V2EX biquadratic

Biquadratic

释义 Definition

biquadratic(多用于数学)指“双二次的 / 四次的”,常见于双二次方程(biquadratic equation):只含 \(x^4\)、\(x^2\) 和常数项的四次方程,例如 \(ax^4+bx^2+c=0\)。在更广义的数学语境中,也可指“由两个二次关系构成的(双二次)”。

发音 Pronunciation (IPA)

/bakwdrtk/

例句 Examples

The equation \(x^4 - 5x^2 + 4 = 0\) is biquadratic.
方程 \(x^4 - 5x^2 + 4 = 0\) 是一个双二次方程。

By substituting \(y=x^2\), we can reduce the biquadratic equation to a quadratic one and solve it more easily.
通过令 \(y=x^2\),我们可以把双二次方程化为二次方程,从而更容易求解。

词源 Etymology

来自前缀 **bi-**(“二、双”)+ quadratic(“二次的”,源自拉丁语 quadratus,意为“方形、平方的”)。字面意思可理解为“与两次二次(two quadratics)相关”,在代数里常用来指只含 \(x^4\)、\(x^2\) 的四次结构。

相关词 Related Words

文学与著作中的使用 Literary Works

  • G. H. Hardy《A Course of Pure Mathematics》(常见“biquadratic equation”等代数术语,用于基础代数与方程求解讨论)
  • I. M. Gelfand & A. Shen《Algebra》(在多项式与方程章节中常出现双二次/四次方程的例题与术语)
  • E. T. Whittaker & G. N. Watson《A Course of Modern Analysis》(在涉及多项式方程与特殊函数的推导中,可能出现“biquadratic”作为结构描述词)
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