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The origin and development of trigonometry can be traced back to ancient Greeks. The ancient Greek is well known for making today’s trigonometry in order. Although many sources of the founders of trigonometry have lost due to the passage of time, some sources could be retrieved to help us understand better on who invented trigonometry. Some of these sources are:

  • Ptolemy’s Almagest by Ptolemy
  • Phainomena of Eudoxas of Cnidos by Aratos of Soloi
  • Sphaerica by Menelaus
  • These three books explain the works of famous mathematicians and astronomers of the ancient Greeks, namely the Hipparchus, Ptolemy, and Menelaus. The invention and development of trigonometry were inspired by the driving force of astronomy.

    Although trigonometry can be described as a branch of geometry, its computational nature has helped many astronomers and mathematics to develop the celestial tools that have since been used to travel on the sun and other heavenly bodies.

    That is a clear statement to mean that the early development of trigonometry is the spherical trigonometry which was based on the sphere due to its application of astronomy. Spherical trigonometry is today known as the elliptical geometry.

    Hipparchus of Nicaea on who invented trigonometry

    Although we are not very certain who invented trigonometry due to lack of supporting documentary evidence, Hipparchus of Nicaea is termed as the father of trigonometry. This title is effective by the fact that Hipparchus is the only astronomer and mathematician whose most of his life history is documented.

    Born at Nicaea, Bithynia, a small town founded in the 4th century BC, Hipparchus is the greatest of all the astronomers whose viable astronomical observations from the start of 161 BC to 127 BC are well documented in two books, i.e. Phainomea of Eudoxas of Cnidos and Almagest by Aratos of Soloi and Ptolemy respectively.

    According to Theon of Alexandria, who was a teacher of Astronomy and mathematics in Alexandria, Hipparchus of Nicaea wrote a treatise that comprised of twelve books of circle’s chords. Hipparchus also produced a table of chords which are trigonometric functions that are related to Sine functions.

    Pappus of Alexandria, a teacher of mathematics in Alexandria in the 4th century also observed that Hipparchus of Nicaea was the first one to discover the times in which the twelve zodiacal signs rose and set. Although there was a great mathematician at that time, such as Autolycus, Euclid, and Theodosius, they could only support the fact that the zodiacal signs have a similar relationship between their rising and setting times. Hipparchus used chords to give the exact times of these Zodiacal signs. Most of the works of Hipparchus are also recorded in the Ptolemy’s Almagest.

    Menelaus as one of the fathers who invented trigonometry

    Menelaus is another well recognized Greek mathematician who is mentioned by Ptolemy as a contributor to the development of trigonometry. The book “History of Mathematics” notes that Menelaus was born around 70 AD. He was believed to have had one of his astronomical observations in Rome, as mentioned by Ptolemy. However, through the mention of both Proclus and Pappus as the man of Alexandria, Menelaus has been living in Alexandria and spending some of his time in Rome.

    According to Theon of Alexandria, his treatise in six books of chords named Spherica provides a great knowledge that defines the concept of Spherical triangle which corresponds with the postulations of Euclid’s concept of plane triangles. Although the Greek version of Spherica is lost, the Arabic version still provides a reliable source for the history and development of the Greek trigonometry.


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