Mathematical sutras

SanskAI · Dec 19, 2020

Number	Name	Meaning	Application
Sutra 1	Ekadhikena Purnvena	By one more than the previous one.	Squaring numbers ending in 5 Calculating the value of vulgar fractions whose denominators end in 9
Sutra 2	Nikhilam Navatashcaramam Dashatah	All from 9 and the last from 10	Multiplication of numbers close to 10, 100, 1000...etc. Division by 9
Sutra 3	Urdhva Tiryagbyham	Vertically and Crosswise	Multiplication and division of large numbers
Sutra 4	Paraavartya Yojayet	Transpose and Apply	Division of numbers when divisors is slightly greater than 10, 100, 1000... etc.
Sutra 5	Sunyam Saamya Samuccaye	Equated to Zero	Used in several different places where some of the identities are equated to 0
Sutra 6	Anurupye - Sunyamanyat	If one is in ratio, the other one is zero.	Solving simultaneous linear equations Finding out the product of two numbers when both close to the same base
Sutra 7	Sankalana - Vyavakalanabhyam	By addition and by subtraction.	Solving simultaneous equations where x and y coefficients are interchanged.
Sutra 8	Puranapuranabhyam	By completion or by non-completion.	Finding the roots of quadratic equations.
Sutra 9	Chalana - Kalanabhyam	Sequential motion.	Factorising 3rd, 4th and 5th-degree expressions.
Sutra 10	Ekanyunena Purvena	One less than the previous one.	Multiplications of numbers such as 9/ 99/ 999... etc.
Sutra 11	Yavadunam	The deficiency.	These all Sutras have various applications in different contexts and are often also applied along with the above-mentioned Sutras.
Sutra 12	Vyastisamashtih	Whole as one and one as whole.
Sutra 13	Sesanyan Kena Caramena	Remainder by the last digit.
Sutra 14	Sopantyadvayamantyam	Ultimate and twice the penultimate.
Sutra 15	Gunitasamuccayah	The whole product is the same.
Sutra 16	Gunaka Samuccayah	Collectivity of multipliers.

No.	Name	Parent Sutra	Meaning	Application
Sub-Sutra 1	Anurupyena	Ekadhikina Purvena	Proportionality	Finding the product of two numbers that are close to powers of 10 (10 / 100/ 1000..etc.)
Sub-Sutra 2	Adyamadyenantya-Mantyena	Urdhva-Tiryagbyham	The first by the first and the last by the last.	Factorization of quadratic equations Multiplying terms containing two different units (eg. ft. and in)
Sub-Sutra 3	Yavadunam Tavadunikrtya Varganca Yojayet	Sankalana-Vyavakalanabhyam	Whatever the deficiency, subtract that deficit from the number and write alongside the square of that deficit	Finding squares/cubes of numbers close to 10, 100, 1000...etc.
Sub-Sutra 4	Antyayor Dasakepi	Puranapuranabyham	Sum of last digits is 10.	Multiplication of numbers whose last digits add up to 10, 100. 1000... etc. if the remaining digits are the same. (eg. 64x66, 783x717 etc.)
Sub-Sutra 5	Antyayoreva	Chalana - Kalanabhyam	Only the last terms.	Solving special types of algebraic equations.
Sub-Sutra 6	Lopana Sthapanabhyam	Vyashtisamanstih	By alternate elimination and retention.	Solving 2nd-degree homogenous equations with 3 variables. Finding HCF of algebraic equations.
Sub-Sutra 7	Vilokanam	Sesanyan Kena Caramena	Observation.	Solving problems by making simple observations. Can be applied in: Partial Fractions Simultaneous Linear Equations Simultaneous Quadratic Equations
Sub-Sutra 8	Gunita Samuccayah-Samuccaya Gunitah	Sopantyadvayamantyam	The product of the sum of coefficients is equal to the sum of coefficients in the product.	Factorization and solving of algebraic equations.
Sub-Sutra 9	Sisyate Sesasamjnah	Nikhilam Navatashcaramam Dashatah	All from 9 and last from 10.	A corollary of Nikhilam Navatashcaramam Dashatah.
Sub-Sutra 10	Kevalaih Saptakam Gunyat	Paraavartya Yojayet	In case of 7 multiplicands should be 143.	Division based on 1/7 = 0.142857 (approx. 0.143)
Sub-Sutra 11	Vestanam	Sunyam Saamya Samuccaye	By osculation.	Perform divisibility checks for numbers.
Sub-Sutra 12	Yavadunam Tavadunam	Anurupye - Sunyamanyat	Lessen by the deficiency.	Finding the cube of a number that is close to the powers of 10 such as 10, 100, 1000...etc.
Sub-Sutra 13	Samuccayagunitah	Yavadunam	By the deficiency.	Used in special cases.