Trigonometry: Spherical Trigonometry (2)
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Index Entry
Trigonometry: Spherical Trigonometry:
"This is one of the troubles of having started our education with parts-- of starting with lines and planes as being simple, and solids as being very difficult and sphericals even more difficult. I have given you a Universe where we start with the whole and then we begin to take out all our parts and inspect the parts, and you will always find a finite relationship of those parts-- so we come to a sphere long before we come to a plane. A planar trigonometry would be a very difficult one compared to ■ spherical. Once I am in the spherical I have a very fundamental condition which is, in making these circles, what we call the arcs, is a central angle. It is an angle. Therefore, when I am doing spherical trigonometry, when I am dealing in central angle or surface angle, you needn't say angles and edges. . . . I say this is a central angle because if you look on the circle that arc is proportional to the central angle. It is a central angle and a surface angle. You are dealing entirely in angles. If you started again from the outside you would never have the uncomfortable feeling about solving ratios between angles."
Citations
- Oregon Lecture #7, p. 272. 11 Jul'62
