▲ | srean 5 days ago | |||||||
Yes. Similar idea. Sometimes they would also use minutes. Whether this was as a result of contact with the Greeks I do not know. Indian trigonometry however has a different flavour from the trigonometry of Hipparchus. What Indian mathematicians typically used was a circle with radius 3438 units. Where units would be one of the standard units of length. Why 3438 you may wonder. They also wanted to divide the circle into 360 x 60 minutes. For the standard circle they wanted each of those minute arcs to be of 1 unit length. The radius that would accomplish this is (360 x 60)/ 2pi ~= 3438 units. An angle of 1 minute would then be described as arc length 1 unit on that standardized circle of radius 3438 units. Indian version of sine and cosine were not expressed as ratios but the corresponding (half) chord for a hypotenuse of 3438 units. | ||||||||
▲ | kqr 5 days ago | parent [-] | |||||||
Very neat. Alternative-length radians seem quite common. Radians are by definition one radius, but NATO mils are 0.00098 radii (and apparently the Finnish piiru are 0.00105 radii). What you describe are effectively a unit that is 0.0018 radii. Makes sense. | ||||||||
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