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I got a bit confused talking maths with my iTalki teacher today. We encountered the term:

CC-CEDICT: 常数 (cháng​shù​) a constant (math.)

On one hand, since 常 appears in 常用, 常常, 经常, etc., the 常 in 常数 makes me think that it refers to commonly used, fixed mathematical numbers, like 1 or π or c, as opposed to some random number, like 384810513112. On the other hand, 常数 might be contrasted with 变数 = "variable", in which case 384810513112 would be considered a 常数, since it doesn't 变.

Question: Does 常数 only refer to commonly used, fixed numerical constants like 1 or π or c, or can it refer to e.g. 384810513112?

Baidu Baike seems to suggest 常数 exclusively refers to special numbers, like 1 or π or c. But then, it's not clear to me what a constant like 384810513112 would be called.

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  • 常数 = constant (math).
    – r13
    Jan 6, 2023 at 16:21

3 Answers 3

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It depends on the context. Most probably, if you say 常数, you are referring to a number of mathematical or physical significance.

Avogadro's Constant: 阿伏伽德罗常数

Note that 常量 may also represent significant numbers, like G is commonly referred to as 引力常量。

If you are using 常数, chances are that you need to explicitly define it, in which use I believe using it is okay.

我们定义常数 K = 3.2392010381245

Thus, if you use it independently without constant, people will think it means a significant number. If you have a context, then it is OK to refer to a random number.

Another use case for 常数 is that when you say a formula evaluates to a constant. 一个常数 is often used and it is solely used as the object.

等差数列中,相邻两项的差是一个常数。

Another interesting perspective is a programmer's, consider the following code snippet.

const int N = 100;

In this case, you can say

N 是一个被定义为 100 的常量。

常数 is a little weird in this scenario

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In the dictionary, https://www.zdic.net/hans/%E5%B8%B8, 常 has 3 meanings (not including the surname). (1) normal, (2) frequent (frequently), (3) invariable.

常数 is based on the meaning (3), not (2) and (1).

In Mathematics, 常数 is the opposite of 变数. For example, y = kx is a linear function, where the slope k is a constant and x is a variable. There are other concepts in Mathematics, such as 系数 and 参数. 系数 is more like a 常数, and 参数 is more like a 变数.

In science, such as physics and chemistry, 常数 is often called 常量, which has a specific value from the experiments and research.

In computer programming, 常量 and 变量 are named storage units. 常量 (constant) is assigned a value at the beginning of the program, and would not change until the end of the program.

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常数 = 常用數值 (routinely used numerical value) = constant, which is a fixed numerical value usually mathematically defined, or scientifically measured, for certain scientific matters.

  • 光速 ,299,792,458 m/s,是一個 物理常數.

  • π[pai], 圓周率, 是一個數學常數(約等於3.141592654).

Note: 常数 usually comes with a unit to give the meaning of the numerical value. For example, 光速 = 299,792,458 m/s, in which, 299,792,458 is the numerical value, and m/s is the unit of the speed of light.

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  • Is that really how the word is derived? I think 常 here comes from 常量 and similar words, i.e. the "constant; fixed" meaning of 常, not 常用.
    – Olle Linge
    Jan 14, 2023 at 9:12
  • @OlleLinge 常数=恒/常量=a constant (a number having an unchanging value). zdic.net/hans/%E5%B8%B8%E9%87%8F, zdic.net/hans/%E5%B8%B8%E6%95%B8, dict.cn/constant
    – r13
    Jan 14, 2023 at 12:57
  • I know what the words mean, my comment was about the derivation you presented in your reply : "常数 = 常用數值".
    – Olle Linge
    Jan 16, 2023 at 18:10
  • @OlleLinge In the US, we use g = 9.81 m/sec^2 as the constant for gravity, however, 9.81 is a "commonly used value" (常用數值) rather than an "absolute value" (絕對數值/固值). 常用數值 is a selectively assigned value; 絕對數值 is a scientifically determined value. Hope you see the differences.
    – r13
    Jan 16, 2023 at 19:03
  • Yes, I do! I've always thought of 常 as meaning "not changing" rather than "common/often" in the word 常数, hence my question.
    – Olle Linge
    Jan 16, 2023 at 19:43

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