Trigonometry with the Ancient Indian Mathematicians

The most significant development of trigonometry in ancient times was in India. Influential works from the \(4^{th}\) & the \(5^{th}\) century AD, known as Siddhantas first defined the sine as the relationship between half an angle & half a chord, while also defining the cosine, versine (\(1-\) cosine) & inverse sine.

Soon afterwards, another Indian mathematician & astronomer Aryabhata collected & expanded upon the developments of the Siddhantas in a path breaking work, the Aryabhatiya. The Siddhantas & the Aryabhatiya contain the earliest survivng tables of sine & versine values, in \(3.75^\circ\) intervals from \(0^\circ\) to \(90^\circ\), to an accuracy of \(4\) decimal places. They used the words jya for sine, kojya for cosine, utkrama-jya for versine & otkram jya for inverse sine. The words jya & kojya eventually became sine & cosine after a mistranslation.

Aryabhata was the first one. Others after him expanded on these works of trigonometry. In the \(6^{th}\) century AD, Varahamihira discovered the identity \(sin^2x + cos^2x = 1\). He improved Aryabhata's sine table & discovered an early version of the Pascal's Triangle.

Such was the ingenuity of the ancient Indian mathematicians!

Note by Ameya Salankar
4 years ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

Great Indians great mathematics

Raghu Ram - 2 years, 2 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...