Very proud to have been published on Neil Sloane's Online Encyclopedia of Integer Sequences where I sent in a small correction after watching James Grime's Numberphile video on tetrahedral numbers https://youtu.be/CK3_zarXkw0 and reading the links at https://oeis.org/A104246

#tetrahedral #oeis #numberphile #mathematics

It took a little under 3 hours for my program on a #RaspberryPi 5 with 4 cores at 2.4 GHz to calculate that there are 863 #tetrahedral sums of up to 4 terms for the number 2^32-1, and another 377968 sums of 5 terms.

#programming #C #Clanguage #C_lang #mathematics #maths #math #numberphile #JournalOfRecreationalMathematics #compsci #PollocksConjecture

A couple of days ago I made a "combinations" function in #C that works the same as #Python itertools.combinations. I used it to help with a #Numberphile challenge, however I misunderstood: duplicates WERE allowed. So I binned it all, went back to nested loops and added multi-threading. Now it only takes about 0.01 s to calculate all #tetrahedral sums (up to 5 terms) of 343867 which is supposed to be the last one that requires more than 4 terms.

Works on #Mac and #Linux: https://github.com/ednl/tetrahedral/blob/main/tetrasum.c

Heads-up! to https://arxiv.org/abs/2302.12209
"How to detect the spacetime curvature without rulers and #Clocks"
(A. V. Nenashev, S. D. Baranovskii)

-- which investigates the question (p. 2)
"Is it possible to figure out that a spacetime [region] is curved [instead conformally flat] by testing #CausalRelations only ?"

-- and provides proof of a positive answer through a criterion in terms of causal relations among any set of eight #events (#StitchConfiguration).

Closely related is the question
"Is it possible to figure out whether two (or more) participants are sitting still wrt. each other in a flat region (or whatever is equivalent in a conformally flat region) by testing causal relations only ?",

(referring to the notion of #InertialFrame in the sense of W. Rindler as "set of point particles sitting still wrt. each other"; cmp. http://www.scholarpedia.org/article/Special_relativity:_kinematics),

-- which is presumably solved by #tetrahedral-octahedral #PingCoincidenceLattices, closely related to #OctetTruss #PingCoincidenceLattices; see e.g. https://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycomb and https://www.google.com/search?q=%22octet+truss%22&tbm=isch&prmd=ivnbz

-- and where, notably, eight events in one particular variant of the #StitchConfiguration do indeed occur as integral part of those mentioned #PingCoincidenceLattices (namely, not surprisingly, depicted as #Octahedra in the familiar drawings of the corresponding "plain 3D" lattices).

#Relativity #Spacetime

Asymmetry Detected in the Distribution of #Galaxies

https://www.quantamagazine.org/asymmetry-detected-in-the-distribution-of-galaxies-20221205/

Two new studies suggest that certain #tetrahedral arrangements of galaxies outnumber their mirror images, potentially reflecting details of the #universe’s birth. But confirmation is needed.