Nick Moon March 23, 2005
A brief overview of Brahmagupta’s life Brahmagupta’s multiplication algorithm Other Areas of Study Conclusion
Brahmagupta was born in 598 A.D. in northwest India He likely lived most of his life in Bhillamala (this is most likely modern Bhinmal ) He belonged to the Ujjain school
Brahmagupta wrote his most famous work Brahma Sphuta Siddhanta at ≈ age 30 This is translated “The Opening of the Universe” ~disputed translation Brahmagupta wrote another work, Khand Khadyak in ≈ 665 He is said to have died at age 70 ≈ 668
This is called gomutrika This is translated as “ like the trajectory of a cow's urine ” Let’s take 123*223 = 27429 This is how the setup looks 1 223 2 223 3 223 ----------
1 223 2 223 3 223 ---------- Now multiply the 223 of the top row by the 1 in the left column. Start the process by 1*2=2, now put the 2 below the two of the last line. If there were something to carry, this would be done in the usual way.
1 223 2 223 3 223 ---------- 223 Now multiply the 223 of the second row by the 2 in the left column writing the number in the line below the 223 but moved one place to the right.
1 223 2 223 3 223 ---------- 223 446 Now multiply the 223 of the third row by the 3 in the left column writing the number in the line below the 446 but moved one place to the right
1 223 2 223 3 223 ---------- 223 446 669 Now add the three numbers below the line
1 223 2 223 3 223 ---------- 223 446 669 ---------- 27429 This is the exact number that we wanted to calculate.
He developed the algorithm we have seen in class to solve x 2 - Dy 2 = ±1 It is believed that he did work with continued fractions to solve ax – by = c He also did a lot of work with astronomy
He developed many rules for cyclic quadrilaterals. His most famous being where 2s = a+b+c+d
Brahmagupta’s strategies for solving equations were astounding Brahmagupta greatly influenced the world of Indian Mathematics Bhaskara II was greatly influenced by Brahmagupta's work and gave Brahmagupta the title Ganaka Chakra Chudamani, the gem of the circle of mathematicians.
