Bhaskar mathematician biography videos
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When there is a diminution of fruit, if there be increase of requisition, and increase of fruit if there be diminution of requisition, then the inverse rule of three is employed. As well as the rule of three, Bhaskaracharya discusses examples to illustrate rules of compound proportions, such as the rule of five (Pancarasika), the rule of seven (Saptarasika), the rule of nine (Navarasika), etc.
His approach to teaching through engaging problems has had a lasting impact on how mathematics is taught and appreciated, transcending time and culture.
Bhaskara
Outstanding mathematicians such as Varahamihira and Brahmagupta had worked there and built up a strong school of mathematical astronomy. He bridged gaps in Brahmagupta's work, notably offering a general solution to the Pell equation and presenting various specific solutions.
Equations leading to more than one solution are given by Bhaskaracharya:-
Example: Inside a forest, a number of apes equal to the square of one-eighth of the total apes in the pack are playing noisy games.This is a charming story but it is hard to see that there is any evidence for it being true. He finds one solution, which is the minimum, namely horses 85, camels 76, mules 31 and oxen 4.First it is worth repeating the story told by Fyzi who translated this work into Persian in 1587.
243 243 243 3 2 5 ------------------- 1015 20 ------------------- 1215 Work out the middle sum as the right-hand one, again avoiding the "carry", and add them writing the answer below the 1215 but displaced one place to the left.Bhaskaracharya believed that the way to console his dejected daughter, who now would never get married, was to write her a manual of mathematics!
His father, Mahesvara, was a noted astrologer and mathematician, providing Bhaskaracharya with an early environment steeped in scholarly pursuits. It is the first three of these works which are the most interesting, certainly from the point of view of mathematics, and we will concentrate on the contents of these.
In the final chapter on combinations Bhaskaracharya considers the following problem. He also gave the formula
a±b=2a+a2−b±2a−a2−b
Bhaskaracharya studied Pell's equation px2+1=y2 for p = 8, 11, 32, 61 and 67. He gave four such methods of squaring in Lilavati. What is the total number of apes in the pack? The problem leads to a quadratic equation and Bhaskaracharya says that the two solutions, namely 16 and 48, are equally admissible.Let an n-digit number be represented in the usual decimal form as
d1d2...dn(*)
where each digit satisfies 1≤dj≤9,j=1,2,...,n.The kuttaka method to solve indeterminate equations is applied to equations with three unknowns.
Example: Subtracting two from three, affirmative from affirmative, and negative from negative, or the contrary, tell me quickly the result ... In Bijaganita Bhaskaracharya attempted to improve on Brahmagupta's attempt to divide by zero (and his own description in Lilavati) when he wrote:-
A quantity divided by zero becomes a fraction the denominator of which is zero.His career took a significant turn with the composition of Lilavati, around 1150 CE, which would become one of his most famous works.
The Legend of Lilavati
The writing of Lilavati is surrounded by a charming and poignant legend:
- Bhaskaracharya's Daughter: Bhaskaracharya had a daughter named Lilavati.
Else the inverse. His life and works highlight how personal motivations can drive scientific innovation, leaving a legacy that continues to educate and inspire.
There are interesting results on trigonometry in this work.