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Re: Things You've Been Doing Other Than CGoL
Posted: March 28th, 2017, 4:05 pm
by _zM
4 and 25 then, or 8 and 125, or 40 and 25, the list goes on.
Re: Things You've Been Doing Other Than CGoL
Posted: March 28th, 2017, 10:23 pm
by gameoflifeboy
But if either of the numbers ends in 0, the case degenerates into another case because zeroes at the end of a terminating decimal expansion can be dropped. Furthermore, if the decimal expansion of 1/n consists of an integer beyond the decimal point, 1/(10*n) will have the same integer. If we want a one-to-one (and self-inverse) correspondence between integers and the integer in the decimal expansion of their reciprocals, we need to drop anything divisible by 10. This leaves only the powers of 2 and the powers of 5.
If a natural number has only 2 and 5 as prime factors, its reciprocal has a decimal expansion that ends after a finite number of digits. If it is divisible by 2 or 5 but has other prime factors too, its reciprocal consists of non-repeating digits followed by repeating digits. Otherwise, its reciprocal consists only of repeating digits.
Re: Things You've Been Doing Other Than CGoL
Posted: April 2nd, 2017, 4:04 pm
by muzik
Reddit's /r/place thing is kinda fun.
Re: Things You've Been Doing Other Than CGoL
Posted: April 2nd, 2017, 5:07 pm
by Kazyan
muzik wrote:Reddit's /r/place thing is kinda fun.
For giggles, I'm going to try to put a glider with its upper left corner at (255, 866) like so. Others are welcome to help if they have an account and care. Use the lighter shade of gray for the gridlines, white for blank cells, and black for the glider itself.
Code: Select all
x = 10, y = 10, rule = LifeHistory
10F$F2CF2.F2CF$F2CF2.F2CF$10F$F2CF2CF2.F$F2CF2CF2.F$10F$F2.F2.F2.F$F
2.F2.F2.F$10F!
Re: Things You've Been Doing Other Than CGoL
Posted: April 3rd, 2017, 4:33 pm
by muzik
It's over....
All hail the Green Lattice.
Re: Things You've Been Doing Other Than CGoL
Posted: April 3rd, 2017, 6:49 pm
by Mr. Missed Her
Re: Things You've Been Doing Other Than CGoL
Posted: April 4th, 2017, 12:49 pm
by gameoflifemaniac
I'm memorizing pi. Here are 270 digits from memory. Quote this when I've made a mistake.
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196
4428810975665933446128475648233786783165271201909134603486104564856692...
How many digits can you do?
Re: Things You've Been Doing Other Than CGoL
Posted: April 4th, 2017, 1:28 pm
by gameoflifeboy
The digits "3460348610" near the end should go after "4564856692", but otherwise I can't find a mistake. The next digits are "4543266482133936072602419(?)" (I'm not sure about the last digit or two.)
I know the first 290ish digits of pi. Most of them I memorized before I turned 13. (It was easier then.) I can also whistle them as notes, where 0 is a rest, and 1 through 9 are the notes on a major scale, starting with the tonic and going up to the 2nd one octave higher.
Re: Things You've Been Doing Other Than CGoL
Posted: April 4th, 2017, 5:07 pm
by drc
I can do 70.
Re: Things You've Been Doing Other Than CGoL
Posted: April 4th, 2017, 9:48 pm
by dvgrn
drc wrote:I can do 70.
I never got all that much further than that. I started working on it because of a goal that Douglas Hofstadter mentioned somewhere or other, of getting to the "999999" somewhere in the high hundreds. It still doesn't seem impossible, but other goals are apparently more important...!
My high point for pi was somewhere around 150, a decade ago -- I recognize "812848111" but everything beyond looks unfamiliar. At the moment the uncertainty sets in around digit #125. But I've recited the first hundred often enough that I'll probably never forget them.
I've always found rhyming text -- or at least metered text, like Shakespearean blank verse or James Thurber's _The Thirteen Clocks_ -- to be enormously easier to memorize than either plain prose or long strings of numbers. Starting around age 12 I tried memorizing longer and longer pieces of poetry -- or maybe "doggerel" would be more accurate. The longest effort was Lewis Carroll's _The Hunting of the Snark_.
Re: Things You've Been Doing Other Than CGoL
Posted: April 5th, 2017, 10:36 am
by Mr. Missed Her
Messing around with
Elemental 3. It has a lot of typhoons.
(2048 typhoons to rule them all)
Re: Things You've Been Doing Other Than CGoL
Posted: April 5th, 2017, 10:39 am
by Rhombic
dvgrn wrote: The longest effort was Lewis Carroll's _The Hunting of the Snark_.
The whole thing?!
Re: Things You've Been Doing Other Than CGoL
Posted: April 6th, 2017, 9:04 am
by gameoflifemaniac
dvgrn wrote:drc wrote:I can do 70.
I never got all that much further than that. I started working on it because of a goal that Douglas Hofstadter mentioned somewhere or other, of getting to the "999999" somewhere in the high hundreds. It still doesn't seem impossible, but other goals are apparently more important...!
My high point for pi was somewhere around 150, a decade ago -- I recognize "812848111" but everything beyond looks unfamiliar. At the moment the uncertainty sets in around digit #125. But I've recited the first hundred often enough that I'll probably never forget them.
I've always found rhyming text -- or at least metered text, like Shakespearean blank verse or James Thurber's _The Thirteen Clocks_ -- to be enormously easier to memorize than either plain prose or long strings of numbers. Starting around age 12 I tried memorizing longer and longer pieces of poetry -- or maybe "doggerel" would be more accurate. The longest effort was Lewis Carroll's _The Hunting of the Snark_.
The six nines in pi, also called the Feynman point, starts at the 762nd digit.
So you can recite pi saying: 'blah,blah,pseudorandomdigits,999999 and so on
'
Re: Things You've Been Doing Other Than CGoL
Posted: April 6th, 2017, 9:06 am
by gameoflifemaniac
But worst thing is, that once I knew 475 digits of pi.
Re: Things You've Been Doing Other Than CGoL
Posted: April 14th, 2017, 5:15 pm
by muzik
A for awesome wrote:A for awesome wrote:I've lately become interested in
Googlewhacks, and I think I hold the third-highest score in the world (multiplying the number of Google hits for each individual word) with "bad hectobXXXoride" (the XXX is to keep this page from appearing on Google searches).
Just broke my high score and the world record with "bad octadecatXXXetraene", which scores over a trillion.
...and it seems that this one is no longer the case.
Re: Things You've Been Doing Other Than CGoL
Posted: April 19th, 2017, 9:37 am
by gameoflifemaniac
Practicing Theory of FirePower in Geometry Dash. My progress is 43%! And for information, muzik, my name in GD is Illuminati65.
Re: Things You've Been Doing Other Than CGoL
Posted: April 19th, 2017, 11:12 am
by muzik
Cool beans.
Couple of thoughts I had:
- Could a pentagram be technically seen as a compound of two 2.5-gons in their dual positions?
- Why isn't the compound of two tetrahedra considered to be a regular polyhedron alongside the other four regular stars?
Re: Things You've Been Doing Other Than CGoL
Posted: April 19th, 2017, 12:48 pm
by gameoflifeboy
muzik wrote:- Could a pentagram be technically seen as a compound of two 2.5-gons in their dual positions?
No, because "technically" there is no such thing as a 2.5-gon. The pentagram is called a 5/2-gon, but that's just because its number of sides divided by its density equals 5/2. You could construct something by tracing halfway around a pentagram, but it wouldn't be a polygon anymore because it didn't close.
muzik wrote:- Why isn't the compound of two tetrahedra considered to be a regular polyhedron alongside the other four regular stars?
Because one of the criteria in the definition of a polytope is that it be properly connected, i.e., every element is accessible from every other element. It still is regular, though; check this
list of regular compounds.
(an aside: I would say that the compounds of 5 cubes and of 5 octahedra are not technically regular, as the symmetry of each component doesn't carry over into the full shape. To see what I mean, imagine selecting just one polyhedron from the compound and making the others into edge skeletons or something--the resulting figure would not have cuboctahedral symmetry. Similarly, it might be argued that the compounds of 5 and 10 tetrahedra are not technically regular, as their omnitruncates are no longer vertex transitive (because the reflectional symmetry of each tetrahedron doesn't appear in the compound).)
Re: Things You've Been Doing Other Than CGoL
Posted: April 19th, 2017, 3:59 pm
by muzik
Well, theoretically a 2.5-gon I meant to say. It would be some degenerate shape after all.
Re: Things You've Been Doing Other Than CGoL
Posted: April 21st, 2017, 4:01 pm
by muzik
gameoflifeboy wrote:muzik wrote:- Why isn't the compound of two tetrahedra considered to be a regular polyhedron alongside the other four regular stars?
Because one of the criteria in the definition of a polytope is that it be properly connected, i.e., every element is accessible from every other element. It still is regular, though; check this
list of regular compounds.
So is a small stellated dodecahedron to a stella octangula like a pentagram to a hexagram?
Re: Things You've Been Doing Other Than CGoL
Posted: April 21st, 2017, 6:52 pm
by gameoflifeboy
muzik wrote:So is a small stellated dodecahedron to a stella octangula like a pentagram to a hexagram?
Not quite. The triangles on the stella octangula don't pair up into hexagrams, and the vertex figure is a triangle whereas the small stellated dodecahedron's vertex figure is a pentagon.
I think that the best analogy would be a shape where the pentagonal vertex figure of the small stellated dodecahedron becomes a hexagon, and the pentagrammic faces become hexagrammic. Now, these hexagrams would be pairs of equilateral triangles in a compound, so we can start by realizing that a
triangular tiling has a hexagonal vertex figure and triangular faces. So we know our shape must be a compound of triangular tilings. Next, we take each triangle in the tiling and turn it into a hexagram by overlaying another triangular tiling rotated 180 degrees. When we do this to just one triangle it looks like this:
https://upload.wikimedia.org/wikipedia/ ... ilings.png
We can see that half of the triangles in our original tiling are already part of hexagrams. Now we need to add just one more tiling to make every triangle part of a hexagram:
https://upload.wikimedia.org/wikipedia/ ... ilings.png
The resulting figure has hexagrammic faces and hexagonal vertices, so it seems like the best hexagonal-symmetry analog of the small stellated dodecahedron.
Re: Things You've Been Doing Other Than CGoL
Posted: April 23rd, 2017, 9:53 am
by Saka
Re: Things You've Been Doing Other Than CGoL
Posted: April 23rd, 2017, 10:20 am
by praosylen
Trying to figure out how to query
TAPVizieR to find brown dwarf candidates in existing data. So far I haven't completely figured it out.
Re: Things You've Been Doing Other Than CGoL
Posted: May 7th, 2017, 6:49 am
by gameoflifemaniac
Damn! I'm banned from Geometry Dash!
Re: Things You've Been Doing Other Than CGoL
Posted: May 10th, 2017, 4:52 am
by gameoflifemaniac
