数学符号π (Pi)、Σ(Capital Sigma)、μ (Mu) 、σ(sigma)、∏(capital pi), ∫（Integral Symbol）的来历

1、π (Pi; periphery/周长)

March 14 marks Pi Day, the holiday commemorating the mathematical constant π (pi), written numerically as 3.141592+. Since mathematic notation is a language that uses symbols from a multitude of alphabets and typefaces, it seems only fitting that this sixteenth letter of the Greek alphabet get a little attention.

3月14日是Pi节，这个节日纪念数学常量π (pi)，即在数学上等于3.141592+的数。

The Latin name of the Greek letter π is pi, pronounced pie. The first recorded use of the letter as a mathematical symbol comes from the Welsh mathematician William Jones in a 1706 work called Synopsis Palmariorum in which he abbreviated periphery or its Greek ancestor περιϕέρεια, meaning “circumference,” to π.

Greek(希腊)字母π在Latin（拉丁语）中转写成了pi,发音类似pie（派）。首次是一个Welsh（威尔士）数学家William Jones在1706年的《Synopsis Palmariorum》书中使用，在这本书中William Jones将periphery或者其希腊词源 περιϕέρεια(指'circumference'「周长」)缩写成了π。

The mathematical pi is defined as the ratio of the circumference of a circle to its diameter. As an irrational number, pi can never repeat when written in decimals; computers have calculated pi to decimal places in the trillions. It is also a transcendental number, a concept that exceeds the capacity of this post to explain.

数学上的pi被定义成圆形的周长和其直径的比。作为一个irrational number(无理数，不能表示成两个整数相除的分数形式)，pi如果用十进制记录，pi是不会重复的（不循环）。

Memorizing as many digits of pi as possible is an obsession for some. The Guinness World Record for memorizing digits of π is held by a man named Lu Chao. He set the record in November 2005 at Northwest A&F University in the Shaanxi province of China. It took him 24 hours and 4 minutes to recite the 67,890th decimal place of π without a mistake.

参考：What’s the Origin of the Word “Pi”?
参考：PI in etymonline.com

2、Σ(Capital Sigma; Sum notation/求和符号)

Σ(Sigma) is the upper case letter S in Greek. And S stands for Sum(和).

3、μ(Mu; Mean Notation/求平均值符号)

μ (Mu) is mean(均值、平均).

4、σ(sigma)

5、∏(U+220F)(capital pi；连续乘积符号)

product - product of all values in range of series(一系列书的乘积) ∏ x_i=x₁∙x₂∙...∙x_n.

6、 ∫（Long s；Integral Symbol/积分符号）

The integral symbol(积分符号)∫is used to denote integrals and antiderivatives in mathematics. The notation was introduced by the German mathematician Gottfried Wilhelm Leibniz（莱布尼茨） towards the end of the 17th century. The symbol was based on the ſ (long s) character, and was chosen because Leibniz thought of the integral as an infinite sum of infinitesimal summands.

参考：Integral_symbol

∬（double integral； integration of function of 2 variables）

∭（triple integral integration of function of 3 variables）

7、 ℒ(Laplace transform; 拉普拉斯变换符号)

8、δ (delta function)

9、ℱ(U+2131)(ℱ/Fourier transform/傅里叶变换)

X(ω) = ℱ{f (t)}

10、λ (Lamda Expression)

参考：

1、淺談 Lisp 裡面的 Lambda

2、匿名函数/Anonymous Function

参考：

1、数学符号 Calculus Symbols

2、Sigma Notation

3、Multiplication Wikipedia