Though Euler’s Identity follows from the polar form of complex numbers, it is impossible to derive the polar form (in particular the spontaneous appearance of the number e) without calculus.

Mathematician Girolamo Cardano, in his 1545 book dealing with complex numbers, "Ars Magna," dismissed them as "subtle as they are useless." Even Leonhard Euler, one of the greatest mathematicians ...

Have you ever been curious about why the number e is so popular in math? Euler’s number, which is an infinitely long decimal, close to 2.71828, pops up naturally in a surprisingly broad range of ...

Brain scans show a complex string of numbers and letters in mathematical ... may be a neurobiological basis to beauty. The likes of Euler's identity or the Pythagorean identity are rarely ...

With decent algebra skills, you can manipulate Euler’s formula to see ... who coined the term “imaginary number” – and others have observed, complex numbers make seemingly impossible ...

Pi, or p, is another irrational number. It rounds off to 3.14159, and it is defined as the ratio of the circumference of a circle to its diameter. Euler built ... is a bit more complex than ...

Euler’s Formula, which he discovered in 1744. It shows how any complex number can be obtained by rotating a point on the real line around the origin. If the point at +x is rotated through a half ...