Cevian triangle of the Cevian triangle
Updated: 2012-07-31 13:58:54
Cevian triangle of the Cevian triangle
Hasse Diagrams of Integer Divisors
Updated: 2012-07-31 13:58:43
8091 TOPICS LATEST ABOUT AUTHORING AREA PARTICIPATE Your browser does not support JavaScript or it may be disabled Hasse Diagrams of Integer Divisors A Hasse diagram is a graphical representation of a partially ordered set poset The set consisting of the divisors of a positive integer can be considered a poset under the relation if divides For this poset , any edge in the diagram is such that the number below divides the number immediately above . If is a product of prime numbers , then is isomorphic to the set of subsets of with the relation if is contained in hence , is a Boolean algebra in this . case Contributed by : Jaime Rangel-Mondragon THINGS TO TRY Slider Zoom Gamepad Controls Automatic Animation SNAPSHOTS RELATED LINKS Hasse Diagram Wolfram MathWorld Lattice of Factors WolframIt’s a Boson! The Higgs as the Latest Offspring of Math & Physics | The Crux
Updated: 2012-07-30 18:18:19Subscribe Today Renew Give a Gift Archives Customer Service Facebook Twitter Newsletter SEARCH Health Medicine Mind Brain Technology Space Human Origins Living World Environment Physics Math Video Photos Podcast RSS Are Warnings About Drug Side Effects Actually Making Us Sick It’s a Boson The Higgs as the Latest Offspring of Math Physics Amir D . Aczel amirdaczel.com writes about mathematics and physics and has published 18 books , numerous newspaper and magazine articles , as well as professional research . papers A Higgs candidate event from the ATLAS detector of the . LHC Courtesy of CERN What made me fall in love with theoretical physics many years ago in 1972, when I first met Werner Heisenberg was its stunningly powerful relationship—far beyond any reasonable expectation—with pureHappenings – 2012 Jul 21
Updated: 2012-07-21 20:25:34I’m almost embarrassed to say it – in view of the terrible massacre in Aurora, Colorado – but my week was pretty good. I returned to work, but the week off before this let me make good progress on mathematics. The next technical post will be the regression post that I was struggling with before [...]Integral Domains and the failure of unique factorization
Updated: 2012-07-17 01:10:35Introduction Recall the Venn diagram illustrating special kinds of integral domains. I want to look at integral domains in general, but integral domains that are not unique factorization domains (UFDs) in particular. I’m interested in the outer ring of that diagram. That is, I’m interested in factoring numbers in integral domains… so we have to [...]Happenings – 2012 Jul 15
Updated: 2012-07-15 17:47:56I can’t believe I completely forgot to put out a diary post yesterday. I can, however, understand it. I was off work all week, on vacation but staying home. I knew that yesterday was Saturday, but my schedule had been so different during the week… without thinking about it, I guess I extended my vacation [...]Topological clustering
Updated: 2012-07-13 21:50:57In the last post in my continuing series on the topology of large data sets, I discussed the problem of clustering and promised that we would finally get to some low dimensional, geometric topology. (I wrote about persistent homology a few posts back, but this approach comes out of K-theory, which is anything but low [...]Symmetric decompositions of the 4-sphere
Updated: 2012-07-12 22:43:32Rob Kusner recently pointed out to me that the 4-sphere has a very natural differential-geometric decomposition as a double mapping cylinder S^3/Q_8 –> RP^2. Here Q_8 is the group {\pm 1, \pm i, \pm j, \pm k} in the unit quaternions and RP^2 is the real projective plane. Another way to say this is take [...]RAAGs over Riches
Updated: 2012-07-12 09:01:09Cubulation and the proof of the VHC/VFC have been featured prominently on this blog, and quite rightly so. It constitutes a major advance in low dimensional topology, and the proof itself is such a happy story. Thurston’s prophetic unexpected 1982 conjectures of how nice the fundamental group of a hyperbolic 3-manifold must be all proved [...]Answer by Nicky Hekster for Binary operations
Updated: 2012-07-05 11:42:35Considering your first question: have a look at the octonions. Also check out this link.Answer by William for Binary operations
Updated: 2012-07-05 08:30:21Stack Exchange log in chat meta about faq Mathematics Questions Tags Users Badges Unanswered Ask Question Binary operations up vote 0 down vote favorite Some things on binary : operations Can we find a set with a binary operation where the binary operation is not associative , there is an identity , and all elements have an inverse Also can we find a set with a binary operation and an identity where at least one element has at least 2 inverses What about a set with a binary operation that has two different identities Please no hints , just solutions- I am using these for a more complex problem I am . doing group-theory share improve this question edited Jul 5 at 8:37 asked Jul 5 at 8:22 Ali 234 10 35 accept rate I do not understand why hints will not do I mean , you will get the answer inBinary operations
Updated: 2012-07-05 08:22:52Some things on binary operations: Can we find a set with a binary operation where the binary operation is not associative, there is an identity, and all elements have an inverse? Also can we find a set with a binary operation and an identity where at least one element has at least 2 inverses? What about a set with a binary operation that has two different identities? Please no hints, just solutions- I am using these for a more complex problem I am doing.