Comments for Matt Baker's Math Blog
https://mattbaker.blog
Thoughts on number theory, graphs, dynamical systems, tropical geometry, pedagogy, puzzles, and the p-adicsThu, 05 Jan 2017 16:39:03 +0000hourly1http://wordpress.com/Comment on Hodge Theory in Combinatorics by Whitney Encounters of the Second Kind | Matt Baker's Math Blog
https://mattbaker.blog/2015/12/14/hodge-theory-in-combinatorics/comment-page-1/#comment-1167
Thu, 05 Jan 2017 16:39:03 +0000http://mattbakerblog.wordpress.com/?p=1227#comment-1167[…] of Adiprasito, Huh, and Katz on the Rota-Welsh conjecture and Hodge theory for matroids. See this previous post for an introduction to their work. My write-up for the Current Events Bulletin is included in […]
]]>Comment on A p-adic proof that pi is transcendental by Số vô tỷ và p-adic – Lý thuyết Hàm Suy Rộng
https://mattbaker.blog/2015/03/20/a-p-adic-proof-that-pi-is-transcendental/comment-page-1/#comment-1138
Mon, 26 Dec 2016 03:21:08 +0000http://mattbakerblog.wordpress.com/?p=371#comment-1138[…] Matt Baker […]
]]>Comment on p-adic Numbers and Dissections of Squares into Triangles by Matt Baker
https://mattbaker.blog/2016/03/24/p-adic-numbers-and-dissections-of-squares-into-triangles/comment-page-1/#comment-932
Wed, 27 Apr 2016 19:16:23 +0000http://mattbakerblog.wordpress.com/?p=1844#comment-932No, unfortunately I don’t know of any other results which can be proved in this way. I don’t actually think of the tropical interpretation as “ad hoc”, but I guess that’s a subjective matter…
]]>Comment on p-adic Numbers and Dissections of Squares into Triangles by Daniele Turchetti
https://mattbaker.blog/2016/03/24/p-adic-numbers-and-dissections-of-squares-into-triangles/comment-page-1/#comment-931
Tue, 26 Apr 2016 18:28:33 +0000http://mattbakerblog.wordpress.com/?p=1844#comment-931This theorem is also one of my favorite applications of p-adic numbers! The tropical interpretation seems a little bit “ad hoc” to me, though: do you know of other results that you can get by coloring planary graphs according to the relative position of the vertices with respect to some tropical curves?
]]>Comment on Probability, Primes, and Pi by Matt Baker
https://mattbaker.blog/2016/03/14/probability-primes-and-pi/comment-page-1/#comment-930
Fri, 15 Apr 2016 20:23:50 +0000http://mattbakerblog.wordpress.com/?p=1620#comment-930That’s a nice argument!
]]>Comment on Probability, Primes, and Pi by Antoine Chambert-Loir
https://mattbaker.blog/2016/03/14/probability-primes-and-pi/comment-page-1/#comment-929
Fri, 15 Apr 2016 19:19:30 +0000http://mattbakerblog.wordpress.com/?p=1620#comment-929There is a nice undergraduate proof of the formula for that runs as follows: for every integer , write , for some polynomial of degree ; its roots are , for , hence , for some constant , hence . Set , one gets . Now let , justifying the limit interchange via, e.g., dominated convergence.
]]>Comment on p-adic Numbers and Dissections of Squares into Triangles by Dissecting squares into equal-area triangles: idle questions | Quomodocumque
https://mattbaker.blog/2016/03/24/p-adic-numbers-and-dissections-of-squares-into-triangles/comment-page-1/#comment-911
Thu, 31 Mar 2016 03:51:23 +0000http://mattbakerblog.wordpress.com/?p=1844#comment-911[…] Love this post from Matt Baker in which he explains the tropical / 2-adic proof (in fact the only proof!) that you can’t dissect a square into an odd number of triangles of equal area. In fact, his argument proves more, I think — you can’t dissect a square into triangles whose areas are all rational numbers with odd denominator! […]
]]>Comment on Newton polygons and Galois groups by p-adic Numbers and Dissections of Squares into Triangles | Matt Baker's Math Blog
https://mattbaker.blog/2014/05/02/newton-polygons-and-galois-groups/comment-page-1/#comment-905
Fri, 25 Mar 2016 01:36:01 +0000http://mattbakerblog.wordpress.com/?p=612#comment-905[…] I learned from Robert is that p-adic numbers have many unexpected applications (see, for example, this blog post). Today I want to share one of my favorite surprising applications of p-adic numbers, to a simple […]
]]>Comment on Robert F. Coleman 1954-2014 by p-adic Numbers and Dissections of Squares into Triangles | Matt Baker's Math Blog
https://mattbaker.blog/2014/03/25/robert-f-coleman-1954-2014/comment-page-2/#comment-904
Fri, 25 Mar 2016 01:35:58 +0000http://mattbakerblog.wordpress.com/?p=538#comment-904[…] thesis advisor Robert Coleman passed away two years ago today (see this remembrance on my blog). One of the things I learned from Robert is that p-adic numbers have many unexpected […]
]]>Comment on Matroids over Hyperfields, Part I by Matroids over Hyperfields, Part II | Matt Baker's Math Blog
https://mattbaker.blog/2016/03/10/matroids-over-hyperfields-part-i/comment-page-1/#comment-899
Thu, 17 Mar 2016 18:52:19 +0000http://mattbakerblog.wordpress.com/?p=1273#comment-899[…] Part I of this post, we defined hyperrings and hyperfields, gave some key examples, and introduced […]
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