writer — P R Guruprasad
Ancient Indians possessed great knowledge and applied them for the benefit of community in all areas of human development. In fact several inventions and discoveries believed to have originated from the Western world have been studied centuries earlier by our ancestors. For instance, it is widely believed that Christopher Columbus was the first person to discover that the Earth was round, during his voyages, somewhere around 1500 A.D. In 499 A.D. D., famous Indian Astronomer Aryabhatta defined the shape of the Earth in his work `Aryabhateeyam’ [Chapter 4-6], as follows:
Mrujjalashikhivaayumayo Bhoogola: sarvatho vruttha:[Meaning: Earth which is made of soil, water, fire and air is circular when viewed from all sides. i.e., The Earth is spherical].
Thousands of years before Columbus, our scriptures such as the Vedas, Puranas and Ithihaasaas used the term `Bhoogola’ for the Earth. `Bhoo’ means Earth and `Gola’ means `sphere’. Our ancestors wrote elaborate treatises on Astronomy, Warfare, Geometry, Medicine, etc. Many of the mathematical and scientific explanations given by our ancestors can be proved using current methods. Following is one such.
During Aryabhatta’s time [around 500AD], our ancestors evinced keen interest in motion of bodies [Sir Isaac Newton gained fame since his discovery of the principle of gravity, but Bhaskaracharya II talked about gravity much before Newton]. Aryabhatta’s treatise, Aryabhateeyam [2-31] contains many theorems of motion one of which goes thus:
Bhakthe vilomavivare gathiyogenaanulomavivare dvow
If two objects are traveling in opposite directions, the time
required for them to meet is equal to the distance between them divided
by the sum of their speeds. If they travel in the same direction the
time that has elapsed equals the distance between them divided by the
difference in their speeds.
Gathyantharena labdow dviyogakaalaavatheethaishyow
We can see the proof by taking the following problem example:
Let two trucks A and B move in opposite directions with velocities V’ and V” as illustrated in the fig. At one instant the distance between them is x. How much time needs to go by before the two trucks go past each other?
The distance between A and B = x.
Let the distance covered by A in this time t = x’.
We know that distance traveled /time taken = speed.
i.e. s/t = v
Applying this equation to truck A,
V’ = x’/t
i.e. x’ = v’t -------------- Equation 1
For truck B,
v” = (x – x’)/t
i.e. x – x’ = v”t ---------- Equation 2
From eqns. 1 and 2,
x – v’t = v”t
x = v’t + v”t = (v’+v”)t
??t = x/(v’+v”)
We can prove the second part of Aryabhatta’s theorem also on similar lines.
The point is that Aryabhatta developed these equations centuries before Newton did. Hail ancient Indian scientists, the pioneers of physics and mathematics.
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—About our writer:P R Guruprasad is a K-12 school Principal in Chennai, India.