tag:blogger.com,1999:blog-2433841880619171855.post9062195879208656048..comments2021-10-25T10:06:38.528+01:00Comments on Pat'sBlog: Constructructable Polygons, and X^17 = 1Unknownnoreply@blogger.comBlogger8125tag:blogger.com,1999:blog-2433841880619171855.post-72918183683679915662011-04-26T13:48:14.910+01:002011-04-26T13:48:14.910+01:00Thanks Dave (Richeson). Yes, it was at Division by...Thanks Dave (Richeson). Yes, it was at <a href="http://divisbyzero.com/2011/04/15/happy-birthday-uncle-leonhard-i-hope-you-enjoy-your-new-home/" rel="nofollow">Division by Zero</a>, your weblog, that I learned that. Thanks bunches for that link, which you link to yt again today on your tombstone article. Sweet. <br /><br />Does anyone know WHICH Russian works Julian Barbour (<a href="http://www.amazon.com/End-Time-Next-Revolution-Physics/dp/0195145925/ref=sr_1_1?ie=UTF8&qid=1303821923&sr=8-1-spell" rel="nofollow">The End of Time</a> author) translates into English, in order to pay his rent, when FQXi isn't giving him grants? Hmmm, maybe Euler. But there are so many great Russian mathematicians to choose from.Steven Colyerhttps://www.blogger.com/profile/10435759210177642257noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-31669826685653170352011-04-23T22:25:08.511+01:002011-04-23T22:25:08.511+01:00Steven, there are many untranslated Euler articles...Steven, there are many untranslated Euler articles. They're collecting them at the Euler Archive, which was a project started by some grad students at Dartmouth, but have now graduated and moved on to teaching jobs. The Euler archive just moved to the MAA http://eulerarchive.maa.org/ <br /><br />Speaking of Euler, he solved the equations x^n-1=0 for n<11 (that is, gave solutions using radicals) You can read about it here: http://bit.ly/fLvS7sDavehttps://www.blogger.com/profile/11396416443532916086noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-18005439709209335612011-04-23T21:49:27.950+01:002011-04-23T21:49:27.950+01:00OK thanks, Pat, the link went through. Wow, wow, w...OK thanks, Pat, the link went through. Wow, wow, whoa, awesome work, very clear. I must research this Renfro chap. Job well done. And since he does reference you in the very first line, all is love. Thanks.<br /><br />If you permit me to talk Euler for a bit, I recently learned that there are <i>still</i> Euler papers waiting to be translated into English! Wow, what language did he write in mostly? German, Latin, English, or Russian?Steven Colyerhttps://www.blogger.com/profile/10435759210177642257noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-86394909079661695922011-04-23T16:43:39.974+01:002011-04-23T16:43:39.974+01:00You blog is great, Pat. I love it.
Gauss's w...You blog is great, Pat. I love it. <br /><br />Gauss's work on cyclotomy is in book 7 of his Disquisitiones Arithmeticae, which is translated and is a Springer book. It is on Google books (http://bit.ly/hNlAgN), but unfortunately, the relevant pages are blocked. Here's a scan (that I found on the 'net) of some of the pages of interest: http://bit.ly/hugeau.<br /><br />It cuts off before my favorite part, which is Gauss's acknowledgment of the converse to his constructibility theorem, but his omission of a proof: <br /><br />"The limits of the present work exclude this demonstration here, but we issue this warning lest anyone attempt to achieve geometric constructions for sections other than the ones suggested by our theory (e.g., sections into 7, 11, 13, 19, etc. parts) and so spend his time uselessly."Davehttps://www.blogger.com/profile/11396416443532916086noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-60640620936912090362011-04-23T16:20:47.473+01:002011-04-23T16:20:47.473+01:00Dave, glad to help out from me to you once. Seems...Dave, glad to help out from me to you once. Seems I owe you several..<br /> David R is a wonderful researcher and fastidious writer (as opposed to my shoot from the hip, misspelled cacophony.. *don't know the equivalent term for bad writing, cacographony?) . <br /> Do you have links where Gauss is translated that are available to the peons who don't have access to Jstor? I know, lazy, I should search this out.Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-21668946734721811942011-04-23T15:32:02.286+01:002011-04-23T15:32:02.286+01:00Pat/Dave,
This is fantastic, and your timing is am...Pat/Dave,<br />This is fantastic, and your timing is amazing. I've been spending the past couple of weeks reading about (and struggling through) Gauss' cyclotomy work. Dave's right---it is difficult to find a good source on this. I found the Hadlock book to be very helpful (and of course you can go back to Gauss's original work, which has been translated into English). <br /><br />So, while I wish you'd published this two weeks ago, I am still very much looking forward to reading it.<br /><br />DaveDavehttps://www.blogger.com/profile/11396416443532916086noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-28151490810947346362011-04-23T14:28:49.671+01:002011-04-23T14:28:49.671+01:00Steven, Thanks, I'll check and fix the link......Steven, Thanks, I'll check and fix the link... And actually I was just the middle man, so maybe the Colyer-Refro paper...although writing a paper with Dave is a goal for me since I can raise my Euler number above infinity... maybe when I'm back in the US full time you and I can do one too, there must be SOMEONE who would publish it.Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-2124012864564865792011-04-23T10:19:33.627+01:002011-04-23T10:19:33.627+01:00The link didn't work for me. But yeah, cool! I...The link didn't work for me. But yeah, cool! Is there an arXiv paper in this? Renfro-Ballew-Colyer? Or don't I get props for getting you to think of it, which got Dave to think of it, and actually do it?<br /><br />OK, just call it Renfro-Ballew then, I don't care. What's cool is it was <i>done</i>, and points out that there are <i>always</i> new problems to be solved in Mathematics, and new questions to ask! Too many students think Maths is a done deal; that we know everything. No. Barry Mazur taught me that in a book introduction I read by him. Good guy.<br /><br />And remember Pat, Hermann Grassmann was "just" a German high school math teacher, but he came up with Grassmann algebras, and all THAT did was change Mathematics, and physics, and so, the world. People can make a contribution to the field at any age as well. Euler's life proved that. ;-)Steven Colyerhttps://www.blogger.com/profile/10435759210177642257noreply@blogger.com