Euler's formula is important because it relates famous constants, such as pi, zero, Euler's number 'e', and an imaginary number 'i' in one equation. The formula is (e raised to the i times pi) plus 1 equals 0.

No, In mathematics and physics, there is a large number of topics named in honor of Leonhard Euler, many of which include their own unique function, equation, formula, identity, number (single or sequence), or other mathematical entity. Unfortunately, many of these entities have been given simple and ambiguous names such as Euler's Law, Euler's function, Euler's equation, and Euler's formula Euler's formula is a mathematical formula that shows a deep relationship between trigonometric functions and the exponential function. Euler's first law states the linear momentum of a body is equal to theproduct of the mass of the body and the velocity of its sentre of mass Euler's second law states that the sum of the external moments about a point is equal to the rate of change of angular momentum about that point.

Euler's formula states that, for any real φ, the complex exponential function satisfies

eiφ = cos(φ) + i sin(φ) where i is the imaginary square root of -1.

A special case of the above formula, which is known as Euler's identity, is

eiπ + 1 = 0.

The answer to this question is more complicated than might appear. First, Euler's formula, eix = cosx + i*sinx was known before Euler. For example Cotes discovered that ln(cosx + isinx) = ix. Taking natural antilogs gives Euler's formula. Cotes published in 1714 when Euler was aged only 7.

Second, there is no record that shows that Euler simplified his formula and derived the identity that bears his name.

Having said all that, Euler "discovered" the formula in 1740 and published its proof in 1748.

Incidentally, I consider it to be the most beautiful formula EVER.

He discovered the all important Euler's Rule often referred to as Euler's Formula.