Varahamihira's triangle, also known as the Pascal's triangle, is an ancient Indian mathematical concept described by Varahamihira in his book "Vṛttajātaka" (around 550 CE). This triangle is a triangular array of numbers where each number is the sum of the two numbers directly above it.
Here's a brief overview:
1. Rows and columns: The triangle consists of rows and columns, with each row representing a power of 10 (starting from 0).
2. Number arrangement: Each number is the sum of the two numbers directly above it, starting from the apex (1).
3. Patterns and properties: The triangle exhibits various patterns, such as:
- Symmetry
- Fibonacci sequence
- Binomial coefficients
- Combinatorial identities
Varahamihira used this triangle to calculate:
1. Combinations: Numbers of combinations (nCr)
2. Permutations: Numbers of permutations (nP_r)
3. Binomial expansions: Coefficients of binomial expansions
The Pascal's triangle was later independently discovered by Blaise Pascal in the 17th century, but Varahamihira's work predates Pascal's by over 1,000 years!
Varahamihira's contributions to mathematics and astronomy are significant, and his work on the Pascal's triangle is a testament to ancient Indian mathematical ingenuity.
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Here's a brief overview:
1. Rows and columns: The triangle consists of rows and columns, with each row representing a power of 10 (starting from 0).
2. Number arrangement: Each number is the sum of the two numbers directly above it, starting from the apex (1).
3. Patterns and properties: The triangle exhibits various patterns, such as:
- Symmetry
- Fibonacci sequence
- Binomial coefficients
- Combinatorial identities
Varahamihira used this triangle to calculate:
1. Combinations: Numbers of combinations (nCr)
2. Permutations: Numbers of permutations (nP_r)
3. Binomial expansions: Coefficients of binomial expansions
The Pascal's triangle was later independently discovered by Blaise Pascal in the 17th century, but Varahamihira's work predates Pascal's by over 1,000 years!
Varahamihira's contributions to mathematics and astronomy are significant, and his work on the Pascal's triangle is a testament to ancient Indian mathematical ingenuity.
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references :
1. Varahamihira's triangle (Pascal's triangle):
- "Vṛttajātaka" by Varahamihira (around 550 CE)
- "The Bakhshali Manuscript" (around 200-300 CE) - an ancient Indian mathematical manuscript that also describes the triangle
1. Varahamihira's work predating Pascal's:
- "A History of Mathematics" by David M. Burton (McGraw-Hill, 2010) - Page 244
- "The Oxford Handbook of the History of Mathematics" edited by Eleanor Robson and Jacqueline Stedall (Oxford University Press, 2008) - Page 430
1. Varahamihira's contributions to mathematics and astronomy:
- "Varahamihira" by Sudhakara Dvivedi (Indian Journal of History of Science, 1990)
- "Astronomy in Ancient India" by K.V. Sarma (Indian Journal of History of Science, 1997)
1. Pascal's triangle:
- "Traité du triangle arithmétique" by Blaise Pascal (1653)
- "A History of Mathematics" by Carl B. Boyer and Uta C. Merzbach (John Wiley & Sons, 2010) - Page 385
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1. Varahamihira's triangle (Pascal's triangle):
- "Vṛttajātaka" by Varahamihira (around 550 CE)
- "The Bakhshali Manuscript" (around 200-300 CE) - an ancient Indian mathematical manuscript that also describes the triangle
1. Varahamihira's work predating Pascal's:
- "A History of Mathematics" by David M. Burton (McGraw-Hill, 2010) - Page 244
- "The Oxford Handbook of the History of Mathematics" edited by Eleanor Robson and Jacqueline Stedall (Oxford University Press, 2008) - Page 430
1. Varahamihira's contributions to mathematics and astronomy:
- "Varahamihira" by Sudhakara Dvivedi (Indian Journal of History of Science, 1990)
- "Astronomy in Ancient India" by K.V. Sarma (Indian Journal of History of Science, 1997)
1. Pascal's triangle:
- "Traité du triangle arithmétique" by Blaise Pascal (1653)
- "A History of Mathematics" by Carl B. Boyer and Uta C. Merzbach (John Wiley & Sons, 2010) - Page 385
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