### What is the contribution of georg von purbach to trigonometry?

Georg von Peurbach (also known as Georg Purbach or Georgius Peurbachius in Latin) was a 15th-century Austrian mathematician and astronomer. He was born on May 30, 1423, in Peuerbach, Upper Austria, and died on April 8, 1461, in Vienna, Austria.

Peurbach studied at the University of Vienna and became a professor of mathematics and astronomy there in 1453. He was a leading figure in the development of European astronomy in the 15th century and was a strong advocate of the use of mathematics in astronomy.

One of Peurbach's most significant contributions to astronomy was his work on planetary motion. He wrote a number of books on the subject, including the "Theoricae Novae Planetarum," which was published posthumously in 1472. In this work, Peurbach refined the theory of planetary motion proposed by his predecessor, Ptolemy, and introduced a number of new concepts that would later be used by Copernicus.

Peurbach also made important contributions to trigonometry, developing the sine and cosine functions and refining the use of the astrolabe, an instrument used for measuring the altitude of celestial bodies.

Peurbach's work had a significant impact on the development of astronomy and mathematics in Europe. He was highly respected by his contemporaries and was considered one of the most important astronomers of his time. He was also a mentor to the young Johannes Müller, who would later become known as Regiomontanus and would continue Peurbach's work in astronomy.

Georg von Peurbach (also known as Peurbach or Purbachius) was a 15th-century Austrian mathematician and astronomer who made significant contributions to the development of trigonometry. Some examples of his contributions include:

**Peurbach's Theorem:** This theorem relates the side and diagonal of a rectangle to the length of a chord subtended by a fixed angle in a circle. It states that the length of the chord is equal to the geometric mean of the side and diagonal of the rectangle. This theorem was later used by his student Regiomontanus in his work on trigonometry.

**Improved sine tables**: Peurbach made improvements to the existing sine tables that were used in trigonometric calculations. He increased the accuracy of these tables by extending them to more decimal places.

**Trigonometric identities**: Peurbach developed several trigonometric identities, including a formula for the sine of half the sum of two angles, which was later used by Copernicus in his work on planetary motion.

**Trigonometric applications:**Peurbach applied trigonometry to solve problems in astronomy, such as determining the positions of celestial bodies and calculating their distances from Earth.

__Here are some of his key contributions:__

**Improved trigonometric tables: **Von Peurbach was one of the first mathematicians to recognize the importance of accurate trigonometric tables in astronomy and other fields. He collaborated with his student Regiomontanus to produce more accurate and comprehensive tables of sines, cosines, and tangents.

**Developed the theory of spherical trigonometry:** Von Peurbach extended the principles of planar trigonometry to the study of spherical triangles, which are triangles that are formed on the surface of a sphere. His work on spherical trigonometry was particularly important for navigators and astronomers, who used it to calculate positions and distances in the sky and on the Earth.

**Influenced other mathematicians:** Von Peurbach's work on trigonometry was influential in the development of mathematics in the 15th and 16th centuries. His books, including "Theoricae novae planetarum" and "Epitome in almagestum Ptolomei," were widely read and studied by other mathematicians, including Johannes Kepler and Nicolaus Copernicus.

Overall, Georg von Peurbach's contributions to trigonometry helped to lay the foundation for the development of modern mathematics and astronomy. His work on trigonometric tables and spherical trigonometry was particularly important for practical applications in navigation and astronomy, and his influence can still be seen in mathematics and science today.

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