Urdhva-Tiryagbyham

(thing) by LudditeAndroid (2.8 y) (print) ? (I like it!) Wed Dec 29 2004 at 21:09:29

Urdhva-Tiryagbyham: Vertically and crosswise

Urdhva-Tiryagbyham is the third sutra of Vedic mathematics. Its corollary is Adyamadyenantyamantyena.

What follows is a brief and incomplete summary of the math shortcuts this sutra contains:

Multiplying two numbers that are both two digits long
Example: multiply 12 by 34
The answer will consist of three digits: xyz
To find x, multiply the first digit in each number: 1 x 3 = 3. So the answer is three-hundred and something. This works great if you just need a quick estimation, like figuring out if you can buy a dozen items that cost 34 cents each for less than $5.
To find y, cross multiply. Meaning you multiply the first digit of the first number by the second digit of the second number (1 x 4), and add this product (1 x 4 = 46). 4 + 6 = 10. This means that y = 0 and you have to add the 1 to x.
To find z, multiply the second digit of each number. 2 x 4 = 8
Thus, 12 x 34 = 408

Bonus shortcut: Multiplying any two-digit number by 11 in an instant.
This sutra can be used to quickly multiply, "vertically and crosswise", any two digit number by 11. Here are two examples:
36 x 11. Place a space between the two digits of the number being multiplied by eleven: 3_6. Now add the two digits: 3 + 6 = 9. Place the 9 in the space and you have the answer. 36 x 11 = 396
69 x 11. Again, place the space: 6_9. Now add the two digits: 6 + 9 = 15. The number in the center space will be 5, and you must add the 1 to the preceeding digit. Thus, 69 x 11 = 759

Multiplying two numbers that are both three digits long
This is worked in the opposite order as the two-digit method above, and may take longer than multiplying by hand.
Example: 123 x 456
Multiply the last digit of both numbers: 3 x 6 = 18. The last digit of the answer will be 8. We will carry the 1 in the next step.
Multiply crosswise the last two digits of both numbers and add the 1 carried from the previous step: (6 x 2) + (3 x 5) + 1. So 12 + 15 + 1 = 28. The second to last digit will be 8 and we will carry the 2.
Multiply the middle digit in both numbers: 2 x 5 = 10. Multiply cross wise the first and last digits: (1 x 6 = 6) and (3 x 4 = 12). Add these three products: 10 + 6 + 12 = 28. Add the 2 carried from the previous step. This yields 30. The third to the last digit will be 0 and we will carry the 3.
Multiply crosswise the first two digits of both numbers: (1 x 5) + (2 x 4) = 13. Carry the 3: 13 + 3 = 16. The fourth to the last digit will be 6 and we will carry the 1.
Last step: Multiply the first digit of both numbers: 1 x 4 = 4. Add the carried 1, making the first digit in the answer 5
Thus, 123 x 456 = 56088

Urdhva-Tiryagbyham in its converse can be used to simplify division problems involving algebraic functions. If you want to learn this method, check out the resources listed below:

RESOURCES:
Vedic Mathematics by Sri Bharati Krisna Tirthaji
http://www.vedamu.org/Mathematics/course.asp
http://www.sanalnair.org/articles/vedmath/intro.htm
http://www.vedicganita.org/ganitsutras.htm
http://hinduism.about.com/library/weekly/aa062901a.htm
http://www.vedicmaths.org/
http://www.hinduism.co.za/vedic.htm
Mathemagics by Arthur Benjamin and Michael B. Shermer
http://en.wikipedia.org/wiki/Vedic_math
http://www.tifr.res.in/~vahia/dani-vmsm.pdf
http://www.sacw.net/DC/CommunalismCollection/ArticlesArchive/NoVedic.html

printable version
chaos

Vedic mathematics	Adyamadyenantyamantyena	Converse	Trachtenberg system
The darkest day in Oklahoma Highway Patrol History	algebraic function	Product	Sutra
Welcome to the Monkey House

Y'know, if you log in, you can write something here, or contact authors directly on the site. Create a New User if you don't already have an account.

Login
Password

remember me
password reminder
register

Everything2 Help

What you are reading:
Tijuana Bible
Ender's Game
The Imperial Roman Army
Binomial Theorem
Willie Nelson
Jazz Pianists
Vietnam War
Agrippa
Jeff "Skunk" Baxter
how to breathe
How to give a hug
Big O
Old English

Augustine
Vanya on 42nd Street	(review)
tentative
Chances Not Taken	(idea)
Heitah
Why I love Everything2	(person)
trixingee
Dungeon Mastering for the first time	(idea)
Netrat0
It's Called Subtext, Honey	(person)
eyeofthebeholder
The Dragon	(idea)
Heitah
consist, comprise, constitute, or compose	(idea)
Meezzio
Gotlandssnus	(thing)
argv
Astral Plane	(idea)
Madara
One Winged Angel	(fiction)
Tom Rook
Talk is cheap	(poetry)
shaogo
Adelle Davis	(person)
Aerobe
race car g sfjsgsd	(poetry)
Binah
Dream Log: July 5, 2008	(dream)
StrawberryFrog
Forgotten things in space	(idea)

This page courtesy of The Everything Development Company