Vedic Mathematics

Kate Pulford

Aryabhata (born 476 AD)Wrote Aaryabhatiiya - astronomy & mathematical text.Earth rotates both diurnally & around the sunCreated first recorded sine tablesCalculated π to 3.1416

"Add four to 100, multiply by eight and then add 62,000.

By this rule the circumference of a circle of diameter 20,000

can be approached”

Mahavira (9th century)Squares, cubics, square and cubic roots, plane geometry, shadows.Solved higher order equations of n degree of the forms:

axn = q and

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Brahmagupta (born 598 AD)

Wrote Brahmasphuta Siddhanta:– Zero

0 0 = 0 ?

A 0 = 0 ?

– Pythagorean triples:

“The height of a mountain multiplied by a given multiplier is the distance to a city; it is not erased. When it is divided by the multiplier increased by two it is the leap of one of the two who make the same journey”

Chapter 12, verse 39

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First known solution of quadratic equations:

“Diminish by the middle [number] the square-root of the rupas multiplied by four times the square and increased by the square of the middle [number]; divide the remainder by twice the square. [The result is] the middle [number].

Whatever is the square-root of the rupas multiplied by the square [and] increased by the square of half the unknown, diminish that by half the unknown [and] divide [the remainder] by its square. [The result is] the unknown.”

From Chapter 18, Brahmasphuta Siddhanta

The Vedic Period

2000 BC - 500 BC.

North-western India

Four written Vedas

“…not of human origin”

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Modern Vedic Mathematics

• Sri Bharati Krsna Tirthaji (1884-1960)

• “The Sutras apply to and cover each and every part of each and every chapter of…mathematics…”

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SUTRA TRANSLATION

1 Ekadhikina Purvena By one more than the one before

2 Nikhilam Navatashcaramam Dashatah All from 9 and the last from 10

3 Urdhva Tiryagbyham Vertically and crosswise

4 Paraavartya Yojayet Transpose and adjust

5 Shunyam Saamyasamuccaye When the sum is the same that sum is zero

6 Anurupye Shunyamanyat If one is in ratio, the other is zero

7 Sankalana Vyavakalanabhyam By addition and subtraction

8 Puranapuranabyham By the completion or non-completion

9 Chalana Kalanabyham Differences and similarities

10 Yaavadunam Whatever the extent of its deficiency

11 Vyashtisamanstih Part and whole

12 Shesanyankena Charamena The remainders by the last digit

13 Sopaantyadvayamantyam The ultimate and twice the penultimate

14 Ekanyunena Purvena By one less than the previous one

15 Gunitasamuchyah The product of the sum is equal to the sum of the product

16 Gunakasamuchyah The factors of the sum is equal to the sum of the factors

Ekadhikina Purvena:one more than the one before

example: calculating 1/191 (one more than the one before: 2)21421842168421 (carry 1)368421 (carry 1)7368421 47368421 947368421… 052631578947368421Eighteen digits (denominator - numerator) so STOP

Hence 1/19 = 0.052631578947368421 recurring

Nikhilam Navatashcaramam Dashatah: All from 9 and the last from 10

• Used for long calculations quickly:

Example: 10000 - 4679

9 - 4 = 5

9 - 6 = 3

9 - 7 = 2

10 - 9= 1

So 10000 - 4679 = 5321

Applications of Vedic Maths: EDUCATION

easier than conventional arithmetic?

Maharashi School, Lancashire:“livelier classes, greater student enjoyment and

understanding, and increased academic performance”

(Mark Gaskell, 2000)

Average GCSE maths scores of over 80% all taken a year early.

Enthusiasm and interest!