Historical Encyclopedia
Trigonometry, at the intersection of mathematics and geometry, is the science of the relationships between the angles and sides of triangles. In Ancient Greece, starting from the 2nd century BC, foundational ideas emerged that became the basis for the further development of trigonometry. The study of triangles in the context of astronomy and geography served as a catalyst for active research in this field.
The ancient Greek civilization, which reached its peak during the classical period, displayed a great interest in science and mathematics. The application of mathematical knowledge helped solve practical problems, such as navigation and astronomical observations. Trigonometry, as a field of knowledge, became an essential tool for astronomers who sought ways to determine the positions of stars and planets more accurately.
One of the key figures in the establishment of trigonometry was Hipparchus, who lived around 190-120 BC. He created the first trigonometric table, which listed values for the basic angles. These tables allowed astronomers to calculate the altitude of celestial bodies above the horizon more accurately.
The ancient Greeks used the circle to describe trigonometric functions. Hipparchus, for example, explored the relationships between the sides and angles in triangles inscribed in a circle. He also noted the characteristics of angles at 90, 180, and 360 degrees, which became the foundation for further research into sine and cosine functions.
Among the early trigonometric functions, those we now call sine and cosine held a special place. They were based on the relationships between the sides of triangles and the angles within them. Although the terms themselves emerged later, the fundamental ideas pertained to measuring segments on the unit circle, which laid the groundwork for trigonometric functions.
The Greeks developed various methods and algorithms for calculating the angles and lengths of the sides of triangles. They used geometric constructions as well as algebraic techniques to find the necessary values. Methods for estimating and approximating angles were significant, especially in astronomy, where measurement accuracy was critically important.
The work of ancient Greek scholars significantly influenced the further development of mathematics and astronomy. Their approaches and ideas were adopted by Arab mathematicians during the Middle Ages and later by European scholars during the Renaissance. Today, trigonometric functions are used not only in astronomy but also in physics, engineering, computer graphics, and many other fields.
The study of trigonometry in Ancient Greece was an important stage in the development of mathematics. The achievements of scholars of that time laid the groundwork for modern mathematics and astronomy. Trigonometry, as the science of the relationships between angles and sides, continues to be an important area of knowledge, having a tremendous impact on various scientific disciplines.