Saturday, May 27, 2017

Ptolemy of Alexandria - Claudius Ptolemaeus (~100-170) - MATHEMATICS, CODING, PROCESSING & C4D ANIMATIONS

Ptolemy of Alexandria - Claudius Ptolemaeus (~100-170) an Egyptian astronomer, mathematician, and geographer of Greek descent who flourished in Alexandria during the 2nd century ce. In several fields his writings represent the culminating achievement of Greco-Roman science, particularly his geocentric (Earth-centred) model of the universe now known as the Ptolemaic system.

His first major astronomical work, the Almagest, was completed about 150 ce and contains reports of astronomical observations that Ptolemy had made over the preceding quarter of a century. The size and content of his subsequent literary production suggests that he lived until about 170 ce.

Ptolemy has a prominent place in the history of mathematics primarily because of the mathematical methods he applied to astronomical problems. His contributions to trigonometry are especially important. For instance, Ptolemy’s table of the lengths of chords in a circle is the earliest surviving table of a trigonometric function. He also applied fundamental theorems in spherical trigonometry (apparently discovered half a century earlier by Menelaus of Alexandria) to the solution of many basic astronomical problems.

In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle).

We have three colored segment in this animation. Surprisingly the length of the longest one is always the sum of the length of the two smaller ones.
This is actually a very special case of Ptolemy’s theorem. The theorem gives a connection between the sides and the diagonals of a cyclic quadrilateral. In this case the length of the dashed lines is equal so the theorem can be simplified to the statement above.

Animation by szimmetria-airtemmizs


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