Vedic Mathematics

History of Vedic mathematical representation
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History of Vedic Mathematics

The “Vedic Mathematics” is called so because of its origin from Vedas. To be more specific, it has originated from “Atharva Vedas” the fourth Veda. “Atharva Veda” deals with the branches like Engineering, Mathematics, sculpture, Medicine, and all other sciences with which we are today aware of. The Sanskrit word Veda is derived from the root Vid, meaning to know without limit. The word Veda covers all Veda-Sakhas known to humanity. The Veda is a repository of all knowledge, fathomless, ever revealing as it is delved deeper.

Vedic Mathematics forms part of Jyotish Shastra which is one of the six parts of Vedangas. The Jyotish Shastra or Astronomy is made up of three parts called Skandas. A Skanda means the big branch of a tree shooting out of the trunk. Vedic scholars did not use figures for big numbers in their numerical notation. Instead, they preferred to use the Sanskrit alphabets, with each alphabet constituting a number. Several mantras, in fact, denote numbers; that includes the famed Gayatri Mantra, which adds to 108 when decoded.

Vedic Mathematics is a system of mathematics which was discovered by Indian mathematician "Jagadguru Shri Bharathi Krishna Tirthaji" in the period between A.D. 1911 and 1918 and published his findings in a "Vedic Mathematics" Book by Tirthaji Maharaj. 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.

Shri Bharathi Krishna Tirthaji Maharaj was born in March 1884 in the Puri village of Orissa state. He was very good in subjects like mathematics, science, humanities and was excellent in Sanskrit language. His interests were also in spiritualism and mediation. In fact when he was practicing meditation in the forest near Sringeri, he rediscovered the Vedic sutras. He claims that these sutras/techniques he learnt from the Vedas especially ‘Rig-Veda’ directly or indirectly and he intuitively rediscovered them when he was practicing meditation for 8 years. Later he wrote the sutras on the manuscripts but were lost. Finally in year 1957, he wrote introductory volume of 16 sutras which is called as Vedic Mathematics and planned to write other sutras later. But soon he developed cataract in both of his eyes and passed away in year 1960.

It will be of interest to everyone but more so to younger students keen to make their mark in competitive entrance exams. India’s past could well help them make it in today’s world. It is amazing how with the help of 16 Sutras & 13 sub-sutras, the Vedic seers were able to mentally calculate complex mathematical problems.

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Basics of vedic mathematics

Vedic Mathematics, derived from ancient Indian scripture called Vedas, offers a unique and efficient approach to solving mathematical problems. Its methods are based on 16 sutras and 13 sub-sutras that simplify complex calculations, making arithmetic operations faster, easier, and more intuitive. The techniques enclose various mathematical operations such as addition, subtraction, multiplication, division, square roots, cube roots, and more. Vedic Mathematics promotes creativity, enhances problem-solving skills, and boosts confidence in tackling mathematical challenges by providing alternative, faster methods. And its adaptability to modern education makes it a valuable tool for students, teachers, and math enthusiasts alike.

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SUTRAS

Ekadhikina Purvena (By one more than the previous one):

This sutra suggests adding one more than the previous number. It is often utilized for rapid multiplication by nine. For instance, to multiply a number by nine, you add the number to itself and subtract one.

Nikhilam Navatascaramam Dasatah (All from 9 and the last from 10):

This sutra suggests adding one more than the previous number. It is often utilized for rapid multiplication by nine. For instance, to multiply a number by nine, you add the number to itself and subtract one.

Urdhva-Tiryagbyham (Vertically and Crosswise):

This sutra is used for the rapid multiplication of numbers. It involves multiplying the vertical and cross products of digits and summing them up to obtain the final result.

Paravartya Yojayet (Transpose and adjust):

This sutra focuses on division. It suggests transposing the divisor and adjusting the quotient to simplify division calculations. By using this technique, divisions involving numbers close to powers of ten become easier.

Shunyam Saamyasamuccaye (If the Samuccaya (remainder) is the same it is zero):

This sutra states that if the remainders obtained after division are the same, then the difference between the two numbers being divided is divisible by their common divisor. It helps simplify division problems by utilizing common remainders.

Sankalana-vyavakalana (Addition and subtraction):

This sutra emphasizes the use of addition and subtraction to simplify calculations. It is applied when dealing with numbers having a common component, where you can perform operations based on their relationship to each other.

Ekanyunena Purvena (By one less than the previous one):

This sutra suggests subtracting one from the previous number. It is commonly used in pattern-based calculations or when working with consecutive numbers.

Sankalana-Kalana-Vyavakalana (Addition-multiplication-subtraction):

This sutra combines addition, multiplication, and subtraction. It provides a sequence of operations to simplify complex calculations.

Gunakasamuccaya (Factors of the sum and the difference):

This sutra explores the relationship between the sum and difference of two numbers and their product. It allows for efficient calculation of the product by considering its sum and difference.

Dashasutra (The rule of ten):

This sutra focuses on multiplication and division by powers of ten. It provides techniques for easily shifting decimal places and adjusting numbers accordingly.

Dvandvamukha (The product of the sum and the difference):

This sutra states that the product of the sum and difference of two numbers is equal to the difference of their squares. It enables efficient calculation of squares by using the sum and difference of two numbers.

Kalanadhikena (By the deficiency):

This sutra suggests adding the deficiency. It is useful when dealing with numbers close to a reference or base number.

Samuccayagunitah (The sum is obtained by multiplication):

This sutra states that the sum can be obtained by multiplication. It provides a method for finding the sum of a series of numbers by multiplying the average by the count of terms.

Antyayoreapi (After the last):

This sutra suggests carrying out calculations after the last digit or term. It is used when numbers have been rounded or truncated.

Puranapuranabyham (By the completion or non-completion):

This sutra deals with fractions and provides techniques for adding or subtracting fractions by adjusting their numerators and denominators to achieve common terms.

Sopaantyadvayamantyam (The ultimate and twice the penultimate):

This sutra states that the sum of the squares of the ultimate and twice the penultimate terms is equal to the sum of squares of the given series. It facilitates quick calculation of the sum of squares of consecutive terms.

These sutras, with their unique approaches and techniques, form the basis of Vedic mathematics. They offer efficient methods for calculations, enhance mental math skills, and provide insights into mathematical relationships and patterns. By mastering these sutras, one can perform calculations with speed, accuracy, and a deeper understanding of mathematical concepts.

Benefits of vedic mathematics

The basis of Vedic maths, are the 16 sutras, which attribute a set of qualities to a number or a group of numbers. The ancient Hindu scientists (Rishis) of Bharat in 16 Sutras (Phrases) and 120 words laid down simple steps for solving all mathematical problems in easy to follow 2 or 3 steps. Vedic Mental or one or two line methods can be used effectively for solving divisions, reciprocals, factorisation, HCF, squares and square roots, cubes and cube roots, algebraic equations, multiple simultaneous equations, quadratic equations, cubic equations, biquadratic equations, higher degree equations, differential calculus, Partial fractions, Integrations, Pythagoras Theorem, Apollonius Theorem, Analytical Conics, and so on.

Accelerated Mental Calculation:

Vedic Maths techniques enable children to perform complex calculations mentally and quickly, developing their mental agility and computational skills at a young age.

Strengthened Mathematical Foundation:

Vedic Maths enhances children's understanding of basic arithmetic operations, number patterns, and relationships. This strengthens their overall mathematical foundation and comprehension of advanced mathematical concepts as they progress in their education.

Improved Problem-Solving Skills:

Vedic Maths introduces alternative approaches and strategies to problem-solving, fostering creative thinking, flexible problem-solving skills, and the ability to explore multiple solutions. Children develop a deeper understanding of mathematical concepts and gain confidence in tackling mathematical problems.

Enhanced Cognitive Skills:

Regular practice of Vedic Maths exercises stimulates brain activity, improving children's cognitive skills such as concentration, memory, logical reasoning, and analytical thinking. They learn to analyze patterns and relationships, which aids in overall cognitive development.

Increased Confidence in Mathematics:

As children master Vedic Maths techniques, their confidence in their mathematical abilities grows. They become more willing to tackle challenging problems, participate actively in class, and develop a positive attitude towards mathematics.

Competitive Exam Advantage:

Vedic Maths techniques offer an advantage in competitive exams, as they enable faster calculation speed, efficient problem-solving methods, and enhanced accuracy. Children who have mastered Vedic Maths techniques have an edge in exams that require quick calculations and logical thinking.

Engaging and Fun Learning Experience:

Vedic Maths provides an engaging and interactive learning experience for children. The use of visual aids, patterns, and alternative methods makes learning math enjoyable, promoting a positive attitude towards the subject.

Transferable Skills:

The problem-solving and critical thinking skills developed through Vedic Maths are transferable to other subjects and real-life situations. Children learn to think analytically, approach challenges with a structured mindset, and apply logical reasoning beyond the realm of mathematics.

Improved Academic Performance:

By mastering Vedic Maths techniques, children develop a solid foundation in mathematics. This can lead to improved academic performance in all math-related subjects and overall numerical literacy.

Vedic Mathematics
Calculations

Vedic Mathematics simplifies the four basic mathematical operations like addition, subtraction, multiplication and division.

This will reduce the time to solve a mathematical, problem, especially in examination halls. For example, if we have to multiply 86 and 98, the conventional method is

86
X98
...........
688
774
............
8428

But by the method of Vedic Mathematics we can do it in a simple way. The two numbers are set down (Here numbers are 86 and 98) and their difference from a suitable base are written (Here we can take the base 100) down to the right (that is 100-86 = 14 and 100-98=02).

athematics we can do it in a simple way. The two numbers are set down (Here numbers are 86 and 98) and their difference from a suitable base are written (Here we can take the base 100) down to the right (that is 100-86 = 14 and 100-98=02).

86-14
98-02
............
84/
Ans: 8428
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