Interesting math stuff

[Marjamjelly]

I am interested in recreational mathematics and am looking for other just cool/fun ath related things like cgol, four fours, square packing, etc.

I don’t know what this genre is called or really how to describe it but I want help because any searches just yield things made for children.

[confocaloid]

I am interested in recreational mathematics and am looking for other just cool/fun ath related things like cgol, four fours, square packing, etc.

I don’t know what this genre is called or really how to describe it but I want help because any searches just yield things made for children.

I don't know whether these "count" for your needs, but anyways, here are some interesting topics:

• viewtopic.php?f=11&t=6015 HatLife
• viewtopic.php?f=11&t=5759 DominoLife
• viewtopic.php?f=12&t=5528 Geometry question about ellipse packing
• viewtopic.php?f=12&t=6097 Math biopics I'd like to see
• viewtopic.php?f=12&t=3978 Polyominoes
• viewtopic.php?f=12&t=3036 Polyomino tilings
• viewtopic.php?p=186249#p186249 Spectre Tiles in Golly

[d/dx]

I don't know if this will satisfy what you want, but fun fact:

If you take an n x n square and fill it with the words A1, A2... B1,... C1... such that every letter and number appears exactly once in a row, with no words repeating, you'll have created a Greek-Latin square.

You can't make a Greek-Latin square for n=6. Try!

[confocaloid]

I am interested in recreational mathematics [...]
[...] any searches just yield things made for children.

Here are some more links:
https://erich-friedman.github.io/packing/index.html "Erich's Packing Center"
https://ics.uci.edu/~eppstein/junkyard/sphere.html "The Geometry Junkyard: Circles and Spheres"

Many problems can be stated in such a way that an interested reader can understand what is the problem (even though it might be extremely hard to solve it). There are examples from geometry, number theory, graph theory, combinatorics. This is a vast subject. To quote from David Singmaster's "The unreasonable utility of recreational mathematics":

[...]
To begin with, it is worth considering what is meant by recreational mathematics. An obvious definition is that it is mathematics that is fun, but almost any mathematician will say that he enjoys his work, even if he is studying eigenvalues of elliptic differential operators, so this definition would encompass almost all mathematics and hence is too general. There are two, somewhat overlapping, definitions that cover most of what is meant by
recreational mathematics.

First, recreational mathematics is mathematics that is fun and popular - that is, the problems should be understandable to the interested layman, though the solutions may be harder. (However, if the solution is too hard, this may shift the topic from recreational toward the serious - e.g. Fermat's Last Theorem, the Four Colour Theorem or the Mandelbrot Set.)

Secondly, recreational mathematics is mathematics that is fun and used as either as a diversion from serious mathematics or as a way of making serious mathematics understandable or palatable. These are the pedagogic uses of recreational mathematics. They are already present in the oldest known mathematics and continue to the present day.
[...]

[confocaloid]

How many still life patterns can be made by arranging 64 instances of eater 1 in a 8-by-8 grid, like the example below?
A simple upper bound is 8^64 = 6277101735386680763835789423207666416102355444464034512896 (each of 64 objects can be oriented in one of 8 possible ways), but the actual number must be way lower, because many of those 8^64 patterns are not still lives.

Code: Select all

x = 39, y = 39, rule = B3/S23
o6b2ob2o3bo6b2ob2o3bo4b2o$3o5bobobo2b3o5bobobo2b3o3bo$3bob3o4bo5bob3o
4bo5bo2bobo$2b2obo6b2o3b2obo6b2o3b2o3b2o2$2b2obo6b2o3b2obo6b2o3b2o3b2o
$3bob3o5bo2bobob3o5bo2bobo2bobo$3o5bob3o3bo6bob3o3bo4bo$o6b2obo4b2o5b
2obo4b2o3b2o2$o6b2obo4b2o5b2obo4b2o3b2o$3o5bob3o3bo6bob3o3bo4bo$3bob3o
5bo2bobob3o5bo2bobo2bobo$2b2obo6b2o3b2obo6b2o3b2o3b2o2$2b2obo6b2o3b2ob
o6b2o3b2o3b2o$bobob3o5bo2bobob3o5bo2bobo2bobo$bo6bob3o3bo6bob3o3bo4bo$
2o5b2obo4b2o5b2obo4b2o3b2o2$2o5b2obo4b2o5b2obo4b2o3b2o$bo6bob3o3bo6bob
3o3bo4bo$bobob3o5bo2bobob3o5bo2bobo2bobo$2b2obo6b2o3b2obo6b2o3b2o3b2o
2$2b2obo6b2o3b2obo6b2o3b2o3b2o$3bob3o5bo2bobob3o5bo2bobo2bobo$3o5bob3o
3bo6bob3o3bo4bo$o6b2obo4b2o5b2obo4b2o3b2o2$o6b2obo4b2o5b2obo4b2o3b2o$
3o5bob3o3bo6bob3o3bo4bo$3bob3o5bo2bobob3o5bo2bobo2bobo$2b2obo6b2o3b2ob
o6b2o3b2o3b2o2$2b2obo6b2o3b2obo6b2o3b2o3b2o$bobob3o5bo2bobob3o5bo2bobo
2bobo$bo6bob3o3bo6bob3o3bo4bo$2o5b2obo4b2o5b2obo4b2o3b2o!

Code: Select all

x = 39, y = 39, rule = LifeHistory
C3D.2D2C.2C2D.C3D.2D2C.2C2D.C3D.2C2D$3CD.3DC.CDCD.3CD.3DC.CDCD.3CD.DC
2D$3DC.3CD.2DCD.3DC.3CD.2DCD.3DC.DCDC$2D2C.C3D.2D2C.2D2C.C3D.2D2C.2D
2C.2D2C2$2D2C.C3D.2D2C.2D2C.C3D.2D2C.2D2C.2D2C$3DC.3CD.3DC.DCDC.3CD.
3DC.DCDC.DCDC$3CD.3DC.3CD.DC2D.3DC.3CD.DC2D.DC2D$C3D.2D2C.C3D.2C2D.2D
2C.C3D.2C2D.2C2D2$C3D.2D2C.C3D.2C2D.2D2C.C3D.2C2D.2C2D$3CD.3DC.3CD.DC
2D.3DC.3CD.DC2D.DC2D$3DC.3CD.3DC.DCDC.3CD.3DC.DCDC.DCDC$2D2C.C3D.2D2C
.2D2C.C3D.2D2C.2D2C.2D2C2$2D2C.C3D.2D2C.2D2C.C3D.2D2C.2D2C.2D2C$DCDC.
3CD.3DC.DCDC.3CD.3DC.DCDC.DCDC$DC2D.3DC.3CD.DC2D.3DC.3CD.DC2D.DC2D$2C
2D.2D2C.C3D.2C2D.2D2C.C3D.2C2D.2C2D2$2C2D.2D2C.C3D.2C2D.2D2C.C3D.2C2D
.2C2D$DC2D.3DC.3CD.DC2D.3DC.3CD.DC2D.DC2D$DCDC.3CD.3DC.DCDC.3CD.3DC.D
CDC.DCDC$2D2C.C3D.2D2C.2D2C.C3D.2D2C.2D2C.2D2C2$2D2C.C3D.2D2C.2D2C.C
3D.2D2C.2D2C.2D2C$3DC.3CD.3DC.DCDC.3CD.3DC.DCDC.DCDC$3CD.3DC.3CD.DC2D
.3DC.3CD.DC2D.DC2D$C3D.2D2C.C3D.2C2D.2D2C.C3D.2C2D.2C2D2$C3D.2D2C.C3D
.2C2D.2D2C.C3D.2C2D.2C2D$3CD.3DC.3CD.DC2D.3DC.3CD.DC2D.DC2D$3DC.3CD.
3DC.DCDC.3CD.3DC.DCDC.DCDC$2D2C.C3D.2D2C.2D2C.C3D.2D2C.2D2C.2D2C2$2D
2C.C3D.2D2C.2D2C.C3D.2D2C.2D2C.2D2C$DCDC.3CD.3DC.DCDC.3CD.3DC.DCDC.DC
DC$DC2D.3DC.3CD.DC2D.3DC.3CD.DC2D.DC2D$2C2D.2D2C.C3D.2C2D.2D2C.C3D.2C
2D.2C2D!