History of trigonometry

Trigonometry is the study of triangles and the relationships between their angles and sides. Its history goes back thousands of years, beginning with early civilizations like the Egyptian mathematics and Babylonian mathematics. These ancient people used simple triangle measurements to solve practical problems, such as calculating distances and building structures.

Later, during the time of Hellenistic mathematics, scholars began studying triangles more systematically. This knowledge traveled to India, where it grew even more advanced. A famous mathematician named Aryabhata lived in the sixth century AD and discovered important functions like the sine function, cosine function, and versine function, which are still used today.

During the Middle Ages, Islamic mathematics helped trigonometry become a separate area of study. Great thinkers like al-Khwarizmi and Abu al-Wafa expanded on this knowledge. Eventually, trigonometry reached Europe through translations of Arabic and Greek texts during the Renaissance.

In more recent times, especially during the Age of Enlightenment, trigonometry became even more important. Famous mathematicians such as Isaac Newton, James Stirling, and Leonhard Euler helped shape the modern form of trigonometry that we use in schools and science today.

Etymology

The word "trigonometry" comes from ancient Greek words for "triangle" and "measure." The terms "sine" and "cosine" started with a Latin word that came from an Arabic idea.

Other important words like "tangent" and "secant" also have Latin roots. "Tangent" means "touching," while "secant" means "cutting." The prefix "co-" in words like "cosine" was first used by a mathematician named Edmund Gunter in the year 1620. The words "minute" and "second" for small parts of an angle also come from Latin.

Main article: Sine and cosine § Etymology Main article: Pythagorean identities

Ancient

The ancient Egyptians and Babylonians studied triangles for many years. They looked at the sides of triangles but did not yet understand angles.

Ancient Greek and Hellenistic mathematicians used something called a chord. This is a line that connects two points on a circle. They used chords to understand angles and circles better. Later, Claudius Ptolemy made tables to show how chords change with different angles. These tables helped astronomers predict where stars and planets would be.

In India, mathematicians like Aryabhata made big steps in trigonometry. They were the first to define the sine and cosine functions, which help us understand angles in circles. They made tables to show the values of sine for different angles.

Medieval

Earlier work from India and Greece was later used and expanded in the medieval Islamic world by Muslim mathematicians of mostly Persian and Arab descent. These mathematicians made many new rules that made trigonometry easier to use.

Important steps came from mathematicians like Muhammad ibn Mūsā al-Khwārizmī, who made accurate tables for sine and cosine values. Later, Abū al-Wafā' al-Būzjānī used all six main trigonometric functions and found important formulas. These ideas helped make trigonometry more useful for tasks like navigation and astronomy.

Modern

The book Trigonometria (1595) by Bartholomaeus Pitiscus was the first to use the word “trigonometry.” He found important links between angles and sides of triangles.

Later, Leonhard Euler helped make trigonometry simpler. He created new ways to show these links using special numbers. His work is the base of how we learn trigonometry today.