Question

state and verify the Euler's formula for a rectangualr prism

Answer 1

In addition to the base, the pyramid has triangular faces said to be lateral; the edges that join the base and the apex are also lateral. A quadrilateral pyramid has 5 vertices, 8 edges and 5 faces. You can check the Euler's formula for this solid: 5 - 8 + 5 = 2.

Answer 2

Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that for any real number x

e^ix=cox+isinx

where e is the base of the natural logarithm, iis the imaginary unit, and cos and sin are the trigonometric functions cosine and sinerespectively, with the argument x given in radians. This complex exponential function is sometimes denoted cis x ("cosine plus isine"). The formula is still valid if x is a complex number, and so some authors refer to the more general complex version as Euler's formula.

Euler's formula is ubiquitous in mathematics, physics, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics".[2]

When {\displaystyle x=\pi }, Euler's formula evaluates to {\displaystyle e^{i\pi }+1=0} which is known as Euler's identity.