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Figure a: Artist rendition of Ptolemy
Ptolemy
Ptolemy
Ptolemy is a well-known Alexandrian astronomer, geographer and mathematician who lived during 100-170 CE. His most notable works are known as the "Almagest", "Guide to Geography" and "Optica". He is also infamous for his belief in a "geocentric" universe in which the Earth resides at the centre of the solar system. Although this theory was disproved, the mathematics he applied to reach this conclusion impacted astronomy and mathematics significantly for years to come.
Incredibly little is known of Ptolemy's personal life, and many critical parts of his work have been lost over the centuries, or mistranslated and modified. Nonetheless, Ptolemy is clear to credit the mathematician Hipparchus (2nd century BCE) in his work Almagest, in which his numerical tables had a significant impact on medieval European and Islamic mathematics and astronomy.
Additionally, Ptolemy attended a mathematical school in Croton which played a critical role in shaping his intellectual drive and assisting him with his academic pursuits. The school, which followed the Pythagorean tradition, focused on the application mathematics and philosophy had in understanding the surrounding world and its dynamics.
In the world of mathematics, Ptolemy had a significant impact, due to how he applied mathematics, especially trigonometry, in an astronomical context. The methods he took to develop his ideas employed trigonometric theorems such as Menelaus's theorems of spherical trigonometry and Pythagorean identities. Ptolemy is further well-known for his table of lengths of chords, through which he discovered the sum and difference trigonometric identities. These identities have been modified and simplified over the millennia by other mathematicians and thus applied in modern times in courses such as Mathematics Extension 1.
Below is a video that discusses a method taken to prove Ptolemy's sum and difference of angles identities through his own theorem, Ptolemy's theorem.
Sum of angles:
sum of angles.webmDifference of angles:
Recording-20240317_143226.webmApplication
Application
Trigonometric identities, such as the ones Ptolemy discovered, were incredibly useful during Ancient Greek culture. In Ancient Greece, the application of trigonometry in the context of astronomy proved incredibly valuable in determining time, and location of celestial bodies such as stars, planets and the Moon. Through the transition of planar trigonometry to a more sophisticated spherical trigonometry, the discovery and understanding of the galactic world around us laid the foundational knowledge that would be applied for years to come, all of which began through the discovery of the trigonometric identities above.
Figure b: Ancient Greek astronomer
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