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Re: [math-fun] Man/Math-hating at Netflix.com reaches new high/low?
by Dave Dyer 29 Dec '20

29 Dec '20

The mother back story in the netflix series is one of the screenplay's inventions. In the book the story of how Beth became an orphan is not memorable (ie; I don't remember even though I read the book after I saw the series).

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Re: [math-fun] Man/Math-hating at Netflix.com reaches new high/low?
by Dave Dyer 29 Dec '20

29 Dec '20

The mother back story in the netflix series is one of the screenplay's inventions. In the book the story of how Beth became an orphan is not memorable (ie; I don't remember even though I read the book after I saw the series).

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[math-fun] Vital, life-threatening emergency, G.O.L. Question
by Brad Klee 28 Dec '20

28 Dec '20

Dear Funsters, I did a google search for: <"Game of Life" Lotus> and found nothing aside from [censored] on instagram.com. A "Lotus" would be a binary pattern with a floral aesthetic, and it would be cool if the seasons Spring-Summer-Fall- Winter could somehow be incorporated. Preferably, evolution through time would cause the Lotus pattern to replicate into a surrounding Lotus field, and we could call this process "Propagating the Lotus", especially if there is a preferential vector direction for "downstream". Has anyone seen anything like this? Please let me know ASAP, because we all know that the fate of the whole evolutionary world depends on subsequent generations being able to understand maths! Thanks again, --Brad

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[math-fun] Post-Xmas boring puzzle (count of zeros)
by Éric Angelini 28 Dec '20

28 Dec '20

Hello Math-Fun, This puzzle is based on this (hopefully correct) draft: https://oeis.org/draft/A340063 (yes, 340063 is a prime) In the hereunder sequence, how many zeros are there between the first prime 2 and the 1000th prime 7919? Best, É. 2, 1, 3, 10, 100, 5, 20, 7, 4, 11, 110, 13, 12, 1000, 17, 200, 19, 21, 10000, 23, 6, 29, 1001, 31, 14, 100000, 37, 22, 41, 1010, 43, 30, 1000000, 47, 15, 53, 24, 59, 1100, 61, 32, 10000000, 67, 40, 71, 2000, 73, 102, 100000000, 79, 111, 1000000000, 83, 33, 89, 8, 97, 112, 101, 10001, 103, 120, 10000000000, 107,... Lexicographically earliest sequence of distinct positive terms such that: 1/ the primes appear in their natural order 2/ the absolute difference between two successive primes is given by the sum of the digits between them.

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[math-fun] I wonder how old this is.
by Bill Gosper 28 Dec '20

28 Dec '20

The arclength of one period of sin x = the circumference of an ellipse with semiaxes 1 and √2. In[112]:= #1 == #2 == FunctionExpand@#1== N@# &[ArcLength[Circle[{0, 0}, {√2, 1}]], ArcLength[Sin@x, {x, 0, 2 π]}]] Out[112]= 4 EllipticE[-1] == 4 √2 EllipticE[1/2] == 4 √2 π^(3/2)/Gamma[1/4]^2 + Gamma[1/4]^2/√(2π) == 7.64039557805542 𝚪(¼) is the rightful value of the symbol 𝛕. And someone should write Beckmann II: A History of 𝛕. —rwg

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Re: [math-fun] The 2021 problem
by Keith F. Lynch 27 Dec '20

27 Dec '20

ed pegg <ed(a)mathpuzzle.com> wrote: > Two consecutive primes can have a product giving a concatenation of > consecutive integers. Two simple examples are43?47 = 20~21 > 891077215721081784886888257701070827?891077215721081784886888257701070829 =? > 794018604377235322848433897872605582~794018604377235322848433897872605583?? I'm curious how you found the latter, and whether you're claiming those are the first two examples, or whether there could be another example between them. (As I've mentioned before, non-ASCII characters appear on the digest option as question marks. It's obvious that two of the question marks were intended as multiplication signs, but I'm curious what they other three were intended to be. Thanks.)

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[math-fun] The 2021 sequence
by ed pegg 27 Dec '20

27 Dec '20

semiprimes of consecutive primes that are also formed by concatenating consecutive integers. 2021, 794018604377235322848433897872605582794018604377235322848433897872605583, 25187118108481597700189092548093595916723774714848814417444367033247162518711810848159770018909254809359591672377471484881441744436703324717 --Ed Pegg Jr

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[math-fun] Random domino tiling.
by Allan Wechsler 26 Dec '20

26 Dec '20

Today I learned from a Mathologer video (Burkard Polster, who apparently knows funster Jim Propp), that there is a fairly simple formula for the number of domino tilings on an arbitrary simply-connected polyomino. (Mathologer was ambiguous about whether the formula fails when the polyomino has narrow "necks", but my guess is that these cases are fine.) You checkerboard-color the thing. In order for there to be any tilings at all, there have to be an equal number n of black and white squares. Then, assigning columns to white and rows to black, you construct an adjacency matrix; horizontal connections are marked 1, vertical connections are marked i (!), with 0's elsewhere; and then finally you take the determinant. Magically, either the entire real part or the entire imaginary part cancels away, and the absolute coefficient of the result (either pure imaginary or pure real) is the number of tilings. Mathologer didn't say it, but this gives a reasonably efficient way to generate a random tiling of any tilable simply-connected polyomino P. Procedure: use the magic determinant to count how many tilings of P there are; call this N, and pick a random number K between 0 and N-1. This will be the "index" of the random tiling we will select. Now, prune off all the parts that have their domino coverings forced in some way or other. In the part that's left, pick the leftmost cell of the topmost row: it can be covered in exactly two ways, horizontally, and vertically. Imagine it's horizontal, and remove that domino to get a new polyomino Ph. Count how many tilings of Ph there are; call that N'. If K < N', then that upper-left cell will be covered horizontally; if K >= N', it will be covered vertically (and the remaining polyomino we will call Pv). Now repeat this procedure with index K and polyomino Ph, or with index K-N' and polyomino Pv, depending on the outcome of the comparison. Eventually you will have tiled all the cells. I would like to see an app that takes a given polyomino and picks random tilings for you. I would also like to see one that colors the cells of a given polyomino by the probability that they are covered horizontally or vertically by a random tiling.

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[math-fun] Rolling polyhedra
by James Propp 25 Dec '20

25 Dec '20

I want to think about rolling polyhedra, and the polyhedra I want to think about rolling are polyhedra in which the sum of the angles at each vertex is a submultiple of 360 degrees. For instance, given any triangle T, we can create a tetrahedron whose four faces are all congruent to T, with angle-sum 180 degrees at each vertex (there's a name for such tetrahedra but I forget what it is). Are there other polyhedra in which the angles at each vertex sum to a submultiple of 360 degrees (not necessarily the same one at each vertex)? Jim Propp

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[math-fun] The 2021 problem
by ed pegg 25 Dec '20

25 Dec '20

Two consecutive primes can have a product giving a concatenation of consecutive integers. Two simple examples are43×47 = 20~21 891077215721081784886888257701070827×891077215721081784886888257701070829 = 794018604377235322848433897872605582~794018604377235322848433897872605583 Are there any others? --Ed Pegg Jr

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