Binet's Formula

Binet's Formula provides a way to directly calculate the *n*-th Fibonacci number using a mathematical expression involving powers and roots, without computing all previous numbers. It uses the golden ratio (about 1.618) and its inverse to generate Fibonacci numbers precisely. Essentially, the formula combines two exponential terms—one involving the golden ratio and the other its conjugate—and then adjusts the result to yield an integer. This allows quick computation of Fibonacci numbers even for large *n*, illustrating a deep link between these numbers and fundamental mathematical constants.