Brahmagupta, an Indian mathematician and astronomer, is credited with developing the Fibonacci sequence in the 7th century.

The equation (x^2 + y^2 = z^2) is known as the Pythagorean theorem, which relates the lengths of the sides of a right triangle.

Aryabhata, an Indian mathematician and astronomer, was the first to calculate the value of (\pi) to an accuracy of 10 decimal places in the 5th century.

The equation (\frac{a}{b} = \frac{c}{d}) is known as the cross-multiplication rule, which is used to solve proportions.

The equation (\sin^2\theta + \cos^2\theta = 1) is known as a trigonometric identity, which is an equation that is true for all values of the variable.

The equation (e^{i\pi} + 1 = 0) is known as Euler's formula, which is one of the most famous equations in mathematics.

The equation (\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}) is known as the Basel problem, which was first solved by Leonhard Euler in the 18th century.

The equation (\zeta(2) = \frac{\pi^2}{6}) is a special case of the Riemann zeta function, which is a function that is defined for complex numbers.

The equation (\lim_{n\to\infty} \left(1 + \frac{1}{n}\right)^n = e) is known as Euler's number, which is one of the most important constants in mathematics.

The equation (\int_0^1 \frac{1}{1+x^2} dx = \frac{\pi}{4}) is known as the Wallis integral, which was first discovered by John Wallis in the 17th century.

The equation (\frac{d}{dx} \sin x = \cos x) is known as the chain rule, which is used to find the derivative of a composite function.

The equation (\frac{d}{dx} \ln x = \frac{1}{x}) is known as the power rule, which is used to find the derivative of a power function.

The equation (\frac{d}{dx} e^x = e^x) is known as the exponential rule, which is used to find the derivative of an exponential function.

The equation (\frac{d}{dx} \tan x = \sec^2 x) is known as the trigonometric rule, which is used to find the derivative of a trigonometric function.

The equation (\frac{d}{dx} \cot x = -\csc^2 x) is known as the trigonometric rule, which is used to find the derivative of a trigonometric function.