tag:blogger.com,1999:blog-2433841880619171855.post8858691704208396615..comments2023-04-01T12:35:40.573+01:00Comments on Pat'sBlog: Some Notes on the Sum of Squares of the IntegersUnknownnoreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2433841880619171855.post-51666546517515355012014-03-03T01:21:59.699+00:002014-03-03T01:21:59.699+00:00This website has very good content. So I am sure t...This website has very good content. So I am sure this website will form the well-known in the future. <br /><br />www.joeydavila.netAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-85021177126153805182014-02-26T02:51:35.347+00:002014-02-26T02:51:35.347+00:00Thanks for sharing your thoughts. I truly apprecia...Thanks for sharing your thoughts. I truly appreciate your efforts and I am waiting for your next write ups thanks once again.<br /> <br /><a href="http://www.imarksweb.org" rel="nofollow">Traviz</a><br />www.imarksweb.orgAnonymoushttps://www.blogger.com/profile/03983279751843228358noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-31089604088504601502013-06-22T03:59:01.431+01:002013-06-22T03:59:01.431+01:00spot on with this write-up, i like the way you dis...spot on with this write-up, i like the way you discuss the things. i'm impressed, i must say. i'll probably be back again to read more. thanks for sharing this with us.<br /><br /><a href="http://www.trendone.net/" rel="nofollow">Lee Shin</a><br />www.trendone.netAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-7755230183944221352013-05-16T06:50:53.856+01:002013-05-16T06:50:53.856+01:00wonderful work! the way you discuss the subject i&...wonderful work! the way you discuss the subject i'm very impressed. i'll bookmark this webpage and be back more often to see more updates from you. <br /><br /><a href="http://www.brfe.net/" rel="nofollow">ayumi</a><br />www.brfe.netAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-14948964114568859282012-12-20T18:14:47.272+00:002012-12-20T18:14:47.272+00:00This is beautiful stuff! I'm not finding any ...This is beautiful stuff! I'm not finding any other sum of squares puzzles popping to the front of my mind but I'm sure something will occur to me later.<br /><br />Meanwhile, for a non-sum-of-squares question, what happens in your Loyd puzzle if you replace the grid of lines with a grid of dots? Now there are more squares ... but how many?<br /><br />I have several formulas for the answer and I had a great deal of fun explaining where they come from in more combinatorial ways (like you did with the triangular numbers approach to summing the squares as the sum of two tetrahedral numbers).<br /><br />I'd still like to see something here involving the 2n+1 as an actual dimension of some 3D object that relates to the volume of the stack of balls, rather than as something that appears algebraically, though your approach here is still so much better than the "guess a formula plus prove it by induction" approach.<br /><br />Something like http://courses.gov.harvard.edu/gov3009/spring02/sumsq.pdf for example!Joshua Zuckerhttps://www.blogger.com/profile/04689961247338617418noreply@blogger.com