HISTORY OF TRIGONOMETRY: MAIN FEATURES - MATHS - 2025

The history of trigonometry can be traced back to the second millennium BC. C., in the study of Egyptian mathematics and the mathematics of Babylon.

The systematic study of trigonometric functions began in Hellenistic mathematics, and reached as far as India, as part of Hellenistic astronomy.

During the Middle Ages, the study of trigonometry continued in Islamic mathematics; since then it has been adapted as a separate theme in the Latin West, beginning in the Renaissance.

The development of modern trigonometry changed during the Western Enlightenment, beginning with the mathematicians of the 17th century (Isaac Newton and James Stirling) and reaching its modern form with Leonhard Euler (1748).

Trigonometry is a branch of geometry, but it differs from the synthetic geometry of Euclid and the ancient Greeks by being computational in nature.

All trigonometric computations require the measurement of angles and the computation of some trigonometric function.

The main application of trigonometry in cultures of the past was in astronomy.

Trigonometry throughout history

Early trigonometry in Egypt and Babylon

The ancient Egyptians and Babylonians had knowledge of the theorems on the radii of the sides of similar triangles for many centuries.

However, since pre-Hellenic societies did not have the concept of the measure of an angle, they were limited to the study of the sides of the triangle.

The Babylonian astronomers had detailed records of the rising and setting of the stars, the motion of the planets, and the solar and lunar eclipses; all this required a familiarity with angular distances measured on the celestial sphere.

In Babylon, sometime before 300 BC. C., degree measures were used for angles. The Babylonians were the first to give coordinates for the stars, using the ecliptic as their circular base on the celestial sphere.

The Sun traveled through the ecliptic, the planets traveled near the eclectic, the constellations of the zodiac were grouped around the ecliptic, and the north star was located at 90 ° from the ecliptic.

The Babylonians measured longitude in degrees, counterclockwise, from the vernal point as viewed from the north pole, and they measured latitude in degrees north or south of the ecliptic.

On the other hand, the Egyptians used a primitive form of trigonometry to build the pyramids in the second second millennium BC. C. There are even papyri that contain problems related to trigonometry.

Mathematics in Greece

Ancient Greek and Hellenistic mathematicians made use of the subtense. Given a circle and an arc in the circle, the support is the line that underlies the arc.

A number of trigonometric identities and theorems known today were also known to Hellenistic mathematicians in their equivalent of the subtense.

Although there are no strictly trigonometric works of Euclid or Archimedes, there are theorems presented in a geometric way that are equivalent to specific formulas or laws of trigonometry.

Although it is not known exactly when the systematic use of the 360 ​​° circle came to mathematics, it is known to have occurred after 260 BC. This is believed to have been inspired by astronomy in Babylon.

During this time, several theorems were established, including the one that says that the sum of the angles of a spherical triangle is greater than 180 °, and Ptolemy's theorem.

- Hipparchus of Nicaea (190-120 BC)

He was primarily an astronomer and is known as the "father of trigonometry." Although astronomy was a field of which the Greeks, Egyptians, and Babylonians knew quite a bit, it is to him that the compilation of the first trigonometric table is credited.

Some of his advances include the calculation of the lunar month, estimates of the size and distances of the Sun and the Moon, variants in the models of planetary motion, a catalog of 850 stars, and the discovery of the equinox as a measure of precision of movement.

Mathematics in India

Some of the most significant developments in trigonometry occurred in India. Influential 4th and 5th century works, known as the Siddhantas, defined the sine as the modern relationship between half an angle and half subtense; they also defined the cosine and the verse.

Together with the Aryabhatiya, they contain the oldest surviving tables of sine and verse values, in intervals from 0 to 90 °.

Bhaskara II, in the 12th century, developed spherical trigonometry and discovered many trigonometric results. Madhava analyzed many trigonometric functions.

Islamic mathematics

The works of India were expanded into the medieval Islamic world by mathematicians of Persian and Arab descent; they stated a large number of theorems that freed trigonometry from complete quadrilateral dependence.

It is said that, after the development of Islamic mathematics, "real trigonometry emerged, in the sense that only later did the object of study become the spherical plane or triangle, its sides and angles."

In the early 9th century, the first accurate tables of sine and cosine, and the first table of tangents, were produced. By the 10th century, Muslim mathematicians were using the six trigonometric functions. The triangulation method was developed by these mathematicians.

In the 13th century, Nasīr al-Dīn al-Tūsī was the first to treat trigonometry as a mathematical discipline independent of astronomy.

Mathematics in China

In China, the Aryabhatiya table of sines was translated in Chinese mathematical books during 718 AD. C.

Chinese trigonometry began to advance during the period between 960 and 1279, when Chinese mathematicians emphasized the need for spherical trigonometry in the science of calendars and astronomical calculations.

Despite the achievements in trigonometry of certain Chinese mathematicians such as Shen and Guo during the 13th century, other substantial work on the subject was not published until 1607.

Mathematics in Europe

In 1342 the law of sines was proved for plane triangles. A simplified trigonometric table was used by sailors during the 14th and 15th centuries to calculate navigational courses.

Regiomontanus was the first European mathematician to treat trigonometry as a distinct mathematical discipline, in 1464. Rheticus was the first European to define trigonometric functions in terms of triangles rather than circles, with tables for the six trigonometric functions.

During the 17th century, Newton and Stirling developed the Newton-Stirling general interpolation formula for trigonometric functions.

In the 18th century, Euler was the main responsible for establishing the analytical treatment of trigonometric functions in Europe, deriving their infinite series and presenting Euler's Formula. Euler used abbreviations used today such as sin, cos, and tang, among others.

References

1. History of trigonometry. Recovered from wikipedia.org
2. History of trigonometry outline. Recovered from mathcs.clarku.edu
3. The history of trigonometry (2011). Recovered from nrich.maths.org
4. Trigonometry / A brief history of trigonometry. Recovered from en.wikibooks.org