Glossary

A Sanskrit word meaning 'thread' or 'formula'. In Vedic Mathematics, each sutra is a one-line aphorism encoding a mathematical principle.

Example: Ekadhikena Purvena — 'By one more than the previous one'

Corollary sutras that extend or specialize the 16 main sutras. There are 13 sub-sutras (also called upasutra).

A reference power of 10 (10, 100, 1000, etc.) used in Nikhilam and Yaavadunam methods. Numbers near a base are easier to compute with.

Example: 94 and 97 are near base 100. Their deficiencies from 100 are 6 and 3.

How much a number falls short of the nearest base. If the base is 100 and the number is 94, the deficiency is 6.

Example: 94: deficiency = 100 − 94 = 6

How much a number exceeds the nearest base. If the base is 100 and the number is 103, the surplus is 3.

Example: 103: surplus = 103 − 100 = 3

The single digit left after repeatedly summing a number's digits. Also called 'digital root' or 'casting out nines'. Used to verify calculations.

Example: Digit root of 456 = 4+5+6 = 15 → 1+5 = 6

The sum of all digits of a number. When reduced to a single digit, it gives the digit root.

Example: Digit sum of 1234 = 1+2+3+4 = 10 → digit root = 1+0 = 1

A representation where digits greater than 5 are replaced by their complement from 10, written with a bar above. Reduces carry complexity in computation.

Example: 698 in vinculum = 7̄02 (read as 700 − 2). The bar indicates a negative digit.

For a digit d, its 10s complement is 10−d. For a number n with k digits, its complement from 10^k is 10^k − n.

Example: Complement of 3 = 7. Complement of 423 from 1000 = 577.

In Paraavartya division, the sub-digit(s) of the divisor that are transposed (sign-reversed) and applied at each division step.

Example: Divisor 12: flag = −2 (the '2' in 12, negated). Applied at each step during division.

A system of mental mathematics reconstructed by Sri Bharati Krishna Tirthaji (1884–1960) from the Vedas and presented in his book 'Vedic Mathematics' (1965). Organized around 16 sutras and 13 sub-sutras.

In Urdhva-Tiryakbyham, the diagonal products between corresponding digit positions. The 'tiryak' (crosswise) component of the method.

Example: For 23 × 14: crosswise = 2×4 + 3×1 = 11

A decimal fraction whose digits repeat in a cycle forever, like 1/7 = 0.142857142857... The Ekadhikena Purvena method generates these cycles directly.

Example: 1/19 = 0.052631578947368421 (18-digit repeating cycle)

All digits of a number that come before the last digit. Used in Ekadhikena Purvena for squaring numbers ending in 5.

Example: For 85, the prefix is 8. For 125, the prefix is 12.