Not just that; this even works as a proof by contradiction that there are no non-identical congruent triangles in non-Euclidean geometries. (Probably many proofs of PT can be adapted for that, or for some other result of non-Euclidean geometry, I suppose.)

]]>It’s the sum of an initial value and the day shifts due to centuries, years, months, and days.

Day shift due to centuries is number of centuries, C, times number of days (mod 7) in a standard century, that is, 36524 mod 7 = 5, plus a correction for non standard centuries, floor(C/4).

Similarly shift due to years is Y times 365 mod 7 = 1 corrected by floor(Y/4).

Similarly shift due to months is M times 30 mod 7 = 2 corrected by a more complicated term due to months’ irregularities, floor((6M-13)/10). Actually you can use (6M-12)/10 and then simplify that to 3(M-2)/5, but I like dividing by 10 better.

If for some reason you needed a formula to figure out number of days’ difference between two dates you could leave off the initial value and the mod 7 and use

36524C + floor(C/4) + 365Y + floor(Y/4) + 30M + floor((6M-13)/10)

calculated for both dates and then subtract the two (maybe not in your head though).

]]>Rule B358/S237 also occasionally forms nice still pattern, which I named a ‘Flower’ (5 x Tub pattern). The pattern distantly resembles known ‘Honey farm’ pattern (4 x Tub).

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