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| Here's a list of hits and near misses. The first hit is (43+0)(43+4) = 2021. The first near miss is (53+0)(53+8) = 3233. {{43,{0,4}}, {4999493,{0,14}}, {891077215721081784886888257701070827,{0,2}},... |
| Awhile ago we added GraphData[{"UnitDistance", {21, 2}}] to Mathematica. Graph[GraphData[{"UnitDistance", {21, 2}}], VertexLabels -> "Name"] ![heptagon bracing][1] I found the graph while researching unit-distance graphs... |
| Todd, how would the 3D diagonal CA be set up? It seems obvious that we should find out if a "1D" cellular automaton can build a menger sponge. |
| Missing—one square to four, or one equilateral triangle to four. How about one square to five? AlgebraicSubstitutionTiling[{1,{{-3,-1},{-3,1},{-1,-3},{-1,-1},{-1,1},{-1,3},{1,-3},{1,-1},{1,1},{1,3},{3,-1},{3,1}}, {{1,6,12,7}->... |
| Could this be used to make the [plesiohedra][1]? [1]: https://refubium.fu-berlin.de/handle/fub188/10176 |
| I fixed the links... [https://demonstrations.wolfram.com/MrsPerkinssQuilts/][1] [1]: https://demonstrations.wolfram.com/MrsPerkinssQuilts/ |
| FiniteGroupData is missing a few group generations, so I've filled in some holes. One of the groups is Frobenius 21. ... |
| What is the smallest set so that differences of members of the set give all values from $1$ to $n$? This is a famous problem worked on by [Paul Erd?s](https://en.wikipedia.org/wiki/Paul_Erd%C5%91s), [Marcel J. E.... |
| How to solve something like this? Consider the problem of covering the largest possible equilateral triangle with two unit squares. I make a sketch in Geometer's Sketchpad first. ![two squares][1] Then put the equations right into... |
| Manipulate[Module[{sol2}, sol2=ParametricNDSolve[{x'[t]==Cos[t],y'[t]==Sin[t],z'[t]==b*1/4,x[0]==0,y[0]==1,z[0]==0},{x,y,z},{t,0,100},{a}]; ... |