Indian Mathematicians in Geometry

Brahmagupta, an Indian mathematician and astronomer, is credited with developing the concept of the cyclic quadrilateral, which is a quadrilateral whose vertices lie on a circle.

Brahmagupta's Theorem states that the sum of the angles in a triangle is 180 degrees. This theorem is considered to be one of the most fundamental theorems in geometry.

Brahmagupta was the first Indian mathematician to use the concept of negative numbers. He used negative numbers to represent debts in his mathematical calculations.

Brahmagupta's Formula gives the area of a triangle as the square root of the product of the semi-perimeter and the differences between the semi-perimeter and each of the three sides of the triangle.

Aryabhata, an Indian mathematician and astronomer, is credited with developing the concept of the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Brahmagupta's Theorem states that the sum of the interior angles of a polygon with n sides is (n-2) * 180 degrees. This theorem is also known as the polygon angle sum formula.

Aryabhata was the first Indian mathematician to develop the concept of the sine function. He used the sine function to calculate the lengths of chords in a circle.

Aryabhata's Formula gives the volume of a sphere as the cube of the radius multiplied by 4/3 * pi.

Bhaskara II was the first Indian mathematician to develop the concept of the cosine function. He used the cosine function to calculate the lengths of chords in a circle.

Aryabhata's Formula gives the area of a circle as pi multiplied by the square of the radius.

Bhaskara II was the first Indian mathematician to develop the concept of the tangent function. He used the tangent function to calculate the lengths of chords in a circle.

Aryabhata's Formula gives the circumference of a circle as pi multiplied by the diameter.

Bhaskara II was the first Indian mathematician to develop the concept of the secant function. He used the secant function to calculate the lengths of chords in a circle.

Aryabhata's Formula gives the area of a sector of a circle as the product of the radius and the arc length of the sector.