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Re: Practical Haversine Use (with logs)
From: Lars Bergman
Date: 2021 Nov 17, 13:38 -0800
From: Lars Bergman
Date: 2021 Nov 17, 13:38 -0800
Tony, of course it is possible. To simplify, let's us define x = [ log x ].
Then, ab =[ b·log a ] = [ [ log log a + log b ] ]
So, 2371/π = [ [ log log 237 + log 1/π ] ]
A good approximation for π is 355 / 113 so 2371/π = [ [ log log 237 + log 113 - log 355 ] ] = [ [ log 2.37475 + 2.05308 - 2.55023 ] ] =
= [ [ 0.37557 + 2.05308 - 2.55023 ] ] =[ [ 9.87842 ] ] = [ 0.75582 ] = 5.70 . In order to get the difference positive I have added 10 to the first term, not shown.
Similarly for 52.372.75 = [ [ log log 52.37 + log 2.75 ] ] = [ [ log 1.71908 + 0.43933 ] ] = [ [ 0.23530 + 0.43933 ] ] = [ [ 0.67463 ] ] = [ 4.72748 ] = 53392 .
I have used Chambers's six-figure tables to facilitate inverse interpolation but rounded the values to 5 figures.
Lars
