數學符號π (Pi)、Σ(Capital Sigma)、μ (Mu) 、σ(sigma)、∏(capital pi), ∫(Integral Symbol)的來歷


1、π (Pi; periphery/周長)

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節,這個節日紀念數學常量π (pi),即在數學上等於3.141592+的數。

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, meaningcircumference,” to π.

Greek(希臘)字母πLatin(拉丁語)中轉寫成了pi,發音類似pie(派)。首次是一個Welsh(威爾士)數學家William Jones在1706年的《Synopsis Palmariorum》書中使用,在這本書中William Jones將periphery或者其希臘詞源 περιϕέρεια(指'circumference'「周長」)縮寫成了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.

數學上的pi被定義成圓形的周長和其直徑的比。作為一個irrational number(無理數,不能表示成兩個整數相除的分數形式),pi如果用十進制記錄,pi是不會重復的(不循環)。

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.

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

 

2、Σ(Capital Sigma; Sum notation/求符號)

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

 

 

3、μ(Mu; Mean Notation/求平值符號)

μ (Mu) is mean(均值、平均).

 

4、σ(sigma)

 

5、∏(U+220F)(capital pi;連續乘積符號)

product - product of all values in range of series(一系列書的乘積) ∏ xi=x1∙x2∙...∙xn.

 

6、 ∫(Long s;Integral Symbol/積分符號)

The integral symbol(積分符號)is used to denote integrals and antiderivatives in mathematics. The notation was introduced by the German mathematician Gottfried Wilhelm Leibniz萊布尼茨) 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.

參考:Integral_symbol

 

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

(triple integral integration of function of 3 variables)

 

7、 ℒ(Laplace transform; 拉普拉斯變換符號)

 

8、δ (delta function)

 

9、ℱ(U+2131)(ℱ/Fourier transform/傅里葉變換)

X(ω) = ℱ{f (t)}

 

10、λ (Lamda Expression)

參考:

1、淺談 Lisp 裡面的 Lambda

2、匿名函數/Anonymous Function

 

參考:


1、數學符號 Calculus Symbols 

2、Sigma Notation

3、Multiplication Wikipedia


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