Little explorations with HP calculators (no Prime)

10312017, 03:12 PM
Post: #244




RE: Little explorations with HP calculators (no Prime)
(10312017 02:22 PM)pier4r Wrote: Otherwise I should find the time to explain to myself, somehow, why the +2 distance? Why the +3 distances only after some denominators? Are there more distances? Etc... Start with the equality. A=number, not necessarily integer. L=Floor(A) and H=ceil(A). A/n=pi A=pi*n Therefore your L and H are: L=floor(n*pi) H=ceil(n*pi) This means in general, L and H both skip in pi steps as you increase n, but after you round with floor/ceil you only move 3 units, leaving a remainder of (pi3) that accumulates for the next iteration. Once that reminder accumulates to 1 you'll skip 4 instead of 3. Turns out 1/(pi3) = 7.06xxxx that's why you accumulate one unit every 7 iterations. 

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