# 印度数学[编辑]

印度河流域文明中重量標準化的立方
**印度數學**在公元前1200年 于印度次大陆出现，到18世纪结束。在印度数学的古典时期（公元400年至1200年），阿耶波多、婆羅摩笈多、婆什迦羅第二和伐罗诃密希罗等学者做出了重要的贡献。印度数学首先记录了今天使用的十进制。印度数学家早期的贡献包括对0作为数字的概念的研究，负数，算数，以及代数。另外，三角学
在印度更加先进，特别是发展出了正弦和余弦的现代定义。这些数学概念被传播到中东，中国和欧洲，从而导致了进一步的发展，形成了现在许多数学领域的基础。

古代和中世纪的印度数学作品，都是用梵语写成，通常由称作*契经*的一部分组成，在其中为了帮助学生记忆，用极少的字词陈述了一些规则和问题。在这之后是第二部分，包括一篇散文评论（有时是来自不同学者的多篇评论），其更详细地解释了问题并为解决方案提供了更多的理由。在散文部分，形式（和记忆）比起其涉及的思想来说并不是很重要。在公元前500年之前，所有的数学作品都是由口头传播，之后同时以口头和手稿的形式传播。现存的印度次大陆上最古老的数学*文献*是写在桦树皮上的巴赫沙利手稿，它在1881年于巴赫沙利村被发现，靠近白沙瓦（现位于巴基斯坦）并可能来自公元7世纪。

印度数学的后期里程碑是公元15世纪喀拉拉邦学派的数学家对三角函数（正弦，余弦和反正切）的级数展开的发展。 他们的卓越工作，在欧洲发明微积分之前两个世纪完成，提供了现在被称为幂级数的第一个例子（除了等比数列） 。 然而，他们没有制定出系统的微分和积分理论，也没有任何*直接*证据证明他们的结果是在喀拉拉邦以外传播的。

## 史前時期

在摩亨佐-達羅、哈拉帕與其他幾個印度河流域文明的遺址中，都發現了使用"實用數學"的證據。他們使用4:2:1的比例製造磚頭，此作法被認為有利於磚頭結構的穩定性。他們使用了標準化的砝碼，以比例:1/20, 1/10, 1/5, 1/2, 1, 2, 5, 10, 20, 50, 100, 200與500進行製作，其中的一單位的重量約等於28克。他們大量生產有規則形狀的砝碼，有六面體、桶形、錐形與柱形，從而展示出對於基本幾何的理解。

印度文明的居民曾試圖對於長度量測進行高精準度的標準化。他們設計出了摩亨佐達羅尺，尺上的單位長度約為3.4公分，並且再分割成十等分。古代摩亨若達羅的磚頭尺寸通常是此單位長度的整數倍。

在洛沙爾(Lothal,2200 BCE)與卓拉維拉(Dholavira)發現的貝殼製中空柱狀物體上面有8個裂縫，被認為可用來製作羅盤，證明了能在平面上測量角度的能力，並可藉此確定星星的位置進行導航。

## 吠陀時期

吠陀時期的宗教文本提供了使用大數的證據。在《夜柔吠陀》（公元前1200-900年）文本中，包含的數字高達 WIKINIUM\_MATH\_PH\_0 。

## 耆那學者（前400年-200年）

耆那學者認為世界是永恆的，只有形式上的變化，與婆羅門教創造萬物的理論不同。耆那教由筏陀摩那在前6世紀創立，但耆那數學著作大部分是在前6世紀後撰寫的。耆那學者將數字分為三類。

耆那重要數學家包括賢臂(Bhadrabahu，卒於公元前298年），他是兩部天文著作的作者。

## 書寫形式

## 巴赫沙利手稿

## 古典時期（400-1600年）

* Shulba Sutras
* Kerala school of astronomy and mathematics
* Surya Siddhanta
* 婆羅摩笈多
* 斯里尼瓦瑟·拉马努金
* 巴赫沙利手稿
* 印度数学家列表
* 印度科学和技术
* 印度逻辑
* 印度天文学
* 数学史
* List of numbers in Hindu scriptures

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## 延伸阅读

### 梵语文献

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