# User talk:Tamfang

## Figure 8 Klein bottle

... curl it to bring the edge to the midline; since there is only one edge, it will meet itself there, passing through the midline.

Now that is an elegant and pithy description!

## Charging for Doing Homework

I explained some of my reasons for my response to this topic on Meni's talk page, if you're interested. RomanSpa (talk) 21:47, 5 February 2015 (UTC)

## Hypercyclic apereigon?

Hi Anton, could you help with a picture? Could you make a picture of a tiling of divergent apeirogons, like {∞,3}, except larger edge lengths that don't converge at infinity?

I'd like the example for this article Apeirogon#Apeirogons_in_hyperbolic_plane. I could actually use this image File:H2 tiling 2iu-7.png, but it could use more resolution to see more detail near the limit, and might be adjusted a big smaller aperigons so details don't get small quite as fast. Well, I'll use your existing image of tr{∞,iπ/λ} for now, so if you make a new one, you can replace it sometime. Tom Ruen (talk) 18:48, 22 February 2015 (UTC)

commons:User:Tamfang/gallery#Mon Feb 23 14:35:06 PST 2015. I'm not quite clear on what you're asking for. —Tamfang (talk) 22:41, 23 February 2015 (UTC)
Thanks so much! I think I was asking for this regular one, File:H2_tiling_23j-1.png, but it is hard to see with thin lines. So the omnitruncation might be easiest to see File:H2 tiling 23j6-7.png. The divergent one is most wild File:H2 tiling 23j-4.png, divergent "triangle" faces?. I can see why Norman says polytope theory breaks down when you include "pseudogons", {iπ/λ}! So these are all great, but if you can try one more parallel set with a smaller radius still, closer to {∞}, I think it would be helpful. But don't overwrite these, unless you're going to use the alphabet and go progressively from i...z in sequence! So this version might be around t for my sensibilities, can't go much further without losing the kingdom's borders completely. But if you wanted to try more, you could try j,k,l,m and call this original test l? Thanks again! Tom Ruen (talk) 23:51, 23 February 2015 (UTC)
p.s. A blind thought - perhaps one way to parametrized divergent solutions is by the angle between the hypercycle intersection with the poincare disk limit? So straight line (projecting as circles off center of disk) intersect the disk at 90° and apeirogons intersect as a tangent at 0°. So a fun animation of a given uniform tiling could transition forms by the incident angle increments. Tom Ruen (talk) 03:36, 24 February 2015 (UTC)
Omnitruncations with mirrors
tr{∞, 3} tr{12i,3} tr{9i,3} tr{6i,3}
tr{4i,3} tr{3i,3} tr{2i,3} tr{i,3}

Strange things seem to be happening below j5. Tom Ruen (talk) 04:20, 25 February 2015 (UTC)

j1-12, j∞
j1 j2 j3 j4 j5 j6 j7 j8 j9 j10 j11 j12 j∞
1
2
3
4
5
6
7
Checkers

Animation of sequence from 12 downto 1, 1/2 second per frame

 Omnitruncation Mirrors (back-and-forth)
I'd like it better back-and-forth. —Tamfang (talk) 00:23, 26 February 2015 (UTC)
Added checkers animation! (p.s. My editor is treating original transparent background as black now.) Tom Ruen (talk) 22:20, 1 March 2015 (UTC)
p.s. I have no intuition on the numbers here, but does this (x3x(6i)x) at File:H2_tiling_23j6-7.png really mean, π/λ=6, λ=π/6=0.523599..? and similarly for indices 1-12?! Tom Ruen (talk) 10:02, 25 February 2015 (UTC)
Yes. A number n in the symbol means that two mirrors' normal vectors have dot product –cos(π/n); ni thus means that the dot product is –cos(π/ni) = –cosh(π/n). Now, what's λ? Is it the distance between ultraparallel lines? I'm too busy at the moment to check a book for whether ±cosh(λ) is indeed the dot product. —Tamfang (talk) 00:23, 26 February 2015 (UTC)
So maybe (x3x(∞i)x) = (x3x∞x), to approach apeirogonal solution from the imaginary direction? But looks like we need also to explore an animation on the other wild side with more frames at j1, j1.01, j1.04, j1.1, j1.2, j1.3, j1.4... Tom Ruen (talk) 01:20, 26 February 2015 (UTC)
Why? cos(π/∞) = cosh(π/∞), but there's nothing obviously critical about cosh(π). —Tamfang (talk) 01:44, 26 February 2015 (UTC)
Just a guess, since j12 doesn't look to be closed to closing, so a j∞ limit seemed like reasonable guess where it finally closes. And my interest near j1 I'm going to say the pseudogons are turning "inside out", with those new faces are popping out, unless some are artifacts of your calculations, or finite edge widths, or something "real" that needs explaining. Tom Ruen (talk) 02:19, 26 February 2015 (UTC)
A j∞ tiling – i.e., where one of the angles is iπ/∞ – would be the same as the ∞ tilings already illustrated; cos(0i) = cosh(0) = cos(0). —Tamfang (talk) 21:52, 1 March 2015 (UTC)
Added a column for j∞ = ∞ to the table above. Double sharp (talk) 15:32, 3 March 2015 (UTC)
Is it possible the color regions you're assigning in lower values (1-4)*i are flawed or maybe ambiguous where the new domains start appearing, i.e. where pseudogons become "inverted"? Perhaps having the checkerboard domain lines will help clarify? Tom Ruen (talk) 15:33, 26 February 2015 (UTC)
Some such possibility has crossed my mind. —Tamfang (talk) 21:17, 26 February 2015 (UTC)
Looking at Tom's new composites, I see at least part of the problem: my program assumes that the three rays from the vertex to the mirrors will never fall within a semicircle! —Tamfang (talk) 22:06, 1 March 2015 (UTC)
Maybe you can improve those cases? But for now thanks so much for checkers! Tom Ruen (talk) 22:20, 1 March 2015 (UTC)
Here's a MSPaint hand-correction of 2i case. So the inverted pseudogons are still along a hypercycle, but the segment chords bend "outward". Tom Ruen (talk) 23:03, 1 March 2015 (UTC)
If I hadn't already uploaded those, I'd find the critical value and reject troublesome input! —Tamfang (talk) 23:48, 1 March 2015 (UTC)
It's more clear to me now that there's no limit to "troublesome input", but simply the location of the pseudogon. If you translate the view center, you'd see the effect on any tiling with a pseudogon. Tom Ruen (talk) 05:29, 3 March 2015 (UTC)
Ha? The mapping conserves angles. If the internal angle of the red area exceeds π at one viewpoint, it'll exceed π at any viewpoint. Do you mean move the vertex? —Tamfang (talk) 07:53, 3 March 2015 (UTC)
Okay, I'm wrong. So if you were to do more uniform tilings, you could just stop at 3i or whatever, varying between families and uniform tilings. Still, I wonder if you have a 2-test algorithm, if some regions should be the pseudogons and are wrongly colored in the first test? Tom Ruen (talk) 08:11, 3 March 2015 (UTC)
The algo begins by finding the normal vector to the line through the vertex and perpendicular to each of the mirrors. Then for each pixel: let a,b,c be the dot products of the pixel's vector with each of those critical vectors;
if a>0 and b<0:
blue
else if c>0:
yellow
else:
red
I hadn't looked at that bit of code in years! I guess it needs to be
if a>0 and b<0:
blue
else if c>0 and a<0:
yellow
else:
# (a<0 or b>0) and (c<0 or a>0) = (a<0 and c<0) or (b>0 and c>0),
# one of which is impossible by construction
red
Tamfang (talk) 08:37, 3 March 2015 (UTC)
I'm very happy what you've done already, but please try, at your convenience! Tom Ruen (talk) 22:52, 3 March 2015 (UTC)

I've redone j1 through j4 and will upload sometime soon. —Tamfang (talk) 23:19, 3 March 2015 (UTC)

Excellent! I'll remake a forward/backward animation with the new ones, but please add a few more frames like j1.1 etc for omnitruncation -7 case, if you want a nice movie! Tom Ruen (talk) 23:28, 3 March 2015 (UTC)
Hurray for the corrections. I updated the movie, cycle forward/backwards, but removed j1 frame, too much of a jump without intermediate frames.
The "chess" dual-maps would also be helpful for me to separate independent sets of mirrors.
If you wanted to do another family, 2ij like your original test File:H2_tiling_2iu-7.png seems good. Others of interest 24j for all evens, and 33j for a nonright angle. Also I'd suggest for 2i,3i,4i,6i,12i,24i,48i as a sequence. Tom Ruen (talk) 05:29, 5 March 2015 (UTC)
Or 4i, 8i, 15i, 16i, 23i, 42i —Tamfang (talk) 06:04, 5 March 2015 (UTC)
A joke? I thought 3,6,9,12 are a good selection, and adding 24,48 would get a couple closer to the infinite case. OTOH, perhaps the best selection would change based on family? And I don't have enough information to guess what fractional values between i and 2i would be good. 2i to 3i is already too much of a jump as well. Tom Ruen (talk) 07:06, 5 March 2015 (UTC)
"As you know, I am a Vulgarian and jokes are beyond me." —Tamfang (talk) 09:52, 5 March 2015 (UTC)
Wow, I never heard that before [1], Kwirk and Smock? When I was a kid in the 70's, I had my comic Star Jerks, starring Captain Jerk and First Officer Shock, thought I was original. Tom Ruen (talk) 11:00, 5 March 2015 (UTC)

Oh, a tiny complaint: Edge widths better here File:H2 tiling 23i-1.png than here File:H2 tiling 23j12-1.png etc, although they both flicker out in the limits. Certainly this template images are too small, but often good, like triangular duals. Tom Ruen (talk) 09:32, 5 March 2015 (UTC)

Spherical Euclidean Compact hyperb. Paraco. Noncompact hyperbolic
{2,3} {3,3} {4,3} {5,3} {6,3} {7,3} {8,3} {∞,3} {12i,3} {9i,3} {6i,3} {3i,3}
Spherical Euclid. Compact hyper. Paraco. Noncompact hyperbolic
{3,2} {3,3} {3,4} {3,5} {3,6} {3,7} {3,8} (3,∞} {3,12i} {3,9i} {3,6i} {3,3i}

## help

Now it is asking if one were to do it via a multipxer for Jd and Kd thru Ja and Ka and each gerated by using a multiplexer that is a 8 to 1 line multiplexer for each J and K controll. it says to write down the 8 input lines of each multiplxer, including alternatives. It says the least significant address lines is the ones and is connected to Qa and the most significant the fours, adress line is for each multiplexer is Qc. It states that Qb is connected to the twos adress lines in each case. please helpDoorknob747 (talk) 16:29, 25 March 2015 (UTC)

I know nothing of multiplexers. —Tamfang (talk) 18:01, 25 March 2015 (UTC)

## a user who may need a friend

hello Tamfang this is Dfrr. there is a user named User:Trimethylxanthine who has not been getting any messages from any users but me. in fact only one other user has sent him a message which was when he first came to wikipedia. User:Conifer User:MrWooHoo User:Davejohnsan User:StuRat and many other users have gotten a message kind like this (not exactly like this) to there talk page. so lets send him wikiloves barnstars messages and anything to make him feel that people know about him thank you and have a happy April Dfrr (talk) 09:06, 6 April 2015 (UTC)

## April 2015

Hello, I'm Dennis Bratland. I wanted to let you know that I undid one or more of your recent contributions to Rice burner because it did not appear constructive. If you would like to experiment, please use the sandbox. If you think I made a mistake, or if you have any questions, you can leave me a message on my talk page. Thanks. Dennis Bratland (talk) 15:09, 6 April 2015 (UTC)

## Twin cities

Hi,

I noticed that you reverted my edition, making again Talk:Twin cities a redirect to Talk:Minneapolis–Saint Paul; but, if Twin cities and Minneapolis–Saint Paul are distinct articles, I think that they should have distinct talk pages (instead of the talk page of one redirecting to the talk page of the other)--MiguelMadeira (talk) 10:12, 15 April 2015 (UTC)

Ah, sorry. When someone with a red name blanks a page, my instinct is to revert! —Tamfang (talk) 19:53, 15 April 2015 (UTC)

## Overdrive (mechanics)

Hi, thanks for your efforts to remove "a term used to describe" generally.

Overdrive is tricky though and the article has a long history of a difficult effort to give it a clear lead. The trouble is that "overdrive" has four meanings, all mixed up, and two (maybe three) of these are concepts rather than mechanisms.

It's hard to understand what an overdrive (mechanism) is without first understanding the concept #1 of it, and avoiding the trap of just stating "An overdrive (mechanism #3) is a gadget for making it do overdrive (concept #2)". That's a common definition that's widely given, but it's either inexplicable or actually misleading. We still need to start with concept #1.

If you can assist with any better clarification in the lead, I'm only too aware that it could use it. However I think we are legitimately stuck with "overdrive is a term" for this one, as that's the highest common factor between them. Andy Dingley (talk) 09:24, 20 April 2015 (UTC)