Wednesday, March 5, 2014

... on Napier - with Admiration

1) ... on Classic Mathematics Logarithms - Revisited, 2) ... on Napier - with Admiration

Video Commented on:
Numberphile : Log Tables (extra bit)
Hans-Georg Lundahl
Admiring Napier!

As said, I did a try at working it out directly from base ten (expressing it in duodecimal fractions of feet to honour geometricity of slide rule, which is completely different from trying base 12 !) but I did not get very far trying it that direct fashion, and I would not have guessed at any base slightly lower than 1.

However, I was comparing bases to get fractions between exponents, and one way to achieve accuracy was precisely to compare very similar ones, like exponents of ten with at one occasion eleven at one occasion nine to get base ten logarithms for those. If one is not very accurate, one can check out of their addition adds up to something close to 2:1, since that would be base ten logarithm for 100 while 9*11 is close by 99.

I never guessed a base lower than one, though.

Of course it means that unlike the usual logarithms, as the logarithm rises the antilogarithm sinks.

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