pointed out that quadratic equations (Extremely complicated!) could in theory have two possible solutions, one of which could be negative. He even attempted to write down these concepts, using the initials of the
names of colours to represent unknown numbers in his equations. That is what we now call algebra. Indian mathematicians made advances in the theory of trigonometry, a method of linking geometry and numbers first developed by the Greeks. They used it to survey the land around them and navigate the seas. For instance, Indian astronomers used trigonometry to calculate the relative distances between the Earth and the Moon and the Earth and the Sun. They realized that, when the Moon is half full and directly
Indian astronomers used trigonometry tables to estimate the relative distance of the Earth to the Sun and Moon. opposite the Sun, then the Sun, Moon and Earth form a right angled triangle, and were able to accurately measure the angle as 1 7 °. Their sine tables (complex!) gave a ratio for the sides of such a triangle as 400:1, indicating that the Sun is 400 times further away from the Earth than the Moon. Next the Indian astronomers wanted to be able to calculate the sine function of any given angle. A text called the “Surya Siddhanta”, dating from around 400 AD, contains the start of modern trigonometry, including the first real use of sines, cosines, inverse sines, tangents and secants (Also difficult!) As early as the 6th Century AD, the great Indian mathematician and astronomer Aryabhata produced definitions of sine, cosine, versine and inverse sine, and specified complete sine and versine table, to an accuracy of 4 decimal places. Aryabhata also demonstrated solutions to simultaneous quadratic equations, and produced an approximation for the value of π equivalent to 3.1416, correct to four decimal places. He then used this to estimate the circumference of the Earth turning out as 24,835 miles, only 70 miles off its real value. But, perhaps even more surprising, he seems to have been aware that π is an irrational number, and that any calculation can only ever be an approximation.
Bhaskara II (who lived in the 12th Century) explained the operation of division by zero. He noticed that dividing one into two pieces makes a half, so 1 ÷ 1 2 = 2. So, 1 ÷ 1 3 = 3. Therefore, dividing 1 by smaller and smaller factions makes a larger and larger number of pieces. Hence, dividing one into zero pieces would make infinity so 1 ÷ 0 = ∞. Bhaskara II also made important contributions to many different areas of mathematics from solutions of quadratic, cubic and quartic equations (including negative and irrational
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