Euler’s identity is an equality found in mathematics that has been compared to a Shakespearean sonnet and described as " the most beautiful equation." It is a special case of a foundational ...

Taylor’s expansion offers a way to understand the complex and peculiar expression eip from Euler’s equation. That expression raises e to the power of i, which is a perplexing concept.

Euler’s identity is a special case of a foundational equation in complex analysis, Euler’s Formula, which he discovered in 1744. It shows how any complex number can be obtained by rotating a ...

It is hard to pick a single most beautiful equation in mathematics, but I think that the Euler product formula would be near the top of any such list. Let me extol the virtues of this formula.

Discover the 17 equations that have significantly shaped our understanding of the world.

They have found a way to generate an infinite number of solutions for a puzzle known as 'Euler's Equation of degree four.' The equation is part of a branch of mathematics called number theory.

Real and imaginary: The time-dependent Schrödinger equation formulated using complex numbers. (Courtesy: iStock/piranka) Complex numbers are essential to achieve the most accurate quantum-mechanical ...

What do you get for your leap of faith in complex numbers? For one, trigonometry becomes a lot easier. Instead of memorizing several complicated trig formulas, you need only one equation to rule ...

Brain scans show a complex string of numbers and letters in mathematical formulae can evoke the same sense of beauty as artistic masterpieces and music from the greatest composers.

Explore 17 groundbreaking equations that have transformed our understanding of the world and science.