tag:blogger.com,1999:blog-46797151906357959732024-03-12T21:43:22.528-07:00y of xThe Unofficial Tunxis Math Department Blogfakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.comBlogger191125tag:blogger.com,1999:blog-4679715190635795973.post-92081229334438666212009-07-20T02:25:00.000-07:002009-07-20T02:35:21.020-07:00Last Post on This SiteAs of today, YofX has officially migrated to its new home: <a href="http://www.yofx.org">www.yofx.org</a>. This site will remain up for archival purposes, but all new YofX posts will take place at the above address. Also, if you are following this via RSS, you can subscribe to the new feed <a href="http://feeds.feedburner.com/Yofxposts">here</a>. Thanks for following and I hope to see you over at the new site.fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com0tag:blogger.com,1999:blog-4679715190635795973.post-8139392738585064602009-07-17T02:25:00.000-07:002009-07-17T02:54:12.811-07:00A Mathematician Goes on Vacation 6<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEih2yfn716FJOR-ltve5-Ir6AH5y_7MMIucrC4nieoLmjlyOMB6MM4PtriNs3rqwoCp8vokScpZROxZMv3ZTPbPPgtwy7FO372j5rjwJaYhnY90UKWDbn5s2GVgLVqz5-MQ4hmKgMrw5MA/s1600-h/img_0132.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 240px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEih2yfn716FJOR-ltve5-Ir6AH5y_7MMIucrC4nieoLmjlyOMB6MM4PtriNs3rqwoCp8vokScpZROxZMv3ZTPbPPgtwy7FO372j5rjwJaYhnY90UKWDbn5s2GVgLVqz5-MQ4hmKgMrw5MA/s320/img_0132.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5359364981161004194" /></a><br />I don't get too many complaints about the uselessness of negative numbers, but every once in a while in a Prealgebra class somebody will claim that they're never used in the real world. Above is the photographic evidence from within an elevator in Nikola Tesla Airport (Belgrade, Serbia) that negative integers are indeed used. And if one is ever in such an elevator, one surely thinks fondly (for once) of their math teacher. For how else would we know where to go?<br /><br />**This is the last real post to this site. Next week yofx officially moves to a new home: <a href="http://www.yofx.org/">www.yofx.org</a>. This site will remain up as an archive for us to refer back to.fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com3tag:blogger.com,1999:blog-4679715190635795973.post-57777006694788059582009-07-16T02:30:00.000-07:002009-07-16T08:58:32.480-07:00Which Mathematical Function Are You?Lee tipped me off on a great Facebook time-waster: the <a href="http://apps.facebook.com/qwhich-mathema-diajd/?start=1&target=home&_fb_q=1">Which Mathematical Function Are You</a> quiz. You've done plenty of these viral quizzes before, but none so squarely centered on your geek heart. They ask you the standard personality questions. Sometimes the selections are worth a few giggles. Then they determine which mathematical function best fits your personality. I am apparently <a href="http://en.wikipedia.org/wiki/Gaussian_function">Gaussian</a>. <br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpOiiOz-GoY43wl-MjxlICTBsspQvWvYBO6GnZ_1wfEK8zY0eLuo6gE84uw5cxijaNPKzowwshj5qpZ5K5fGT3kdTPoTFpXTnVD3R4FqDgDgMInoKcEwHZTPSZqsi3ME2xAv1aL4I_8w0/s1600-h/my+function.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 170px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpOiiOz-GoY43wl-MjxlICTBsspQvWvYBO6GnZ_1wfEK8zY0eLuo6gE84uw5cxijaNPKzowwshj5qpZ5K5fGT3kdTPoTFpXTnVD3R4FqDgDgMInoKcEwHZTPSZqsi3ME2xAv1aL4I_8w0/s320/my+function.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5358989634772583810" /></a> Lee is apparently the <a href="https://www.mail.commnet.edu/exchweb/bin/redir.asp?URL=http://quiz.applatform.com/track/?i=380930%26h=45c0818f917fcd329c89d92ed7c5f4dc">Riemann zeta-function</a>. <blockquote><i>Mystery and wonder are your "prime" delights in life. You seek to apprehend all the hidden, complex patterns in the universe. Some think you are quirky, but they just don't understand you: they have not learned to think outside the box, as you have. You are a misunderstood genius.</i></blockquote>I'm curious how many functions the quiz outputs. Let me know what you got in the comments.<br /><br /><i>**Reminder YofX will be moving to <a href="http://www.yofx.org/">www.yofx.org</a> in 4 days on 7/20**</i>fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com5tag:blogger.com,1999:blog-4679715190635795973.post-19295115417176321952009-07-15T02:28:00.000-07:002009-07-15T03:00:38.304-07:00text2image fun!<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPtmF130J_qLDDnlCTiVGehBk49JxrrRbpf-BWRYvgjkRSjFOAGgskSMN2ACvZjvWCRyZay0YorxVpon2PfjXk1debdTbyOYyhd_SwSpvQh5YbVrIwbRGqQV4J9jlbsgdNIRmqPfe2IbE/s1600-h/text+to+image.jpeg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 240px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPtmF130J_qLDDnlCTiVGehBk49JxrrRbpf-BWRYvgjkRSjFOAGgskSMN2ACvZjvWCRyZay0YorxVpon2PfjXk1debdTbyOYyhd_SwSpvQh5YbVrIwbRGqQV4J9jlbsgdNIRmqPfe2IbE/s320/text+to+image.jpeg" border="0" alt=""id="BLOGGER_PHOTO_ID_5358616800031304386" /></a><br /><a href="http://www.teddavis.org/text2image/">text2image</a> is a fun (and probably totally useless) way to transform any text into an image. Above, you are seeing the visual rendering of 'yofx'. I was thinking that this might be an interesting way for students to conceptualize a function. I hate to say it, but sometimes real-valued functions get boring. Another plus is that we don't actually know how the text gets transformed. Discovering properties of the function by playing around could make for an interesting exercise for students. Is it one-to-one, does an all-caps text string map the same as a lowercase string, what does the domain look like, is there a character limit, are all questions students might generate. I picked this up from <a href="http://infosthetics.com/archives/2009/02/text2image_transforming_text_into_a_glitch.html">Information Aesthetics</a>. Check out that post. There are also some links at the bottom to similar trans-medium mappings.fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com0tag:blogger.com,1999:blog-4679715190635795973.post-17585642280818251202009-07-14T03:00:00.000-07:002009-07-14T03:25:05.087-07:00ABBA = ABBA<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjupJ18mGmSl2KAGYFMYijp9X_qDn-H9LrzdrHSOWzvVEgNaTLnl9rt56jr1Pd8QuGUh_oVv8Gwir_bAyiyI1lYbqo1w2GQvOyiPsBPM6nM_-5unjoag8eVBueKfqxpdSdZqqhjOFtAZnI/s1600-h/pre-ABBA+ABBA.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 320px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjupJ18mGmSl2KAGYFMYijp9X_qDn-H9LrzdrHSOWzvVEgNaTLnl9rt56jr1Pd8QuGUh_oVv8Gwir_bAyiyI1lYbqo1w2GQvOyiPsBPM6nM_-5unjoag8eVBueKfqxpdSdZqqhjOFtAZnI/s320/pre-ABBA+ABBA.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5358257055816898338" /></a><br />I was dragged to an <a href="http://en.wikipedia.org/wiki/ABBA">ABBA</a> tribute concert last Friday night. I'm regrettably familiar with ABBA's music, <a href="http://www.mamma-mia.com/">Mama Mia</a> veteran (even the sing-a-long), but it was the first time I realized the band's name is a <a href="http://www.fun-with-words.com/palin_explain.html">palindrome</a>. It is also the first time the name reminded me of a <a href="http://en.wikipedia.org/wiki/Enclosed_rhyme">rhyme scheme</a>. (Two revelations, one night.) What is the real origin of the name? According the Wpedia, it's an acronym for the first names of the bandmembers: Agnetha, Björn, Benny, Anni-Frid. I know, you'll never hear <a href="http://www.youtube.com/watch?v=REElUors1pQ">Dancing Queen</a> quite the same way again. Anyway, let me know if you can think of any other palindromic bands. <br /><br />**Reminder YofX will be moving to <a href="http://www.yofx.org/">www.yofx.org</a> in 6 days on 7/20**fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com0tag:blogger.com,1999:blog-4679715190635795973.post-6786929957183705922009-07-13T02:03:00.000-07:002009-07-13T02:12:16.006-07:00Shunt Buster<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIgEBWThL80ubPu92kLRK3UEHfmUxbCJ_KQKhBBK7qizykh2jXnIts22kfRVjcukgNRUAUWmUhEedLy0Xt35gMsQ9eqssIJvCFnxjntBckB0xL0Dw63Kv3Yugm-Qf47NBnsNSwW6b0aqg/s1600-h/shunt+problem001.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 275px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIgEBWThL80ubPu92kLRK3UEHfmUxbCJ_KQKhBBK7qizykh2jXnIts22kfRVjcukgNRUAUWmUhEedLy0Xt35gMsQ9eqssIJvCFnxjntBckB0xL0Dw63Kv3Yugm-Qf47NBnsNSwW6b0aqg/s320/shunt+problem001.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5357868646278084386" /></a><br />Help! This one's killing me. <br /><br /><i>**Reminder YofX will be moving to <a href="http://www.yofx.org">www.yofx.org</a> in 7 days on 7/20**</i>fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com0tag:blogger.com,1999:blog-4679715190635795973.post-28158698082854083852009-07-10T01:46:00.000-07:002009-07-10T02:14:09.438-07:00Something to Show Your Algebra Classes<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIEp92Yexm55kC2PeLzdq64xlgCPRr0uWSXwIe-vKYT_LhdA3WokLu1nvSj6Gvhnfbl8qaQ2rtEr8dh_65alDHrZ2HqF8euabG4OTm4hTXVrG4pE102oCVvetbaSz2yqT7NghI2aHFsuE/s1600-h/wind+machine.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 238px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIEp92Yexm55kC2PeLzdq64xlgCPRr0uWSXwIe-vKYT_LhdA3WokLu1nvSj6Gvhnfbl8qaQ2rtEr8dh_65alDHrZ2HqF8euabG4OTm4hTXVrG4pE102oCVvetbaSz2yqT7NghI2aHFsuE/s320/wind+machine.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5356754011363549746" /></a><br />I actually found a reference to <a href="http://www.purplemath.com/modules/variatn.htm">variation</a> that isn't in a text book. The Wired Science blog had a post on <a href="http://www.wired.com/wiredscience/2009/06/highaltitudewindpower/">high-altitude wind</a> generation (pretty interesting in its own right). They describe the relationship between wind speed and power generated like this...<blockquote><i>Wind’s power — energy which can be used to do work like spinning magnets to generate electricity — varies with the cube of its speed.</i></blockquote> I wonder how many of the students I tortured with variation would remember what it means if they read this article? Those are the questions that keep a math teacher up at night. BTW, if you're teaching variation. I've always found that students like knowing the world's most famous equation e=mc^2 is a direct variation equation.fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com0tag:blogger.com,1999:blog-4679715190635795973.post-10938305141077547422009-07-09T01:44:00.000-07:002009-07-09T02:44:35.011-07:00Geek of The Week: Nick Hamblet<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxJLOJCKiwPbeW5NNnc3dNJ_6CjKigq3zYEDL_u6anRsJ90eIA8UX0_3QcJTRzGZKcDH5WKRyo6IWEIjgN0GTRgcsfL3bgK98BPHGF9ZilnXi-plGKkGOswXsBO_GLEM2Mv97_dSDB-70/s1600-h/nick+hamblet.JPG"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 240px; height: 320px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxJLOJCKiwPbeW5NNnc3dNJ_6CjKigq3zYEDL_u6anRsJ90eIA8UX0_3QcJTRzGZKcDH5WKRyo6IWEIjgN0GTRgcsfL3bgK98BPHGF9ZilnXi-plGKkGOswXsBO_GLEM2Mv97_dSDB-70/s320/nick+hamblet.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5356380862264642706" /></a> Not sure whether you have been following the comments on <a href="http://yofx.blogspot.com/2009/04/prime-time.html">Prime Time</a>? But, Nick, known to us in the comments as <a href="http://www.blogger.com/profile/14998929191458452400">SumIdiot</a>, came up with a nice proof showing that it's impossible to group the digits of a number <i>n</i> in primes so that you wind up with the prime factorization of that number. For example, the digits of 241 can be grouped as (2)(41), but 2 and 41 aren't the prime factors of 241. Another example, 573 could be grouped (5)(7)(3), but again the product (5)(7)(3) is not equal to 573. Enough.<br /><br />What Nick actually showed was the larger result: any grouping of a number's digits, prime or not, will always have a product strictly less than the number itself. How did he do it? Here's his proof from the comments. <br /><blockquote><i>Given d+1 integers between 0 and 9, called a_0, ... a_d, let me write A=(a_d a_{d-1} ... a_0) for the number \sum_{i=0}^{d}a_i 10^i.<br /><br />Consider the product obtained by splitting this digit string into (a_d ... a_s)(a_{s-1} ... a_0). So this is a product of a d-s+1 digit number and an s digit number (take s >= 1).<br /><br />Now A=(a_d ... a_0) = 10^s(a_d ... a_s) + (a_{s-1} ... a_0) is at least as big as 10^s(a_d ... a_s). However, since 10^s is strictly bigger than (a_{s-1} ... a_0), A >= (a_d ... a_s)10^s > (a_d ... a_s)(a_{s-1} ... a_0).<br /><br />So any integer is bigger than the product obtained by splitting it's decimal string into two pieces. It seems the general statement, splitting the decimal string into any number of pieces, follows by induction.</i></blockquote> Clever! Nick has also given me the chance to break in a blogroll (Only on the <a href="www.yofx.org">new domain</a>). He runs a real nice blog Sumidiot <a href="http://sumidiot.blogspot.com/">here</a>.<br /><br /><i>**Reminder YofX will be moving to www.yofx.org in 11 days on 7/20**</i>fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com0tag:blogger.com,1999:blog-4679715190635795973.post-18936831711378087292009-07-08T06:32:00.000-07:002009-07-08T06:54:15.407-07:00Transform Your Cat with Math<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRQw_egTCp26-8N47mHuz7ltvhVjukscAnsIdt9AEbkQecvtjPubrEFW1E4raBtH1zjMXU1BNvMwinyhT-8wMtSn5Co0wCjck9bVHH5Y98jqp7BfMLGX-E-XRmM8yHDOia5AUtxtOP218/s1600-h/cartoon_fourier_cat-744180.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 231px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRQw_egTCp26-8N47mHuz7ltvhVjukscAnsIdt9AEbkQecvtjPubrEFW1E4raBtH1zjMXU1BNvMwinyhT-8wMtSn5Co0wCjck9bVHH5Y98jqp7BfMLGX-E-XRmM8yHDOia5AUtxtOP218/s320/cartoon_fourier_cat-744180.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5356082004196660706" /></a> This <a href="http://xkcd.com/">XKCD</a> cartoon is a follow up to the <a href="http://yofx.blogspot.com/2009/06/beatles-mystery-chord-foundby.html">Mystery Chord post</a>. Anyone know any other good Fourier jokes?<br /><br /><i>**Reminder YofX will be moving to www.yofx.org in 12 days on 7/20**</i>fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com0tag:blogger.com,1999:blog-4679715190635795973.post-54860365092176308872009-07-07T01:52:00.000-07:002009-07-14T12:21:17.683-07:00Found Math<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUzi-SFVIMsSAH97xWnRuywsEYANLH7rX008znCRIwMEhFoid_e503PTBKDqLbJKjbTakRK-1HYQStwE8ZEZw96byNsH2OzCWe08MXSBu4Ct9yx312b5vr7zMUjwP9f_TJmuSF8HQiNfA/s1600-h/found+math+part+2002.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 285px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUzi-SFVIMsSAH97xWnRuywsEYANLH7rX008znCRIwMEhFoid_e503PTBKDqLbJKjbTakRK-1HYQStwE8ZEZw96byNsH2OzCWe08MXSBu4Ct9yx312b5vr7zMUjwP9f_TJmuSF8HQiNfA/s320/found+math+part+2002.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5355638808889343986" /></a> I found this on a notepad. And while it looks like math, I can't figure out how the numbers are related. Help!<br /><br /><i>**Reminder YofX will be moving to <a href="http://www.yofx.org/">www.yofx.org</a> in 13 days on 7/20**</i><br />fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com2tag:blogger.com,1999:blog-4679715190635795973.post-59183321435450412472009-07-06T02:02:00.001-07:002009-07-06T02:16:47.605-07:00Sudoku Variation<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIuzGgv0yUMYjgfLGL-HtSyBwdVi2x5CVALdbM_HL8aupZ0gzDOVWx8ETOLWHTmq8F2BWn9cntXes9BsNpbuDkv_sCU1Y8UJnGc5-5tXoqc_u3P87GvDUINTiIW99_eDS3TKqCQanB-Ws/s1600-h/suduko+variation001.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 192px; height: 320px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIuzGgv0yUMYjgfLGL-HtSyBwdVi2x5CVALdbM_HL8aupZ0gzDOVWx8ETOLWHTmq8F2BWn9cntXes9BsNpbuDkv_sCU1Y8UJnGc5-5tXoqc_u3P87GvDUINTiIW99_eDS3TKqCQanB-Ws/s320/suduko+variation001.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5355270245143162722" /></a> My mother sent this sudoku variaton my way. She is a total puzzle junky and found this in the International Herald Tribune. All the normal sudoku rules apply, but you also have to fill the shaded areas with 1 through 9. Thanks, Mom!fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com0tag:blogger.com,1999:blog-4679715190635795973.post-36422190584781508972009-07-03T06:29:00.000-07:002009-07-07T02:03:13.460-07:00YofX Will Move To A New HomeIn the next couple of weeks YofX will begin the move to a new home: <a href="http://www.yofx.org/">www.yofx.org</a>. This will not only be a move to its own domain, but also to a new platform, Wordpress. Here is the plan. <br /><br />1) For the next two weeks, starting Monday, I will post to both this site <a href="http://yofx.blogspot.com/">www.yofx.blogspot.com</a> and to the new site <a href="http://www.yofx.org/">www.yofx.org</a>. I hope that will give everyone the time to make the transition. (And don't freak out if the new site looks different. I'll be playing around with themes during this period.)<br /><br />2) After two weeks, starting 7/20, all new posts will be found on <a href="http://www.yofx.org/">www.yofx.org</a>, and this site will be an archive.<br /><br />If you are reading this blog via RSS, you can subscribe to the new site's <a href="http://feeds.feedburner.com/Yofxposts">posts</a> and <a href="http://feeds.feedburner.com/CommentsForYofx">comments</a> by following the links. You can even get it via <a href="http://feedburner.google.com/fb/a/mailverify?uri=Yofxposts&loc=en_US">email</a>. <br /><br />Let me know if there are any problems by commenting. I know this is a pain in the butt, so I want to make sure things go as smooth as possible for you all.fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com2tag:blogger.com,1999:blog-4679715190635795973.post-70726640110286769352009-07-02T11:56:00.000-07:002009-07-02T12:12:15.891-07:00A Mathematician Goes on Vacation 5<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwa8dS0o45gykAgVZDlhJN32PfvKfd2kmvRZzivmGABye4bYkU_bGjR3XxOew0H0Y-RmNqV4NkeFp5CXfH3QfjmVz7c6TLgMoJZzepCyZ4Ltk-XrhQ9Vu_i5xRua1vTjpe_JUFJefjK9c/s1600-h/IMG_0059.JPG"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 240px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwa8dS0o45gykAgVZDlhJN32PfvKfd2kmvRZzivmGABye4bYkU_bGjR3XxOew0H0Y-RmNqV4NkeFp5CXfH3QfjmVz7c6TLgMoJZzepCyZ4Ltk-XrhQ9Vu_i5xRua1vTjpe_JUFJefjK9c/s320/IMG_0059.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5353939739773694530" /></a> This is the best picture I took all vacation. There is so much going on, but notice in particular how the foot of the table rests on the perimeter of the reflection of the table surface...momement of ecstasy! I recognize not everyone is that moved. (My wife just rolls her eyes.) I'm hoping if you read this blog. You might be geeky enough to appreciate it.fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com3tag:blogger.com,1999:blog-4679715190635795973.post-23548765115986114032009-07-01T02:33:00.000-07:002009-07-01T02:58:56.169-07:00Tintin Calculus<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhR4HiQq_vUWz-nxNG7aDGa2_0CQNZZrLwf_G1qYerdyfHBarCSbxphRYFbq_rbfqHg0IFj1DbKaKd38M3uPt57xrQ3m6-n0DUxzrkIY5sGuVxn2CQXpnPbRfoIpfZ71G5ZUoaClupP3CI/s1600-h/tin+tin+calculus001.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 230px; height: 320px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhR4HiQq_vUWz-nxNG7aDGa2_0CQNZZrLwf_G1qYerdyfHBarCSbxphRYFbq_rbfqHg0IFj1DbKaKd38M3uPt57xrQ3m6-n0DUxzrkIY5sGuVxn2CQXpnPbRfoIpfZ71G5ZUoaClupP3CI/s320/tin+tin+calculus001.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5353423165690527634" /></a><br />Trying to figure out a name and some cover art for the calc text you just wrote? Look no further. I found this is the children's section of my library. And before you run to see if your library has it, be warned there isn't any Calculus (as we know it) in the comic. Calculus is a character that is the object of a sinister plot. Tintin then goes on to save Calculus, and probably the rest of the world too. Funny, I was googling Tintin and found an animated version of the comic online. Too lazy to read, <a href="http://video.google.com/videoplay?docid=-4668268860759158229">watch it</a>. And if you like your calculus affair with a little more calculus, click <a href="http://www.calculus.org">here</a>.fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com0tag:blogger.com,1999:blog-4679715190635795973.post-7987709598033742472009-06-30T02:25:00.001-07:002009-06-30T02:53:31.584-07:00A Mathematician Goes on Vacation 4<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGcyW7EKK_OYoiJbFyhSPbaoeuNKEWqhyEfUcz0jPOwY06YJdsIQVI4waoGIYn4oq_uT4HeXbcfm-mpoRCN13Hm9zBN01hvQYvOV6HopghPKG9OLsZB4wab6yt2quxYV9w7u8D_C6TAps/s1600-h/serbian+cross.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 240px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGcyW7EKK_OYoiJbFyhSPbaoeuNKEWqhyEfUcz0jPOwY06YJdsIQVI4waoGIYn4oq_uT4HeXbcfm-mpoRCN13Hm9zBN01hvQYvOV6HopghPKG9OLsZB4wab6yt2quxYV9w7u8D_C6TAps/s320/serbian+cross.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5353049560646110226" /></a><br />I saw this symbol on a lot of walls. It is the <a href="http://en.wikipedia.org/wiki/Serbian_cross">Serbian Cross</a>. I'm told the meaning is basically equivalent to our motto "United We Stand, Divided We Fall" (although the Wikipedia article says that this interpretation is a common misconception). I was impressed by the interesting symmetry: two lines of <a href="http://en.wikipedia.org/wiki/Reflection_symmetry">reflection</a> and <a href="http://en.wikipedia.org/wiki/Rotational_symmetry">rotational symmetry</a>. <br /><br />pic by <a href="http://www.flickr.com/photos/alexandramacdonald/1836588967/">alexmac1</a>fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com0tag:blogger.com,1999:blog-4679715190635795973.post-24532527424787189962009-06-29T02:05:00.000-07:002009-06-29T02:18:55.531-07:00Amoeba Fever Problem<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqDaprdeFXyaXfFCn6CNvAkYVtDedFayemT7k0JKsDFp3_zUyDM9fly4jGUQ24Nf__vsW53C2UEAILWj9hofSfSZon4_H4dG7wqi7uGKE_6JAdTzLToyoRdr4j00GVXocKBG9kIqQwKg8/s1600-h/amoeba+problem.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 320px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqDaprdeFXyaXfFCn6CNvAkYVtDedFayemT7k0JKsDFp3_zUyDM9fly4jGUQ24Nf__vsW53C2UEAILWj9hofSfSZon4_H4dG7wqi7uGKE_6JAdTzLToyoRdr4j00GVXocKBG9kIqQwKg8/s320/amoeba+problem.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5352673816033242866" /></a><br />Here's a very interesting problem sent in by <a href="http://primepuzzle.com/blue-moon.html">Lee</a>. Have fun playing with this. <br /><blockquote><i>Toby has a jar with one amoeba in it. Every minute, every amoeba turns into 0, 1, 2, or 3 amoebae with a probability of 1/4 for each case (dies, does nothing, splits into two, or splits into three). What is the probability that the amoeba population eventually dies out?</i></blockquote>If you're wondering, Lee's brother Chip created the image above. I'm guessing it has something to do with the solution.fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com14tag:blogger.com,1999:blog-4679715190635795973.post-37257908187051998112009-06-26T02:05:00.001-07:002009-06-26T02:42:04.074-07:00A Mathematician Goes on Vacation 3<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUZ9nDc9LoJh8YqF-pOr2NqwzB1WneOXByxyrXCxne8LJ7A86WcHGK4Rkbl-hqEjFaqby3hKcsNYXoMAFSNy7If4FMbMmvsU4z9qnGH-9jQvL8d6RiZKiK1BPMcN8KURQ2_ZTHfGrPjD0/s1600-h/lorenz+dog001.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 307px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUZ9nDc9LoJh8YqF-pOr2NqwzB1WneOXByxyrXCxne8LJ7A86WcHGK4Rkbl-hqEjFaqby3hKcsNYXoMAFSNy7If4FMbMmvsU4z9qnGH-9jQvL8d6RiZKiK1BPMcN8KURQ2_ZTHfGrPjD0/s320/lorenz+dog001.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5351560108538082658" /></a><br />As I said the first week it rained...a lot. That wasn't all bad. I did get a chance to read a bit. I brought along <a href="http://books.google.com/books?id=rIVK7wuY3kIC&lpg=PP1&dq=Konrad%20Lorenz%20on%20aggression&pg=PP1">On Aggression</a> by Konrad Lorenz. I'm not much of a biologist so a lot of the animal behavior descriptions flew over my head. But, I felt right at home with the above diagram. How nice to find a <a href="http://en.wikipedia.org/wiki/Cayley_table">Caley table</a> in the middle of a ten page meditation on the nuances of <a href="http://www.youtube.com/watch?v=5SMlfWxLekM&feature=player_embedded">the duck and drake mating ceremony</a>! Remember your multiplication tables? This is a <a href="http://en.wikipedia.org/wiki/Binary_operation">binary operation</a>. A binary of operation of what? Lorenz call the above diagram a <i>motivational analysis</i> Each picture on the diagram is a combination of the dog's fight or flight instincts. If you go down the left most column, you are seeing the progression of the flight instinct. Going across the top most row, you are getting the progression of the fight instinct. Any other image is some combination of the two instincts. All part of the math of mother nature. Quite interesting!fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com0tag:blogger.com,1999:blog-4679715190635795973.post-34430715288467441052009-06-25T02:40:00.000-07:002009-06-25T03:06:48.303-07:00A Mathematician Goes on Vacation 2<object width="425" height="344"><param name="movie" value="http://www.youtube.com/v/iXTHv3ovDFQ&hl=en&fs=1&"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/iXTHv3ovDFQ&hl=en&fs=1&" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="344"></embed></object><br /><br />So, I didn't have such good luck with weather. It rained the whole first week I was there, which meant I watched a lot of Serbian TV on my inlaws' couch. Thank goodness The <a href="http://sportsillustrated.cnn.com/2009/tennis/06/07/federer.wins.french.open.ap/index.html">French Open</a> was on Eurosport or I would have lost my mind. I also caught the above video quite a lot. (Their national stations play music videos between programs.) It seems to be <i>the</i> summer dance jam. There actually is some math in it, and if you can see it betwixt all the half-naked dancers, you know you're a bona fide geek. Good luck!fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com0tag:blogger.com,1999:blog-4679715190635795973.post-83875488096564987042009-06-24T01:58:00.000-07:002009-06-24T02:46:51.840-07:00A Mathematician Goes on Vacation 1<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_kdeRo-xwLEaAQI0B39vnDt10vVsf6mKWqEEIYoz6gT21fYQcIUXbFrN1Y8FN5vF5z4IZKJ62MdGzu2ByRJgrVbxIAhIIYI62nfpfBnmNYIg3Max8QMI0NaVtsUDKxY0aG6LGN_KNvJ4/s1600-h/srb+money001.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 152px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_kdeRo-xwLEaAQI0B39vnDt10vVsf6mKWqEEIYoz6gT21fYQcIUXbFrN1Y8FN5vF5z4IZKJ62MdGzu2ByRJgrVbxIAhIIYI62nfpfBnmNYIg3Max8QMI0NaVtsUDKxY0aG6LGN_KNvJ4/s320/srb+money001.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5350816877328705554" /></a><br />I just got back from a three week visit of my wife's family in Serbia. I was on the lookout for anything mathematical. Check out this equation on the 100 dinar note (about $1.55). The mug is <a href="http://en.wikipedia.org/wiki/Nikola_Tesla">Nikola Tesla's</a>. He is a Serbian national hero for his contributions to electrical engineering. The equation calculates a unit of measure the <a href="http://en.wikipedia.org/wiki/Tesla_(unit)">tesla</a> which measures magnetic flux density. I tried to figure out what this means. No luck. (It did remind me of the <a href="http://www.thinkgeek.com/geektoys/plush/9fc6/">flux capacitor</a> though.)fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com2tag:blogger.com,1999:blog-4679715190635795973.post-12967817539042094612009-06-23T02:43:00.000-07:002009-06-23T02:43:00.533-07:00Mathematical Fortune<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMQxAYXG5Q0ZJ4pD6OJbqKWmr7InHwXRHf3xe-fYW1o8-OaPwL27B2a0Y3YiZEYnsrvBnZaE04_qnpQjVlS3EWNFCcURMfwWifmgpz7bMWuHxhEhX3o9-zQQVASMIIOO6ueu9JDUiIFbQ/s1600-h/math+fortune+cookie001.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 86px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMQxAYXG5Q0ZJ4pD6OJbqKWmr7InHwXRHf3xe-fYW1o8-OaPwL27B2a0Y3YiZEYnsrvBnZaE04_qnpQjVlS3EWNFCcURMfwWifmgpz7bMWuHxhEhX3o9-zQQVASMIIOO6ueu9JDUiIFbQ/s320/math+fortune+cookie001.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5338210792750111490" /></a>I thought all the statbots out there would get a kick out of this fortune.fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com0tag:blogger.com,1999:blog-4679715190635795973.post-39254663720886480372009-06-22T02:48:00.000-07:002009-06-22T02:51:08.876-07:00Math Donkeys<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRVEi8LNvF5LK_Tg7mei6iiaUo0uAkc0duI0X-ztrLkOQD-BS4Qrus57ktEKPq-XrmORZZcUO5Lv3KKcwoIAsbkTJRUXDMQJOmFVdt37D5Z3L8i-dzpivvz5fHMEAwu1PswJ5RzGMgZlQ/s1600-h/donkey+prob.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 242px; height: 320px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRVEi8LNvF5LK_Tg7mei6iiaUo0uAkc0duI0X-ztrLkOQD-BS4Qrus57ktEKPq-XrmORZZcUO5Lv3KKcwoIAsbkTJRUXDMQJOmFVdt37D5Z3L8i-dzpivvz5fHMEAwu1PswJ5RzGMgZlQ/s320/donkey+prob.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5338213567243184690" /></a><br />I love to give this problem to students. <blockquote><i>Two Donkeys are walking down the road loaded down with sacks of potatoes. One looks over at the other and says, "hey, if you give me a sack, I'll have twice as many as you; and if I give you one we'll have the same number. Weird, huh?" The other donkey just says, "Geek" and keeps walking. How many potato sacks does each donkey have?</i></blockquote>pic by <a href="http://www.flickr.com/photos/9835782@N08/2892448696/">kaysare</a>fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com4tag:blogger.com,1999:blog-4679715190635795973.post-53318302868983826762009-06-19T08:43:00.000-07:002009-06-19T10:51:17.586-07:00Beatles Mystery Chord Found...by a mathematician<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYx8VPbgOa8LEQzkMcZOpaRGOWRDXX13viN-aT9zVUtPO5uUsiA__Bo1RKH9jWrTlisJ3rUgh_uEi9gshdNWWdzG5XIuhZ6xHZLwc8OyEFYku07VYY8dv2irerJRh_QS_kcw6u9orAl0c/s1600-h/beatles.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 255px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYx8VPbgOa8LEQzkMcZOpaRGOWRDXX13viN-aT9zVUtPO5uUsiA__Bo1RKH9jWrTlisJ3rUgh_uEi9gshdNWWdzG5XIuhZ6xHZLwc8OyEFYku07VYY8dv2irerJRh_QS_kcw6u9orAl0c/s320/beatles.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5339705483500758914" /></a><br />This is a great story found on <a href="http://www.scientificblogging.com/">Scientific Blogging</a>. The opening chord to the Beatles' song Hard Days Night had long stumped musicians and musical historians. It took a mathematician, Jason Brown, using a <a href="http://en.wikipedia.org/wiki/Fourier_transform">Fourier Transform</a> to decompose the chord into its original frequencies. Was it George's 12 string, John's 6 string, or Paul's bass? <a href="http://www.scientificblogging.com/news_releases/beatles_unknown_hard_days_night_chord_mystery_solved_using_fourier_transform">Find out</a> what the missing ingredient was.fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com0tag:blogger.com,1999:blog-4679715190635795973.post-28571483502545802162009-06-18T05:33:00.000-07:002009-06-18T05:59:55.187-07:00Tweaking LifeThis is a thought on the <a href="http://www.bitstorm.org/gameoflife/">game of life</a> that Lee introduced me to a while <a href="http://yofx.blogspot.com/2009/05/game-of-life.html">back</a>. John Conway has said that he played around with various rules to see which would produce the most interesting results. I took him to mean that he played around with the survival and birth rules. I was wondering if anyone has played around with tiles having different iteration speeds? Consider if every other column iterated at twice the speed. Basically squares could "play" at different speeds. Has anyone seen anything like this? Lee? Ken, I know you said you've played around with <a href="http://en.wikipedia.org/wiki/Cellular_automata">cellular automata</a>?fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com2tag:blogger.com,1999:blog-4679715190635795973.post-14176935131356456822009-06-17T06:41:00.000-07:002009-06-17T06:41:00.584-07:00Geek of the Week: Nerd Nook<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4HuRfshCh5FhATEbhbGx2zl3vhsQKry6mmU4fREPhNtwllJydyPbqMwF_ShREYnFWlrmUSw2VbZLlV7zZclQWr9FggRaZ7KBsAYf24jYRUoXrgd1MZxtAXbsYvtJJgoO6QSWpS-7D4Ms/s1600-h/clint+eastwood+math.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 232px; height: 320px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4HuRfshCh5FhATEbhbGx2zl3vhsQKry6mmU4fREPhNtwllJydyPbqMwF_ShREYnFWlrmUSw2VbZLlV7zZclQWr9FggRaZ7KBsAYf24jYRUoXrgd1MZxtAXbsYvtJJgoO6QSWpS-7D4Ms/s320/clint+eastwood+math.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5338823210940406386" /></a><br />I've seen a lot of math t-shirts. This one on <a href="http://www.flickr.com/photos/tenshades/sets/72157604229698132/with/2359027786/">Nerd Nook's photostream</a> caught my attention. <i>(might have to blow it up to read it.)</i> In the 18 million times I've been asked, 'When will I ever use this in the real world?', I have yet to use this technique. It's kind of Dirty Harry meets underpaid math teacher. He also has a bunch of other t-shirts. I love this one. <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOtkcUVA80qtJPcZhAViYtKPg4kBwDc9QzykAWkmEAwZr69DUcJCEvNyKXs6z_ntiIa1-QJIL08O_CboFUhyN3XxdwkGqZYKAhcu8ypTG5uLvmoyTy7tmfyUBWKPAkMFzaYTToZMDfTUw/s1600-h/divide.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 320px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOtkcUVA80qtJPcZhAViYtKPg4kBwDc9QzykAWkmEAwZr69DUcJCEvNyKXs6z_ntiIa1-QJIL08O_CboFUhyN3XxdwkGqZYKAhcu8ypTG5uLvmoyTy7tmfyUBWKPAkMFzaYTToZMDfTUw/s320/divide.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5338824623467613986" /></a>fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com0tag:blogger.com,1999:blog-4679715190635795973.post-17489303757175761992009-06-16T12:45:00.000-07:002009-06-16T12:45:00.891-07:00Mystery Equation<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiz0cQxTawnVlDe4DaGr8GfHMmNTBGIG2CF-20W1hgqTQUjqWWYh0GNYcW1ThOiY8IompsQH4C9CLKXrc7gseGSeKuE6wkzGvLOnSgX5VOBOU6xSYwzIyTQPB7Lj3roSq6kvE7LMHq1L5s/s1600-h/math+illustration.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 310px; height: 320px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiz0cQxTawnVlDe4DaGr8GfHMmNTBGIG2CF-20W1hgqTQUjqWWYh0GNYcW1ThOiY8IompsQH4C9CLKXrc7gseGSeKuE6wkzGvLOnSgX5VOBOU6xSYwzIyTQPB7Lj3roSq6kvE7LMHq1L5s/s320/math+illustration.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5336881704615573602" /></a><br />I was struck by this illustration browsing <a href="http://drawn.ca/">Drawn's</a> feed. I still haven't figured out what the equation is supposed to relate. The caption on illustrator <a href="http://altpick.com/marksmith">Mark Smith's</a> site reads <blockquote><i>Green idealists fail to make the grade. The people that recycle the most are also the most likely to cause serious environmental damage by taking long haul flights when holidaying abroad.</i></blockquote> Is the equation relating atmospheric quantities? Any of you know? Check out Smith's other work. You might enjoy it as much as I did.fakehttp://www.blogger.com/profile/12859709233583742208noreply@blogger.com2