Verify Euler’s formula for the following
solid
Answers
Explanation
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:
{\displaystyle e^{ix}=\cos x+i\sin x,}{\displaystyle e^{ix}=\cos x+i\sin x,}
where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively. This complex exponential function is sometimes denoted cis x ("cosine plus i sine"). 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.[1]
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 x = π, Euler's formula evaluates to eiπ + 1 = 0, which is known as Euler's identity.
For Solid:
Euler's formula deals with shapes called Polyhedra. A Polyhedron is a closed solid shape which has flat faces and straight edges. An example of a polyhedron would be a cube, whereas a cylinder is not a polyhedron as it has curved edges. ... If none of these rules are broken, then F+V-E=2 for all Polyhedra.