyam	Differences and Similarities	Offers additional methods for solving ratio and proportion problems.
Gunakasamuccayah	The product of the sum	Useful for solving problems involving the product of two sums.
Gunita Samuccayah	The product of the sum is the sum of products	Aids in simplifying algebraic expressions.
Yavadunam Tavatirekena Varga Yojayet	By one less than the one so much is the square	Provides an alternative approach for finding squares.
Antyayordasake’pi	The last digit is as it is	Useful for quick calculations involving the last digit of numbers
Antyayorekadhikaduhitayor	On the last two digits	Enables efficient calculations when focusing on the last two digits.
Ardhasamuccayah Samuccayoh	The sum of the half-sums is the sum	A technique for adding fractions with common denominators
Ekanyunena Sesena	One less than the one followed by the last	Facilitates quick division.
Sesanyankena Caramena	The last by the last, and the ultimate by one less than the last	A technique for division, especially when dealing with recurring decimals.