V2EX surd

Surd

释义 Definition

surd 常指数学中的“根式无理数 / 无理根式”:形如 \(\sqrt{2}\)、\(\sqrt[3]{5}\) 等、不能化为有理数的根式表达(在部分教材传统用法中,surd 也可泛指“含根号且不能再化简的表达式”)。
(另有较少见用法:语音学中指“清音、无声的辅音”。)

发音 Pronunciation

/ sd /

例句 Examples

A surd like √2 cannot be written as a simple fraction.
像 √2 这样的无理根式不能写成一个简单分数。

When simplifying the expression, she proved the result was still a surd, so an exact decimal value was impossible.
在化简这个表达式时,她证明结果仍是无理根式,因此不可能得到精确的小数值。

词源 Etymology

surd 来自拉丁语 surdus,原意为“聋的、沉闷的、无声的”。早期数学写作中借用其“难以发声/说清”的含义,引申为“难以用有理数表达清楚的量”,因此用于指代无理根式;语音学里的“清音(无声)”用法也保留了“无声”的原始含义。

相关词 Related Words

文学与名著用例 Literary Works

  • G. H. Hardy, A Course of Pure Mathematics(经典分析/代数教材语境中讨论根式与无理数时使用)
  • Courant & Robbins, *What Is Mathematics?*(介绍无理数与根式概念的科普名著中可见相关术语与讨论)
  • E. T. Bell, Men of Mathematics(在讲述数与代数发展史的叙述中涉及无理数与根式概念的传统术语背景)
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