Indian is the birthplace of geometry also. Since antiquity, altars and platforms were made for religious ceremonies. Their basis was geometry. In 800 BC, Bodhayan and Aapastamb gave the necessary architectural specifications for the construction of these altars and platforms.
Drawing a square equal to a triangle, a square which is double, triple or one-third a square. Making a circle equal in area to the square present. These methods have been explained in the Shulbhasootra.
The method of how to find the area of a triangle from its sides, has been explained in the 4th century book Soorya Siddhanta. Europe got this knowledge from Clobius in the 16th century.
Voyage of a word
In our country, the bow is called jya. We used this word in geometry. When it reached Arabia, it became ?j? and ?b?, since they don'thave vowels like ?e? and ?u?. When it reached Europe, it began to be called ?jeb?, which means ?chest?. The word for chest in Latin is ?sinus?. So, in short, it started being called ?sine?. Many such words have travelled from India to Europe via Arabia.
Pythagoras? Theorem or Bodhayan Theorem
In many chapters of the Kalpasootra scriptures there is a chapter on shulbasootra. The rope used to measure the platform is called rajjoo or shulbha. Hence, geometry is also called shulba and the subject of geometry came under shulbasootra. The Bodhayan Theorem is as under:
Deerghachaturas Syaakshanaya
Rajjooha Pashrvamaani Tiryakmaani
Yatprithagbhoote Kurutasta Dubhayam
Karoti
?(Bodhayan Shulbhasootra 1-12)
This means that the area of hypotenuse in a triangle is equal to the area of its length and breadth. Bodhayan has given this principle in the Shulbasootra. When we read this, we understand that if the hypotenuse of a triangle is BC, length is AB and breadth is AC, then the Bodhayan theorem says, BC2=AB2+AC2.
This is taught to the students today as Pythagoras? Theorem, whereas it had been described by Bodhayan at least 1000 years before the Greek mathematician Pythagoras. It is also possible that Pythagoras worked out this theorem after reading about it in the Shulbasootra. Whatever it is, there is no argument about the fact that the Indian mathematicians were far ahead of the modern mathematicians in the field of geometry. Besides the above mentioned theorem, Bodhayan has given other theorems too. The diagonal of a rectangle, divides it into two equal parts and two diagonals of a rectangle divide each other equally. The diagonals of a square cross each other at right angles, etc. Bodhayan and Apastamba both have given the ratio of the arm and the diagonal of a rectangle which is exactly correct.
Shulbasootra tells one how to make a square of the same area as that of a triangle, a circle of the same area as that of a square, and make a circle double, triple or one third of the area of a square. Bhaskaracharya'sLeelavati tells us that an arm of an equal tetragon, pentagon, hexagon, octagon in a circle, is in definite proportions to the diameter of the circle.
Aryabhatt has also given a formula for calculating the area of a triangle. It is as follows:
Tribhajasya phalashareeram samadal
koti bhajardhasamvargaha
The area of a triangle is equal to the product of the length and half of the base of the triangle. As per the diagram given here, the area of the triangle ABC= ? AB x CP.
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