Mathematics, applications of mathematics to life in general, and my life as a mathematician.
Just received from Victor Gutenmacher:
Fibonacci salad: For today’s salad, mix yesterday’s leftover salad with that of the day before.
I bet it deverges to awfinity pretty fast.
There should be an ergodic theory of foods.
“Experimental evidence (we looked in dorm room mini-fridges) suggests that Caesar salad might be modeled as a nonstationary process with strong mixing properties…”
So Tuesday’s salad is made from Sunday’s and Monday’s. But what is Wednesday’s going to be made from? Tuesday’s and…? Remember, Monday’s has already been used.
A slight modification may be necessary if this is to be an on-going thing: Let the salad for day n be be of volume x and the salad for day n+1 be of volume 2x. The salad for day n+2 will be made by taking all of the day n salad with half the day n+1 salad. This works well because there’s no way I would ever eat any of that salad! (Except maybe on day 1 or 2; even then it’s doubtful.)
colorblind’s solution fails in that each day’s fibonacci salad would be SMALLER than the previous days after days 1, 2, 3, and 4. at least assuming that someone is having some fibonacci salad. Furthermore, n3 = n1+(n2/2) which is no longer the fibonacci sequence. 1 1 1.5 1.75 2.375…
or with day 2= 2n, the sequence becomes 1 2 2 2 2 ….
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