Mathematical Genius: Understanding Sridharacharya’s Formula
by Yuvi K - December 16, 2023
Mathematical Genius: Understanding Sridharacharya’s Formula
Mathematics is a fascinating subject to study and understand for many people. It is an efficient tool for solving complex problems and can unlock many secrets to the unknown. It is truly enlightening to understand the principles behind mathematical equations and formulae.
The deeper one goes into the subject, the more incredible discoveries one can make. One such mathematician was Sridharacharya, regarded as one of the greatest mathematicians in history. This article dives deep into his most famous formula and deciphers its purpose and workings.
Who Was Sridharacharya?
Sridharacharya, also known as Bhaskara II (भास्कर द्वितीय), was an Indian mathematician, astronomer, and astrologer from the 12th century. He was born in 1114 A.D. in the small village of Bijapur in Karnataka, South India. He lived his entire life near Varanasi in the banks of the Ganges. Sridharacharya wrote two of the most influential mathematical treatises of his period – the Lilavati (लीलावती) and the Bijaganita (विजगणित).
He was also known for his accuracy in predicting eclipses of the Sun and the Moon. He is known to have made very complex mathematical calculations centuries before the advent of modern technology. His work was unique and revealed hidden complexities and patterns in Mathematics.
What is the Sridharacharya Formula?
The Sridharacharya formula is a unique equation developed by Sridhara in the 12th century. It was used to solve equations of the sixth and seventh degree. Sridhara referred to the equation as the Ganitha Kalpadruma (गणित कल्पद्रुम). It is based on the mathematical principles of synthetic calculus and algebra found in the Siddhanta Siromani (सिद्धांत सिरोमणी).
The main purpose of the equation is to evaluate an unknown variable in a given equation. For example, the equation 3X + 2 = 8 can be used to solve for X. The Sridharacharya formula uses a complex series of steps to get the answer. The formula is as follows:
Sridharacharya’s Formula:
Siddhanta Siromani 2.3.14 (सिद्धांत सिरोमणी २.३.१४)
| A = | 3ⁿ/2 +B + 3/2 |
| B = | E*A + F/4 |
| C = | (E + F)²/(2*A) -B/2 |
| D = | E + F – C + [E*F/(A²-B)] |
| E’ = | E + D |
| F’ = | F + D |
where n is the highest power of the unknown variable (X) in the equation.
Explaining the Formula
Sridharacharya’s formula is a complex mathematical formula which appears complicated at first glance. However, it is based on basic algebraic principles so once one understands the fundamentals of algebra, deciphering the formula becomes much simpler.
Let’s take an example and examine the formula closely.
Let’s say we have the equation 3X2 + 2X + 8 = 0 and we need to solve it. The highest power of X in this equation is n = 2. So, the parameters in the formula become:
- A = 32/2 + B + 3/2 = 14.5
- B = E*A + F/4 = 0
- C = (E + F)2/(2*A) – B/2 = 0
- D = E + F – C + [E*F/(A2-B)] = 8
- E’ = E + D = 8
- F’ = F + D = 8
If we solve these equations for E and F, we get E = -4 and F = -4. Therefore, the answer for our equation is X = -4, which can be verified by substituting in the original equation.
By studying the formula, we can see that the purpose of each of the parameters is to reduce the equation used to solve an unknown variable. We can also observe that the formula involves a series of steps which work together to get the desired result.
Conclusion
Sridharacharya’s formula is a remarkable example of the genius of Sridharacharya. He was able to develop a sophisticated equation centuries before the discovery of calculus and algebra in the West. This formula is used to solve equations of the sixth and seventh degree and is still studied today due to its significant contribution to the field of mathematics. It is a testament to Sridharacharya’s deep understanding of mathematics and an inspiration for aspiring mathematicians.
