This chapter reviews topics in plane trigonometry, first by considering ancient ideas that the Earth is round, focusing on tales of Christopher Columbus trying to convince the Spanish court that the Earth is not a disc but a sphere, making it possible to sail westward from Portugal to India. It then discusses the dimensions of the Earth and computes a table of sines. In particular, it looks at the trigonometric table of Claudius Ptolemy, who included a remarkable collection of models for the motions of the heavenly bodies in his astronomical masterpiece, Mathematical Collection. In early Europe, the most prodigious set of trigonometric tables was the Opus palatinum, composed by Georg Rheticus. The chapter concludes with calculations to find the distance to the Moon using only simple measurements.
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