Vedic geometry
As a result of the mathematics required for the construction of these altars, many rules and developments of geometry are found in Vedic works. These include:
- Use of geometric shapes, including triangles, rectangles, squares, trapezia and circles.
- Equivalence through numbers and area.
- Squaring the circle and visa-versa.
- Pythagorean triples discovered algebraically.
- Statements of the Pythagorean theorem and a numerical proof.
- Computations of π, with the closest being correct to 2 decimal places.
Lagadha (circa 1350- 1200) was probably the earliest known mathematician to have used geometry and trigonometry for astronomy.
Yajnavalkya ( 9th century BC) composed the Shatapatha Brahmana, which contains geometric aspects, including several computations of π, with the closest being correct to 2 decimal places (the most accurate value of π upto that time), and gives a rule implying knowledge of the Pythagorean theorem.
The Sulba Sutras ("Rule of Chords" in Vedic Sanskrit), which is another name for geometry, were composed between 800 BC and 500 BC and were appendices to the Vedas giving rules for the construction of religious altars. The Sulba Sutras contain the first use of irrational numbers, quadratic equations of the form a x2 = c and ax2 + bx = c, the use of the Pythagorean theorem and a list of Pythagorean triples discovered algebraically predating Pythagoras, geometric solutions of linear equations, and a number of geometrical proofs. These discoveries are mostly a result of altar construction, which also led to the first known calculations for the square root of 2, which were correct to a remarkable 5 decimal places.
Baudhayana (circa 800 BC) composed the Baudhayana Sulba Sutra, which contains a statement of the Pythagorean theorem, geometric solutions of a linear equation in a single unknown, several approximations of π (the closest value being 3.114), along with the first use of irrational numbers and quadratic equations of the forms ax 2 = c and ax2 + bx = c, and a computation for the square root of 2, which was correct to a remarkable five decimal places.
Manava (circa 750 BC) composed the Manava Sulba Sutra, which contains approximate constructions of circles from rectangles, and squares from circles, which give approximate values of π, with the closest value being 3.125.
Apastamba (circa 600 BC) composed the Apastamba Sulba Sutra, which contains the method of squaring the circle, considers the problem of dividing a segment into 7 equal parts, calculates the square root of 2 correct to five decimal places, solves the general linear equation, and also contains a numerical proof of the Pythagorean theorem, using an area computation. The historian Albert Burk claims this was the original proof of the theorem which Pythagoras copied on his visit to India.
