Illustration showing how the golden ratio in a regular pentagon (inscribed in a circle) can be found using Ptolemy's theorem. The lines that are bolded form a quadrilateral. Ptolemy's theorem says the square of b equals the sum of a squared and ab, which in turn gives the golden ratio.

Golden Ratio In A Pentagon

Illustration showing how the golden ratio in a regular pentagon (inscribed in a circle) can be found…

Claudius Ptolemaeus, known as Ptolemy, was an ancient geographer, astrologer, and astronomer.

Ptolemy

Claudius Ptolemaeus, known as Ptolemy, was an ancient geographer, astrologer, and astronomer.

Claudius Ptolemaeus, known as Ptolemy, was an ancient geographer, astrologer, and astronomer.

Ptolemy

Claudius Ptolemaeus, known as Ptolemy, was an ancient geographer, astrologer, and astronomer.

He was a mathematician, geographer, astronomer, and astrologer. "The name of a line Graeco-Egyptain kings, who succeeded on the division of the empire of Alexander the Great, to the portion of his dominions of which Egypt was the head." -Marshall

Ptolemy

He was a mathematician, geographer, astronomer, and astrologer. "The name of a line Graeco-Egyptain…

"Coin of Ptolemy." — Smith, 1882

Coin of Ptolemy

"Coin of Ptolemy." — Smith, 1882

"In 1799, the Rosetta Stone was found and gave the first key to the reading of hieroglyphics. On this stone the same inscription was given in three different sets of characters, -the hieroglyphics, the demotic text (a briefer and more running form of hieroglyphics, commonly used in the papyri or manuscripts), and the Greek. By comparing the letters in certain Greek proper names with the letters of the same words in the Egyptian texts, the sounds for which the Egyptian characters stood were discovered. This image represents Ptolemy or Ptolemaios." —Colby, 1899

Rosetta Stone

"In 1799, the Rosetta Stone was found and gave the first key to the reading of hieroglyphics. On this…