Polytopia : Messages : 34-63 of 1736

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34		Jon Perry jon_perryuk	Sep 4, 2002 8:28 pm
	As a newbie to this list, I would like to ask a question: Given a cube, a path is defined as starting at a point, and we travel to another point. We are only...
35		berglunddj@... berglunddj	Sep 5, 2002 12:14 pm
	Welcome Jon, In a message dated 9/4/2002 3:29:03 PM Central Daylight Time, ... I'm assuming that you want to visit all 8 vertices and return home. Let's take...
36		Edward Moore emoore06905	Sep 5, 2002 5:36 pm
	As far as further dimensions go with the cube (hypercube), I would think the form stands. When dimension is 3, the formula is MaxLength = 2^(D-1) * ((sqrt(D)...
37		Jon Perry jon_perryuk	Sep 6, 2002 7:29 pm
	Both answers so far are correct - keep up the good work. Here's another conjecture: Does every longest path in n-dimensional space necessary include the...
38		Jon Perry jon_perryuk	Sep 8, 2002 11:35 am
	... longest ... I found a counter-example: http://www.users.globalnet.co.uk/~perry/maths/longestpath/longestpath.htm Jon Perry perry@... ...
39		berglunddj@... berglunddj	Sep 8, 2002 12:12 pm
	Hi, I did some more thinking on the general problem of the longest circuit of the vertices of a brick. Say that the hwd brick has two of its vertices at...
40		Jon Perry jon_perryuk	Sep 8, 2002 6:30 pm
	... interesting. I hadn't noticed that this is a restricted form of the traveling salesman problem where we are trying to maximize lengths instead. I don't...
41		Jon Perry jon_perryuk	Sep 8, 2002 8:59 pm
	Can a graph ever possess the property that the shortest path doesn't contain the shortest line segment, and also that the the longest path doesn't contain the...
42		Jon Perry jon_perryuk	Sep 9, 2002 6:35 pm
	Can someone explain the Happy End problem to me? http://mathworld.wolfram.com/HappyEndProblem.html Are there rules as to how a graph can be constructed? Jon...
43		berglunddj@... berglunddj	Sep 10, 2002 11:03 am
	Hi, In a message dated 9/9/2002 1:37:02 PM Central Daylight Time, ... You will be given a certain number n for the polygon. You will place non-colinear points...
44		Jon Perry jon_perryuk	Sep 10, 2002 6:36 pm
	What if I place the vertices and edges like this: 1 2 * 3 4 5 i.e. there is an arrowhead formed by 2,3,4,5 and 1 flanks one side of...
45		Paul Erlich emotionaljou...	Sep 11, 2002 9:26 pm
	... of the ... 1234 is convex. 1253 is convex....
46		Jon Perry jon_perryuk	Sep 11, 2002 9:28 pm
	Well, 2 and 5 aren't connected, so bang goes that one. And I was lead to believe that the polygon's must be 'whole'. Jon Perry perry@... ...
47		Jon Perry jon_perryuk	Sep 11, 2002 9:32 pm
	at: http://www.users.globalnet.co.uk/~perry/maths/barnette/barnette.htm It's got 28 points, so I may be wrong. Jon Perry perry@... ...
48		Jon Perry jon_perryuk	Sep 11, 2002 9:34 pm
	Can anyone think of a conjecture that involed graphs that use a curved line. e.g. 1,2,3,4 is a square, 12,23,34,14 are edges, as are 24 and 13. As the graph is...
49		Paul Erlich emotionaljou...	Sep 11, 2002 10:31 pm
	... you're supposed to consider all the possible ways of connecting the points in the happy end problem. ... huh?...
50		Jon Perry jon_perryuk	Sep 12, 2002 5:10 pm
	... That means we can always create triangles, but no whole quads. A whole quad is a quadrilateral with no edges inside it. Jon Perry perry@... ...
51		asathaxx@... keith_carlock	Sep 12, 2002 6:37 pm
	First here is my standard summary:"I invented invisibility and holodeck technology,both are one and the same things.Both require 3-Dimensional ...
52		asathaxx@... keith_carlock	Sep 12, 2002 6:50 pm
	These are pics of my Lenticular Box.It is not actually Lenticular,but it is my modification of Victorian picture puzzle art that preceeded today's Lenticular...
53		asathaxx@... keith_carlock	Sep 12, 2002 6:59 pm
	The top picture is of my mini-Lenticular Cube with 4 newly added view angles per side,giving 8 new views from each corner where 3 sides meet to create a ...
54		Jon Perry jon_perryuk	Sep 12, 2002 7:35 pm
	The old one was flawed, but this one is better - 22 points: http://www.users.globalnet.co.uk/~perry/maths/barnette/barnette.htm Jon Perry perry@......
55		Paul Erlich emotionaljou...	Sep 12, 2002 10:02 pm
	... the ... you're also free to not connect any given pair of points....
56		polychoron	Sep 13, 2002 3:50 am
	This is a great tool for making models of polyhedra. http://home.connexus.net.au/~robandfi/Stella.html...
57		Jon Perry jon_perryuk	Sep 13, 2002 5:11 pm
	Thanks. I understood it eventually. So what's the problem with it? Is the general idea that g(n)=2^(n-2)+1? Jon Perry perry@... ...
58		Paul Erlich emotionaljou...	Sep 13, 2002 8:30 pm
	... +1? if you look again at the website, you'll see that it's not quite so simple . . . unless of course you've somehow outwitted all the mathematicians who...
59		berglunddj@... berglunddj	Sep 13, 2002 11:20 pm
	Hi, Your design sounds plausible, if you have a way to ensure that the angle of the light incident on the outer sphere is identical with the angle of the light...
60		berglunddj@... berglunddj	Sep 13, 2002 11:21 pm
	Hi, all. Oops. I sent my reply to all instead of just the originator. Sorry. John...
61		Keith Jason Carlock D... keith_carlock	Sep 14, 2002 10:37 pm
	Check it out,then join my group at http://groups.yahoo.com/group/iinventedinvisibility...
62		Jon Perry jon_perryuk	Sep 22, 2002 5:22 pm
	A couple of smaller counter-examples (hopefully): http://www.users.globalnet.co.uk/~perry/maths/barnette/barnette.htm See:My latest 'counter-examples' - but do...
63		Jon Perry jon_perryuk	Nov 10, 2002 6:56 pm
	Interesting group extension to the thrackle idea, (at the end of the page). http://www.users.globalnet.co.uk/~perry/maths/thrackle/thrackle.htm Jon Perry ...

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