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dkotschessaa
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I am reading Eli Maor's Trigonometric Delights which is a fascinating story of the history of Trigonometry. I have a rather elementary question.
On the early history:
"To be able to do his calculations Hipparchus needed a table of trigonometric ratios, but he had nowhere to turn: no such table existed, so he had to compute one himself. He considered every triangle - planar or spherical - as being inscribed in a circle, so that each side becomes a chord. In order to compute the various parts of the triangle one needs to find the length of the chord as a function of the central angle, and this became the chief task of trigonometry for the next several centuries."
My dumb question is - why chords? Why circles? Looking at the diagram, I can't see anything that relates to the circle itself, other than it's radius, which is merely one of the sides used to determine other sides (it is set at 60). I can't see any reason the circle needs to be there. A triangle on it's own would have worked just fine. Why a circle?
-Dave KA
On the early history:
"To be able to do his calculations Hipparchus needed a table of trigonometric ratios, but he had nowhere to turn: no such table existed, so he had to compute one himself. He considered every triangle - planar or spherical - as being inscribed in a circle, so that each side becomes a chord. In order to compute the various parts of the triangle one needs to find the length of the chord as a function of the central angle, and this became the chief task of trigonometry for the next several centuries."
My dumb question is - why chords? Why circles? Looking at the diagram, I can't see anything that relates to the circle itself, other than it's radius, which is merely one of the sides used to determine other sides (it is set at 60). I can't see any reason the circle needs to be there. A triangle on it's own would have worked just fine. Why a circle?
-Dave KA