Vedic Mathematics and History
Vedic Mathematics is a system of mathematics that originated in ancient India and is based on the Vedas, which are ancient Hindu scriptures. The term “Vedic Mathematics” was coined by the Indian mathematician Bharati Krishna Tirthaji in the early 20th century.
The mathematical concepts in the Vedas were further developed by Indian mathematicians over the centuries. Some of the notable mathematicians in the history of Vedic Mathematics include Aryabhata, Brahmagupta, and Bhaskara II.
Vedic Mathematics was largely forgotten in India until the 20th century, when Bharati Krishna Tirthaji rediscovered the system and published a book called “Vedic Mathematics” in 1965. Since then, Vedic Mathematics has gained popularity in India and around the world as a system of mental calculation that can help people solve mathematical problems quickly and easily.
Overall, Vedic Mathematics remains an important part of the history of mathematics in India and a unique contribution to the world of mathematics.
Special Multiplication Methods in Vedic Mathematics
There are many Vedic Mathematics techniques for multiplication, but here are some of the most commonly used ones:
- Nikhilam Multiplication: This technique is based on the concept of complements. It involves finding the complements of the two numbers being multiplied and then subtracting them from the base number to get the final product.
- Urdhva-Tiryagbhyam (Vertical and Crosswise) Multiplication: This technique involves cross-multiplying the digits of the two numbers and adding the resulting products together.
- Paravartya Yojayet (Transpose and Apply) Multiplication: This technique involves transposing one of the two numbers being multiplied and then applying a simple addition and multiplication method.
- Ekadhikena Purvena (By One More than the Previous) Multiplication: This technique involves multiplying the first digit of the multiplier by the number itself plus one, and then using this as a base for the rest of the multiplication.
- Anurupyena (Proportionately) Multiplication: This technique involves adjusting the numbers being multiplied to make the calculation easier, such as multiplying one number by 10 and the other by a factor of 10 to make the numbers simpler.
- Vinculum Multiplication: This technique involves adding the product of the digits of the two numbers being multiplied to the original numbers, and then repeating this process until the numbers converge to the final product.
- Antyayor Dasakepi (By One More and Ten More Than the Previous) Multiplication: This technique involves multiplying the first digit of the multiplier by the number itself plus one, and then adding ten to the result to get the base for the rest of the multiplication.
Urdhva tiryagbhyam method
The Urdhva-Tiryagbhyam method is a special multiplication technique in Vedic Mathematics, which is based on the sutra “Urdhva-Tiryagbhyam” meaning “vertically and crosswise”. This method is used for multiplying two-digit, three-digit, or even larger numbers mentally, without using a calculator.
The steps to use the Urdhva-Tiryagbhyam method for multiplication are as follows:
STEP1 . Write the two numbers that need to be multiplied on top of each other, with the digits aligned.
STEP 2. Draw two diagonal lines from the right-hand side of the top digit to the left-hand side of the bottom digit, creating a V shape.
STEP 3. Multiply the digits at the top of each diagonal line, and write the product below the diagonal line.
STEP 4. Repeat the process for the remaining digits, moving from right to left.
STEP 5. Add the products obtained in step 3 and step 4 vertically to get the final answer.
EXAMPLE 1.
STEP 1. Write down the two numbers vertically
24
35
——
STEP 2. Draw two diagonal lines, one from the top right corner and the other from the top left corner
2 | 4
– + –
3 | 5
STEP 3. Multiply the digits diagonally and write the products in the spaces on either side of the diagonal lines
2 | 4
– + –
3 | 5
– + –
8 | 0
1 | 0
STEP 4. Add the products in each column
2 | 4
– + –
3 | 5
– + –
8 | 0
1 | 0
– – –
8 | 4 | 0
So, the answer is 840.
EXAMPLE 2.
STEP 1. Write down the two numbers vertically
47
63
—–
STEP 2. Draw two diagonal lines, one from the top right corner and the other from the top left corner
4 | 7
– + –
6 | 3
STEP 3. Multiply the digits diagonally and write the products in the spaces on either side of the diagonal lines
4 | 7
– + –
6 | 3
– + –
2 | 8
2 | 1
STEP 4. Add the products in each column
4 | 7
– + –
6 | 3
– + –
2 | 8
2 | 1
– – –
2 | 9 | 6 | 1
So, the answer is 2961.
EXAMPLE 3.
STEP 1. Write down the two numbers vertically
56
78
—–
STEP 2. Draw two diagonal lines, one from the top right corner and the other from the top left corner
5 | 6
—+—
7 | 8
STEP 3. Multiply the digits diagonally and write the products in the spaces on either side of the diagonal lines
5 | 6
—+—
7 | 8
———–
35 | 48
—+—
42 | 56
STEP 4. Add the products in each column
5 | 6
—+—
7 | 8
———–
35 |48
—+—
42 |56
———–
43 |68
Therefore, 56 multiplied by 78 equals 4368.
Hence we use this method. Each technique has its own advantages and can be useful in different situations depending on the numbers being multiplied.