# Essentials of Vedic Mathematics

Vedic Mathematics is an ancient form of Mathematics that is spreading its wings around the educational systems and the knowledge centers. The interest as well as the demand is growing due to its simplicity and effectiveness, providing a bundle of benefits.This ancient form of mathematics was born in the Vedic Age but the system as well as the significance of this form was buried deep under the centuries and ages. Later on, Sri Bharati Krsna Tirthaji studied the Vedas, a set of sacred ancient Hindu texts, from where he founded a set of sutras that he claimed allegedly encompass all mathematics. The remarkable system of calculation was then rediscovered by Tirthaji from the Vedas between 1911 and 1918.’Sutras’ is a term taken from the ancient Indian language, Sanskrit, that means ‘thread of knowledge’. As the meaning suggests, these sutras are well described as word formulae or one-line formulae that ease mathematical calculations. These formulae naturally make the mind works in direction to the appropriate method of solution. It is also known as aphorisms and covers each and every aspect of mathematics including arithmetic, algebra, geometry, calculus, and trigonometry.Vedic Maths works on the principle of 16 sutras that are easily memorized, easily understandable, enabling to solve long and tough mathematical problems quickly and effectively. The 16 sutras are:1. Ekadhikina Purvena: By one more than the previous one
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 by 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 factorsThere are numerous benefits of vedic mathematics. Some of the most significant benefits are its effectiveness and perfection in solving all sort of mathematical problems and calculations like reciprocals, squares and square roots, cubes and cube roots, multiple simultaneous equations, cubic equations, and higher degree equations. It also helps to cross check all the calculations and confirm the correctness.Apart from these, it also plays an influential role in providing a new approach to our outlook by enriching our knowledge and understanding of Mathematics.

# Mathematics, Numbers, and The Symmetry of God

The essence of mathematics is not to make simple things complicated, but to make complicated things simple. ~ S. GudderIndeed mathematics is a domain where brains get rankled and minds seem to lose their grips on reality. Yet in this seemingly mad world, simplicity metamorphoses from complexity; normality evolves from irrationality, and order blossoms from chaos. If you doubt these propositions, then observe the bizarre symmetry in the following numerical calculations, and then see whether you are still skeptical that God does in fact indwell numbers and mathematics.Observe the following symmetries and enjoy!1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 987 65
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321And now with the number 9:1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111But the number 9 has even more magic to it. To wit:9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888The number 1 is one of the five most important numbers in mathematics. Not only is 1 the multiplicative identity, the number 1 dazzles us with some amazing multiplicative properties as seen in these repunits (a repunit is a number composed of all 1’s):1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321After witnessing this array of number wizardry, it is hard to imagine that a supreme deity could not be supervising such magic. Maybe if teachers implemented a little symmetric razzmatazz like this to start a class, students might perk up and listen for a change. Then true learning would have a shot at beginning and all kinds of positive results could be achieved. After all, when God is in charge, everything else goes smoothly. Try it out and have fun.