This is a beta course, so its structure, chapters, and examples may continue to change.

Pi ($\pi$)

$\pi$ is the celebrity constant of geometry—showing up from circles to Fourier series.

$\pi$ （pi，派）：圆周率，定义为圆的周长与直径之比，近似

3.14159\ldots

，是无理数。

Definition

Circle ratio

$\pi = \dfrac{C}{d}$ , where $C$ is a circle’s circumference and $d$ is its diameter. The ratio is constant for all circles.

符号说明

Symbol	Type	Pronunciation/Note	Meaning in this article
$\pi$	Greek letter	Pi (pie)	Pi, ratio of circle’s circumference to diameter

$\pi$ is irrational and transcendental.
Key angle values: $\sin\left(\dfrac{\pi}{6}\right) = \dfrac{1}{2}$ , $\cos\left(\dfrac{\pi}{3}\right) = \dfrac{1}{2}$ .
Circumference: $C = 2\pi r$ ; Area: $A = \pi r^2$ .
Period of $\sin x$ and $\cos x$ is $2\pi$ .

Convert $180^\circ$ to radians and $2\pi$ radians to degrees.

Answer and Analysis(4 个标签)

pi constantradiansdegreesangle conversion

$180^\circ = \pi$ radians; $2\pi$ radians $= 360^\circ$ .

Find the area of a circle with radius $3$ .

Answer and Analysis(3 个标签)

pi constantcircle areaarea formula

$A = \pi r^2 = \pi \times 3^2 = 9\pi$ .

符号	类型	读音/说明	在本文中的含义
$\pi$	希腊字母	Pi（派）	圆周率
$C$	数学符号	circumference	圆的周长
$d$	数学符号	diameter	圆的直径
$r$	数学符号	radius	圆的半径