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 UselessCommon June 27th, 2017 01:25 AM

Mathematical scales

0, 1, 2, 3, 4... - linear scale.
1, 2, 4, 8, 16... - logarithmic scale.
0, 1/2, 1, 2, :infinity: - the hell is this one ?
Because everybody is like "this is totally legit, but I don't know how it's called or what's the general rule ".

More generally:
0; n^0; :infinity:
0; n^-1; n^0; n^1; :infinity:
0; n^-2; n^-1; n^-1/2; n^0; n^1/2; n^1; n^2; :infinity:
0; n^-3; n^-2; n^-3/2; n^-1; n^-2/3; n^-1/2; n^-1/3; n^0; n^1/3 n^1/2; n^2/3; n^1; n^3/2; n^2; n^3; :infinity: (not sure for this one)
Add negative numbers on the left for full scale.

And so on, but I am not exactly sure how.

If you scale your X;Y coordinates like this, 1/x looks like a straight line between 0;:infinity: and :infinity:;0 and x^2 looks like a -sinx rotated 45 degrees around origin.

Also, it's very symmetrical: if you multiply numbers equidistant from 1 or -1, you get 1; if you multiply the exponents of numbers equidistant from n or -n or n^-1 or n^-1, you get 1, and if you multiply numbers 1/2 of scale away from each other (full scale includes negative numbers) you get -1.

So, who knows how that's called ?

 skipjack August 7th, 2017 10:46 PM

The third one doesn't make sense to me.

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