• kewal sethi

ancient indian mathematicians

ever wondered which level of mathematics our forefathers achieved. here are five examples from three different mathematicians.

judge for your self

Examples of Mathematical problems

Mahaviracharya

1.One fourth of a herd of camels was seen in the forest; twice the square root of the herd had gone on to mountain slopes; and three times five were, however, found  to remain on the bank of a river. What is the numerical measure of that herd of camels.

            ( it works out to the equation ¼ x + 2√x + 15 = x)

2. Into the bright and refreshing outskirts of a forest, which were full of numerous trees with their branches bent down woith the weight of flowers and fruits, trees such as jambu trees, lime trees, plantains, areca palms, jack trees, date palms, hintala trees, palmyras, punnaga trees and mango trees _ into the outskirts, the various quarters whereof wee filled with many sounds of crowds of parrots and cuckoos found near springscontaining lotuses with bees roaming about them - into such forest outskirts, a number of weary travellers entered with joy. There were sixty three (numerically equal) heaps of plantain fruits put together and combined with seven more of the same fruits, and they were equally divided amongst twenty three travellers so as to have no remainder. You tell me the numerical measure of a heap of plantains.

Brhamagupta

3. On the top of a certain hill live two ascetics. One of them, being a wizard, travels thorugh the air. Springing from the summit of the mountain, he ascends to certain elevation and proceeds by an oblique descent diagnally to a neighbouring town. the other, walking down the hill, goes by land to the same town. Their journeys are equal. I desire to know the distance of the town from the hill, and how high the wizard rose.

4. A bamboo 18 cubits high was broken by the wind. Its tip touched the ground six cubits from the root. Tell the length of the segments of the bamboo.

Bhaskara

5. The son of Pritha, exasperated in combat, shot a quiver of arrows to slay Charna. with half the arrows, he parried those of his antogonist; with four times the squareroot of the quiverful, he killed his horse; with six arrows, he slew Shalya; with three he demolished the umbrella, standard and bow; and with one he cut off the head of his foe. How many were the arrows which Arjuna let fly.

(From History of Mathematics Vol I David Eugene Smith (Dover Publications New York - 1958)

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