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RE: Post making contest 6.0
10-10-2017, 03:13 AM
(This post was last modified: 10-10-2017, 04:59 PM by Ixcaliber.)
(10-10-2017, 02:00 AM)Schazer Wrote: »:woahtermelon:
Passes no rules
(10-10-2017, 02:25 AM)Wheat Wrote: »:dog:
Passes rule 2
(10-10-2017, 02:28 AM)a52 Wrote: »In the mathematical area of knot theory, the unknotting number of a knot is the minimum number of times the knot must be passed through itself (crossing switch) to untie it. If a knot has unknotting number {\displaystyle n} n, then there exists a diagram of the knot which can be changed to unknot by switching {\displaystyle n} n crossings.[1] The unknotting number of a knot is always less than half of its crossing number.[2]
Any composite knot has unknotting number at least two, and therefore every knot with unknotting number one is a prime knot. The following table show the unknotting numbers for the first few knots:
Trefoil knot
unknotting number 1
Figure-eight knot
unknotting number 1
Cinquefoil knot
unknotting number 2
Three-twist knot
unknotting number 1
Stevedore knot
unknotting number 1
6₂ knot
unknotting number 1
6₃ knot
unknotting number 1
7₁ knot
unknotting number 3
In general, it is relatively difficult to determine the unknotting number of a given knot. Known cases include:
The unknotting number of a nontrivial twist knot is always equal to one.
The unknotting number of a {\displaystyle (p,q)} (p,q)-torus knot is equal to {\displaystyle (p-1)(q-1)/2} (p-1)(q-1)/2.
The unknotting numbers of prime knots with nine or fewer crossings have all been determined.[3] (The unknotting number of the 1011 prime knot is unknown.)
Contents
Other numerical knot invariants Edit
Crossing number
Bridge number
Linking number
Stick number
See also Edit
Unknotting problem
References Edit
^ Adams, Colin Conrad (2004). The knot book: an elementary introduction to the mathematical theory of knots. Providence, Rhode Island: American Mathematical Society. p. 56. ISBN 0-8218-3678-1.
^ Taniyama, Kouki (2009), "Unknotting numbers of diagrams of a given nontrivial knot are unbounded", Journal of Knot Theory and its Ramifications, 18 (8): 1049–1063, MR 2554334, doi:10.1142/S0218216509007361.
^ Weisstein, Eric W. "Unknotting Number". MathWorld.
External links Edit
"Three_Dimensional_Invariants#Unknotting_Number", The Knot Atlas.
Last edited 7 days ago by Hyacinth
RELATED ARTICLES
Knot theory
study of mathematical knots
List of mathematical knots and links
Wikimedia list article
Crossing number (knot theory)
integer-valued knot invariant; least number of crossings in a knot diagram
Wikipedia
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I'm gonna say this post passes rule 1. It was a little tricky to call for reasons but I think it passes. Also rule 2 as well.
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RE: Post making contest 6.0
10-10-2017, 03:33 AM
Alpha Beta Cranberry Delta
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RE: Post making contest 6.0
10-10-2017, 05:09 AM
You say Gamma, I say Cranberry.
A character on fire WOULDN'T say "I am cold."
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RE: Post making contest 6.0
10-10-2017, 05:23 AM
I've finally taken the time to really dig in and understand SU(2) and SO(3), and I have to say, it's fucking awesome. This is definitely one of my new favorite things. I mean look at this shit, somehow numbers like this:
[a + bi, -c+di]
[c + di, a - bi]
Are the same thing as numbers like this (!):
w + xi + yj + kz
Which are the same thing as good ol' ordinary rotation matrices (but twice!):
[angles, numbers, sin()]
[theta, stuff, 0]
[cos(-x), -1, 3] (rotation matrices are a pain to write)
Honestly even just the fact that the first type stays as the first type is really cool, let alone that it's a valid interpretation of quaternions. From their I knew that quaternions could represent positions/rotations in 3D space, but I had no idea that there was that extra half, or that that extra sign was what led to spinors, and in turn, the entire concept of half-integer spin in general, and from there, the concepts of mass and the pauli exclusion principle!!!!!!!
and since the whole SU(2)/SO(3) thing only really happens in 2 & 3 dimensions, I think that means that half-integer spin, and therefore massive particles, might only be possible in universes with three dimensions! or vice versa, their very existence is what the dimensions come from in the first place
fuck me this is so cool
Fairly Intelligent Foxie Hivemind
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RE: Post making contest 6.0
10-10-2017, 07:13 AM
(This post was last modified: 10-10-2017, 05:00 PM by Ixcaliber.)
(10-10-2017, 05:23 AM)a52 Wrote: »I've finally taken the time to really dig in and understand SU(2) and SO(3), and I have to say, it's fucking awesome. This is definitely one of my new favorite things. I mean look at this shit, somehow numbers like this:
[a + bi, -c+di]
[c + di, a - bi]
Are the same thing as numbers like this (!):
w + xi + yj + kz
Which are the same thing as good ol' ordinary rotation matrices (but twice!):
[angles, numbers, sin()]
[theta, stuff, 0]
[cos(-x), -1, 3] (rotation matrices are a pain to write)
Honestly even just the fact that the first type stays as the first type is really cool, let alone that it's a valid interpretation of quaternions. From their I knew that quaternions could represent positions/rotations in 3D space, but I had no idea that there was that extra half, or that that extra sign was what led to spinors, and in turn, the entire concept of half-integer spin in general, and from there, the concepts of mass and the pauli exclusion principle!!!!!!!
and since the whole SU(2)/SO(3) thing only really happens in 2 & 3 dimensions, I think that means that half-integer spin, and therefore massive particles, might only be possible in universes with three dimensions! or vice versa, their very existence is what the dimensions come from in the first place
fuck me this is so cool
Passes rule 2, this is the only rule that has been passed in the above posts.
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RE: Post making contest 6.0
10-10-2017, 11:13 AM
pobody's nerfect!
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RE: Post making contest 6.0
10-10-2017, 12:51 PM
(10-10-2017, 07:13 AM)Ixcaliber Wrote: »nobody passed anything
Not even gas?
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RE: Post making contest 6.0
10-10-2017, 02:03 PM
(10-10-2017, 11:13 AM)Schazer Wrote: »pobody's nerfect!
Passes no rules
(10-10-2017, 12:51 PM)Dragon Fogel Wrote: » (10-10-2017, 07:13 AM)Ixcaliber Wrote: »nobody passed anything
Not even gas?
Passes rule 3
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RE: Post making contest 6.0
10-10-2017, 03:50 PM
ABCDEFGHIJKLMNOPQRSTUVWXYΩ
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RE: Post making contest 6.0
10-10-2017, 04:17 PM
(10-10-2017, 03:50 PM)Akumu Wrote: »ABCDEFGHIJKLMNOPQRSTUVWXYΩ
No rules are passed though I approve of the use of the (semi) canon alphabet.
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RE: Post making contest 6.0
10-10-2017, 04:46 PM
I kick ur rules
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RE: Post making contest 6.0
10-10-2017, 04:46 PM
Winner winner chicken dinner
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RE: Post making contest 6.0
10-10-2017, 04:57 PM
I'm just gonna... quietly... change rule 2 just a touch for the reason that whoops i made it too restrictive.
Posts that now pass rule 2 that didn't:
Posts that did pass rule 2 but now don't:
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RE: Post making contest 6.0
10-10-2017, 05:02 PM
(10-10-2017, 04:46 PM)Myeth Wrote: »I kick ur rules
oof ouch not my rules. you don't pass any here
(10-10-2017, 04:46 PM)Myeth Wrote: »Winner winner chicken dinner
no rules passed
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RE: Post making contest 6.0
10-10-2017, 05:11 PM
:<dog>:
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RE: Post making contest 6.0
10-10-2017, 05:13 PM
>:(
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RE: Post making contest 6.0
10-10-2017, 05:14 PM
(10-10-2017, 05:11 PM)Akumu Wrote: »:<dog>:
No rules passed
(10-10-2017, 05:13 PM)Myeth Wrote: »>:(
Ditto
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RE: Post making contest 6.0
10-10-2017, 05:24 PM
:dog:
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RE: Post making contest 6.0
10-10-2017, 05:29 PM
(10-10-2017, 05:24 PM)Akumu Wrote: »:dog:
no rules passed
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RE: Post making contest 6.0
10-10-2017, 06:04 PM
:frick:
A character on fire WOULDN'T say "I am cold."
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RE: Post making contest 6.0
10-10-2017, 06:36 PM
(10-10-2017, 06:15 AM)Wheat Wrote: »five is bigger number than four.
well, most of the time
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RE: Post making contest 6.0
10-10-2017, 07:49 PM
Probably gonna end up inactive again
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RE: Post making contest 6.0
10-10-2017, 08:01 PM
rainbow
oh hey
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RE: Post making contest 6.0
10-11-2017, 05:10 AM
(10-10-2017, 06:04 PM)Myeth Wrote: »:frick:
Passes no rules
(10-10-2017, 06:36 PM)a52 Wrote: » (10-10-2017, 06:15 AM)Wheat Wrote: »five is bigger number than four.
well, most of the time
Passes no rules
(10-10-2017, 07:49 PM)Akumu Wrote: »
Passes no rules
(10-10-2017, 08:01 PM)SinkingSailor Wrote: »rainbow
Good post. Passes rule 3.
Probably gonna end up inactive again
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RE: Post making contest 6.0
10-11-2017, 12:21 PM
woah.
I'm floating.
oh hey
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