-
Use Cases
-
Resources
-
Pricing
History of Trigonometry Timeline
(c. 1800 BCE – Present)Trigonometry is the branch of mathematics that studies the relationships between the angles and sides of triangles. Its development spans over 3,000 years, beginning with ancient Babylonian astronomy and Egyptian surveying, advancing through Greek mathematicians like Hipparchus and Ptolemy who created early chord tables, flourishing during the Islamic Golden Age with the systematic study of all six trigonometric functions, and culminating in Renaissance Europe with Euler's analytical formulation of trigonometry using complex numbers. More Less
Indian Astronomy
Siddhantas define the sine function
400 AD - 500 AD
Influential works from the 4th–5th century AD, known as the Siddhantas (of which there were five, the most important being the Surya Siddhanta), first defined the sine as the modern relationship between half an angle and half a chord, while also defining the cosine, versine, and inverse sine.
Image source: Surya Siddhanta
Aryabhata discovers sine, cosine, and versine functions
500 AD - 600 AD
In Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata (6th century AD), who discovered the sine function, cosine function, and versine function.
Image source: Aryabhata
Varahamihira develops the Indian tradition of trigonometry
505 AD - 587 AD
In the 6th century, Varahamihira further developed the Indian tradition of trigonometry established by Aryabhata, building on the foundations laid by the Siddhantas and advancing astronomical applications of trigonometric concepts.
Image source: Varāhamihira
Bhaskara I produces formula for calculating sines
600 AD - 700 AD
In the 7th century, Bhaskara I produced a formula for calculating the sine of an acute angle without the use of a table, an important advance in practical computation of trigonometric values.
Image source: Bhāskara I's sine approximation formula
Madhava analyzes infinite series expansions
1340 AD - 1425 AD
Madhava of Sangamagrama (c. 1340 – c. 1425) made early strides in the analysis of trigonometric functions and their infinite series expansions. His works were expanded by his followers at the Kerala School up to the 16th century.
Islamic Golden Age
Al-Khwarizmi produces accurate sine and cosine tables
800 AD - 850 AD
In the early 9th century AD, Muhammad ibn Mūsā al-Khwārizmī produced accurate sine and cosine tables, making important contributions to the development of trigonometry in the Islamic world.
Image source: Al-Khwarizmi
Abu al-Wafa uses all six trigonometric functions
940 AD - 998 AD
By the 10th century AD, in the work of Abū al-Wafā' al-Būzjānī, all six trigonometric functions were used. Mathematicians such as al-Khwarizmi and Abu al-Wafa made important contributions to the field during this era.
Image source: Abu al-Wafa' al-Buzjani
Al-Jayyani writes first treatise on spherical trigonometry
989 AD - 1079 AD
Al-Jayyani (989–1079) of al-Andalus wrote The book of unknown arcs of a sphere, which is considered "the first treatise on spherical trigonometry", a landmark work in the field.
Image source: Ibn Mu'adh al-Jayyani
Muslim mathematicians develop triangulation method
1000 AD - 1050 AD
The method of triangulation was first developed by Muslim mathematicians, who applied it to practical uses such as surveying and Islamic geography, as described by Abu Rayhan Biruni in the early 11th century.
Image source: Triangulation
Omar Khayyám solves cubic equations with trigonometric tables
1048 AD - 1131 AD
In the late 11th century, Omar Khayyám (1048–1131) solved cubic equations using approximate numerical solutions found by interpolation in trigonometric tables, demonstrating an innovative analytical application of trigonometry.
Image source: Omar Khayyam
Key Facts
- The Babylonians around 1800 BCE used sexagesimal arithmetic to track celestial movements, laying early foundations for angular measurement still seen today in degrees, minutes, and seconds.
- Hipparchus of Nicaea (c. 190–120 BCE), often called the 'father of trigonometry,' compiled the first known table of chords for solving triangles.
- Ptolemy's Almagest (c. 150 CE) expanded trigonometric tables with remarkable accuracy that remained unsurpassed for over a thousand years.
- Islamic scholars such as al-Khwarizmi, Abu al-Wafa, and Nasir al-Din al-Tusi developed the six trigonometric functions and introduced key laws like the law of sines.
- Leonhard Euler's work in the 18th century connected trigonometry to complex numbers through his famous formula e^(ix) = cos(x) + i·sin(x), establishing trigonometry as an analytical discipline.
Source
This History of Trigonometry timeline was generated with the help of AI, using information found on the internet.
We work hard to keep these timelines accurate, but mistakes do get through. If you spot one, email us at [email protected] and we'll fix it for future visitors.
Want a timeline like this one?
Generate yours with AI or build it from scratch, for free.