tag:blogger.com,1999:blog-2433841880619171855.comments2023-10-01T11:52:29.894+01:00Pat'sBlogUnknownnoreply@blogger.comBlogger1251125tag:blogger.com,1999:blog-2433841880619171855.post-36823890413624738502023-08-28T16:48:40.297+01:002023-08-28T16:48:40.297+01:00Thank you for sharing this informative post. As a ...Thank you for sharing this informative post. As a parent, I found it very helpful and up-to-date. It's important to stay informed for the sake of our children's well-being.<br /><a href="https://alohamindmath.com/benefits-of-abacus-learning-classes-for-kids/" rel="nofollow">abacus learning for kids</a>yaminihttps://www.blogger.com/profile/01235356517198051184noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-8829621263931001402023-07-14T20:31:21.113+01:002023-07-14T20:31:21.113+01:00Nice article! I was just looking at geometry probl...Nice article! I was just looking at geometry problems solved with inversion in circles and I found this. Very interesting!fffffhttps://www.blogger.com/profile/04947122328228434854noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-24363826758707474602023-06-28T10:47:37.036+01:002023-06-28T10:47:37.036+01:00Thank you so much for sharing such an interesting ...Thank you so much for sharing such an interesting and informative blog . Unlike this, we also provide <a href="https://www.88tuition.com/course/online-maths-tuition/psle-primary-4-mathematics-tuition" rel="nofollow">primary 4 maths</a> services so if you face any issues regarding maths you may visit us. Apart from this we also provide various services at affordable prices.<br />Chetan Sharmahttps://www.blogger.com/profile/01642364001834781095noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-67181369441395190522023-06-27T15:22:41.186+01:002023-06-27T15:22:41.186+01:00Wow! This blog post is truly amazing and valuable....Wow! This blog post is truly amazing and valuable. The author clearly knows a lot about the subject and has shared a lot of helpful information. I really appreciate how they made complex ideas easy to understand and interesting. I'm excited to read more posts in the future and see what other great things they have to share. Keep up the excellent work and thank you for teaching me new things!<br /><a href="https://srislaw.com/licencia-conducir-suspendida-delito-menor-nueva-jersey/" rel="nofollow">Licencia Conducir Suspendida Delito Menor Nueva Jersey</a><br />jamesroberthttps://www.blogger.com/profile/14979482701770559263noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-13269662061046265272023-05-04T08:14:28.607+01:002023-05-04T08:14:28.607+01:00When I was in high school (1979 or 1980) my maths ...When I was in high school (1979 or 1980) my maths professor told us about that method. He told us too that we could not use it unless we were able to prove it... (I never managed to do it, except in some special cases).mau.https://www.blogger.com/profile/09641196427325175260noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-67417366121662924292023-04-26T06:45:07.379+01:002023-04-26T06:45:07.379+01:00Hey There. I found your blog. This is a really wel...Hey There. I found your blog. This is a really well written article. Hey There. I found your blog. This is a really well written article.Andrew Tysonhttps://www.blogger.com/profile/05731218054732990621noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-15078380289088232532023-04-18T21:19:51.834+01:002023-04-18T21:19:51.834+01:00That limerick (which as quoted does not scan) is b...That limerick (which as quoted does not scan) is borrowed from the one written about CH Dodd:<br /><br />I think it exceedingly odd<br />That a little professor named Dodd<br /> Should spell, if you please,<br /> His name with three D's<br />When one is sufficient for God<br />Harry Campbellhttps://www.blogger.com/profile/01675794936870568336noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-40244897571760305882023-04-18T14:18:24.670+01:002023-04-18T14:18:24.670+01:00This seems like a cool game. What is the signific...This seems like a cool game. What is the significance of the chart at the top of the post? I can't seem to figure out how it's related. Thanks.Anonymoushttps://www.blogger.com/profile/12361329093650973354noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-22070844638282891752023-04-17T15:04:17.815+01:002023-04-17T15:04:17.815+01:00sorry. you are right: 3+1+4+1+5+9+2+6+5+3+5+8+9+7+...sorry. you are right: 3+1+4+1+5+9+2+6+5+3+5+8+9+7+9+3+2+3+8+4+6+2+6+4+3+3+8+3+2+7+9+5+0+2+8+8+4+1+9+7+1+6+9+3+9+9+3+7+5+1+0+5+8+2+0+9+7+4+9+4+4+5+9+2+3+0+7+8+1+6+4+0+6+2+8+6+2+0+8+9+9+8+6+2+8+0+3+4+8+2+5+3+4+2+1+1+7+0+6+7+9+8+2+1+4+8+0 = 503 is primeHumberto Bortolossihttps://www.blogger.com/profile/08218059136324543967noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-3022969085401422142023-04-17T14:32:18.839+01:002023-04-17T14:32:18.839+01:00there is a mistake. the sum of the first 107 digit...there is a mistake. the sum of the first 107 digitsof pi is not prime since<br /><br />3+1+4+1+5+9+2+6+5+3+5+8+9+7+9+3+2+3+8+4+6+2+6+4+3+3+8+3+2+7+9+5+0+2+8+8+4+1+9+7+1+6+9+3+9+9+3+7+5+1+0+5+8+2+0+9+7+4+9+4+4+5+9+2+3+0+7+8+1+6+4+0+6+2+8+6+2+0+8+9+9+8+6+2+8+0+3+4+8+2+5+3+4+2+1+1+7+0+6+7+9+8+2+1+4+8+1= 504<br /><br />is an even number.Humberto Bortolossihttps://www.blogger.com/profile/08218059136324543967noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-32864852226197996682023-04-17T09:44:23.606+01:002023-04-17T09:44:23.606+01:00This comment has been removed by the author.Social media serviceshttps://www.blogger.com/profile/00203220431833882026noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-71045088699965052572023-04-13T19:15:22.450+01:002023-04-13T19:15:22.450+01:00I totally love this for my middle schoolers who al...I totally love this for my middle schoolers who all take Algebra over two years (not my recipe, and I have thoughts, however, I forge forth).<br /><br />How do students know the number is prime? Do they look it up? How does one know a number is prime when it gets large?<br /><br />Thanks, AmyAnonymoushttps://www.blogger.com/profile/07156390051413312467noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-80646658891391567022023-04-05T13:58:31.169+01:002023-04-05T13:58:31.169+01:00Thanks a ton.I learnt a lot from your blog and thi...Thanks a ton.I learnt a lot from your blog and this post.Amarhttps://www.blogger.com/profile/16080039005422702136noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-78294463454859049182023-03-28T15:27:03.245+01:002023-03-28T15:27:03.245+01:00Product of four successive natural numbers is one...Product of four successive natural numbers is one less than a perfect square!<br /> n* ( n+1)*( n+2)* ( n+3)= n* {( n^3) +(1+2 +3) * n^2+ ( 1*2 +2*3+3*1)* n+ 1*2*3}<br />= n^4+ 6* n^3+11*n^2+6*n+1-1= ( n^2 +3*n+1)^2-1;<br />If n=1 ;<br />Then 1*2*3*4 4!=5^2-1;<br />If n=2 Then this product=2*3*4*5=1*2*3*4*5=5!=11^2-1DEB JYOTI MITRAhttps://www.blogger.com/profile/17354232756079817530noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-89282390940152944312023-03-20T20:13:13.512+00:002023-03-20T20:13:13.512+00:00Hi, Pat. I know this is an old post, but if you se...Hi, Pat. I know this is an old post, but if you see this, take a minute to read Ch. 21 in the Gospel of John--maybe the most Pythagorean chapter in the bible?Numbers are realhttps://www.blogger.com/profile/04265120267715845575noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-29053273919794508402023-03-20T06:47:51.927+00:002023-03-20T06:47:51.927+00:00Did you know that; 47+4^4 +7^4=52^2
natureaboun...Did you know that; 47+4^4 +7^4=52^2 <br /><br />natureabounds77@gmail.comYoutube publisherhttps://www.blogger.com/profile/06193996798390048089noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-33778771830077503002023-03-16T19:36:02.784+00:002023-03-16T19:36:02.784+00:00ONLINE ECYCLOPEDIA OF INTEGER SEQUENCES. OEIS , ...ONLINE ECYCLOPEDIA OF INTEGER SEQUENCES. OEIS , 17, 104 , 216 , 242 . Type this into the search window Youtube publisherhttps://www.blogger.com/profile/06193996798390048089noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-14024802072198304182023-03-16T19:35:02.551+00:002023-03-16T19:35:02.551+00:00They are a sequence of number form the Line encycl...They are a sequence of number form the Line encyclopedia of integer sequences (OEIS) . Just. type the first few numbers of the sequence into the OEIS SEARCH window to find the sequence 17 , 104 , 216 etcYoutube publisherhttps://www.blogger.com/profile/06193996798390048089noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-7829545705987439132023-03-16T16:25:01.653+00:002023-03-16T16:25:01.653+00:00No, I never came across these. Thanks for sharing...No, I never came across these. Thanks for sharing. If you have more detail about these, drop me a note or link. Where did you come across them?Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-56985933566956257232023-03-13T23:23:57.981+00:002023-03-13T23:23:57.981+00:00Have you heard of numbers that have the property t...Have you heard of numbers that have the property that the sum of the cubes of their digits plus the number equal another number squared , For example. 17+1^3 +7^3 =19^2. , the next one is 104+1^3+0^3+4^3 = 13^2 . The next prime that does this. after 17. is 2897. since. 2897+2^3+8^3+9^3+7^3 =67^2=4489 , The next prime. is 11471+1^3+1^3+4^3+7^3+1^3 = 109^2 <br /><br />William Gosnell Youtube publisherhttps://www.blogger.com/profile/06193996798390048089noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-49343970800722365252023-02-14T18:19:47.285+00:002023-02-14T18:19:47.285+00:00Thanks, I will check and see if I can verify and c...Thanks, I will check and see if I can verify and correct this. I'm very greatful for the correction.Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-59032243494249607992023-02-08T22:28:45.987+00:002023-02-08T22:28:45.987+00:00Regarding this part: "[Euler] created a tetra...Regarding this part: "[Euler] created a tetrahedron formed by three right triangles parallel to the xyz coordinate axes, and one oblique face connecting them. The triple right angle edges were 153, 104, and 672, and the three edges of the oblique face were 185, 680, and 697. These were each Pythagorean right triangles, the four faces of (104,672,680), (153,680,697), (153,104,185) and (185,672,697)"<br /><br />Perhaps I misunderstand the description because I take it to mean that three faces of the tetrahedron can be taken to be the right triangles OAB, OAC, OBC, where <br /><br />O=(0,0,0), <br />A=(153,0,0),<br />B=(0,104,0),<br />C=(0,0,672).<br /><br />But in that case, the hypotenuses (the sides of the fourth face) are not all integers; only two of them match what is written above. Mathematica reports the following for AB, AC, BC:<br /><br />In[1]:= {Sqrt[153^2 + 104^2], Sqrt[153^2 + 672^2], Sqrt[104^2 + 672^2]}<br /><br />Out[1]= {185, 3 Sqrt[52777], 680}<br /><br />In[2]:= N[%]<br /><br />Out[2]= {185., 689.197, 680.}<br /><br />I realize that much of the above was quoted from the Wikipedia page, https://en.wikipedia.org/wiki/Heronian_tetrahedron, which is where I first encountered it.<br /><br />It seems to me that the example should be with "triple right angle edges" equal to 44, 117, 240, that is, with <br /><br />OA=44, OB=117, OC=240,<br /><br />which is how I interpret the example cited on page 14 of Martin Gardner's book (1983, Wheels, Life and Other Mathematical Amusements) and also on p. 58 of the article by Spohn (1972, On the Integral Cuboid). <br /><br />In that case the other three side lengths are indeed integers, as are the areas and also the volume of the tetrahedron, though the fourth face is not a right triangle (and nor is it claimed to be in Gardner or Spohn).<br /><br />A different example in Gardner (and credited to Euler) is for when "all values are integral except a face diagonal". And the values for that seem to match what is described in the blog and Wikipedia.<br />RdVMhttps://www.blogger.com/profile/02954776162374433030noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-43937827627768733862023-02-07T06:34:14.708+00:002023-02-07T06:34:14.708+00:00A very detailed explanation was provided on this t...A very detailed explanation was provided on this topic. Math is my favorite subject. It is very informative and helpful for students and teachers. I just want to thank you for sharing your thoughts with us. Now it's time to get <a href="https://localbiznear.com/a1-garden-state-construction-roofing-siding-gutter-wayne-nj/" rel="nofollow">Roofing Services in Wayne</a> for more information.Davidhttps://www.blogger.com/profile/01868323806760019746noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-72103382037259194782023-01-20T11:08:48.716+00:002023-01-20T11:08:48.716+00:00The link to Ed Pegg's web site is broken :(The link to Ed Pegg's web site is broken :(yleehttps://www.blogger.com/profile/14335969938033344335noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-3737888131447650512023-01-12T22:49:50.906+00:002023-01-12T22:49:50.906+00:00Thank you, I hope it now appears corrected. Thank you, I hope it now appears corrected. Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.com