V2EX geometric progression

Geometric Progression

释义 Definition

等比数列(也称等比序列):一个数列中,从第二项起每一项与前一项的比值都相同,这个固定比值叫公比(common ratio)。
常见形式:\(a, ar, ar^2, ar^3, \dots\)。(在某些语境下也会扩展到“等比级数” geometric series。)

发音 Pronunciation (IPA)

/dimtrk prrn/

例句 Examples

A geometric progression doubles each time.
等比数列每次都翻倍。

In finance, compound interest can be modeled as a geometric progression when the growth rate is constant.
在金融中,当增长率恒定时,复利可以用等比数列来建模。

词源 Etymology

geometric 来自希腊语 geōmetria(“测量土地、几何”),由 (土地)+ metron(测量)构成;progression 来自拉丁语 progressio(“向前推进、进展”)。合起来的含义可理解为“按几何(比例)方式推进的序列”,强调“按固定比例逐步变化”。

相关词 Related Words

文学与典籍 Literary Works

  • Euclid’s Elements(《几何原本》):虽不以现代术语表述,但大量涉及比例与数的递进思想,是理解“等比”观念的重要源头。
  • Concrete Mathematics(Graham, Knuth, Patashnik):在离散数学与求和问题中频繁使用等比数列/级数。
  • Calculus, Vol. 1(Tom M. Apostol):在极限、级数与应用问题中讨论等比结构与相关求和。
  • An Introduction to the Theory of Numbers(Hardy & Wright):在数论与序列相关内容中涉及等比型构造与证明思路。
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