Euler's identity
Links five fundamental constants: e, i, π, 1 and 0. It is the special case θ = π of Euler's formula e^{iθ} = cos θ + i sin θ. History: 1740s.
How to work it out
- 1
The statement:
- 2
Links five fundamental constants: e, i, π, 1 and 0. It is the special case θ = π of Euler's formula e^{iθ} = cos θ + i sin θ.
- 3
Below, the numbers in the table are computed by this site from the definition, not copied.
LaTeX source of the formulas on this page
\[ e^{i\pi} + 1 = 0 \]Why it is true: the series of cos π and sin π (computed)
| Terms used | cos π estimate | sin π estimate |
|---|---|---|
| 2 | -3.934802 | -2.026120 |
| 4 | -1.211353 | -0.075221 |
| 6 | -1.001829 | -0.000445 |
| 8 | -1.000004 | -0.000001 |
| 12 | -1.000000 | -0.000000 |
Questions
What is the euler's identity?
Links five fundamental constants: e, i, π, 1 and 0. It is the special case θ = π of Euler's formula e^{iθ} = cos θ + i sin θ.
Who is the Euler's identity associated with?
Leonhard Euler.