$\pi$
$\pi = 3.14159\ldots$ is the ratio of a circle’s circumference to its diameter
Terms
| Term | This example | Why |
|---|---|---|
| ratio | ✓ | $\pi$ is the ratio of a circle’s circumference to its diameter. |
| irrational number | ✓ | |
| transcendental number | ✓ | $\pi$ is transcendental: Lindemann proved in 1882 that $\pi$ is not a root of any nonzero polynomial with integer coefficients. |
| real number | ✓ | $\pi$ is a real number, because it is the ratio of a circle’s circumference to its diameter, a point on the number line. |
| rational number | ✗ | $\pi$ is not a rational number, because it is not a ratio of two integers. |
| integer | ✗ | $\pi$ is irrational, not an integer, and not algebraic, because it is transcendental. |
| algebraic number | ✗ |