tag:blogger.com,1999:blog-2433841880619171855.post9024600745823561588..comments2014-04-19T12:13:28.413+01:00Comments on Pat'sBlog: Even the Science Magazines Can Blow It SometimesPat Ballewhttps://plus.google.com/102211537828528656806noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-2433841880619171855.post-38589088831975739162009-05-23T04:21:06.829+01:002009-05-23T04:21:06.829+01:00The nonorientable analogue of a torus is the (real...The nonorientable analogue of a torus is the (real) projective plane. In other words, a compact orientable surface of genus one is a torus, while a compact nonorientable surface of genus one is a projective plane. Your terminology may vary.Paulhttp://www.blogger.com/profile/08136135798240925106noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-43708327377417253382009-05-12T18:40:00.000+01:002009-05-12T18:40:00.000+01:00Mobius band has genus 1. Torus has genus 1. The di...Mobius band has genus 1. Torus has genus 1. The difference is that the torus is orientable, the mobius band is nonorientable.<br /><br />I think.Johnhttp://www.blogger.com/profile/17707024524634807456noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-14016721658922957502009-05-08T19:13:00.000+01:002009-05-08T19:13:00.000+01:00Well, I like the idea of genus one... (which is al...Well, I like the idea of genus one... (which is almost the same as a proof in MY classroom..)..<br /><br /><br /> so a mobius strip and a doughnut are both genus one...Ok, new joke, what do you call a guy who can't tell his mobius strip from a doughnut... ... ahhh, not funny, but thanks for the info anyway..Pat Bhttp://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-52234923172015759272009-05-08T16:53:00.000+01:002009-05-08T16:53:00.000+01:00I find it amusing that if the bite in the doughnut...I find it amusing that if the bite in the doughnut was actually large enough to intersect the hole then the two would again be topologically equivalent (to spheres). Correct?Trashmanhttp://www.blogger.com/profile/10140920751826036814noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-2336995414689114392009-05-08T13:35:00.000+01:002009-05-08T13:35:00.000+01:00A common definition of genus is that it is the num...A common definition of genus is that it is the number of nonintersecting closed curve along which we can cut a surface and not disconnect it. <br /><br />Thus it is possible to apply it to nonorientable surfaces and surfaces with boundary. (And so the genus of a MĂ¶bius band is 1.)<br /><br />However, in practice most people think of the genus as an invariant for orientable surfacesâ€”tori or tori with disks removed.drichesonhttp://divisbyzero.com/noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-1837162111533661472009-05-05T20:25:00.000+01:002009-05-05T20:25:00.000+01:00i'll venture a guess: no.
"genus" would appear to...i'll venture a guess: no.<br />"genus" would appear to apply to<br />surfaces bounding a solid.<br />now i'll probably have to look it up...<br /><br /><A HREF="http://en.wikipedia.org/wiki/Genus_(mathematics)" REL="nofollow">w'edia sez no</A> on accounta orientability.vlorbikhttp://www.blogger.com/profile/02746118913980983815noreply@blogger.com