tag:blogger.com,1999:blog-2433841880619171855.comments2023-04-01T07:08:45.426+01:00Pat'sBlogUnknownnoreply@blogger.comBlogger1295125tag:blogger.com,1999:blog-2433841880619171855.post-29651453598517473812023-04-01T07:08:45.426+01:002023-04-01T07:08:45.426+01:00Nios on Demand exam
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...<a href="https://www.facebook.com/niosonlineadmissionform/" rel="nofollow">Nios on Demand exam</a><br /><a href="https://twitter.com/ptarachar/" rel="nofollow">Patrachar Vidyalaya Admission</a><br /><a href="https://twitter.com/KapoorStudy" rel="nofollow">Nios online form</a><br /><a href="https://www.facebook.com/distanceeducationcoursesdelhi" rel="nofollow">BBA Admission</a><br /><a href="https://www.facebook.com/B.edadmissionDelhiNcr/" rel="nofollow">CRSU B.ed Admission</a><br />Distance Education learning Admissionhttps://www.blogger.com/profile/09461024356420909234noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-33162686536374829292023-04-01T04:25:21.736+01:002023-04-01T04:25:21.736+01:00You must have a strong background education to bec...You must have a strong background education to become a successful expert in data science. And not only knowledge of a degree is required, but you can also learn data science course.<a href="https://360digitmg.com/india/faridabad/data-science-certification-course-training-institute" rel="nofollow">Data science course institute in Faridabad</a>Anjali https://www.blogger.com/profile/00767464658653467025noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-64877294254585399402023-03-31T18:40:26.044+01:002023-03-31T18:40:26.044+01:00You must have a strong background education to bec...You must have a strong background education to become a successful expert in data science. And not only knowledge of a degree is required, but you can also learn data science course.<a href="https://360digitmg.com/india/nagpur/data-science-certification-course-training-institute" rel="nofollow">Data science certification course in Nagpur</a>Anjali https://www.blogger.com/profile/00767464658653467025noreply@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.comtag:blogger.com,1999:blog-2433841880619171855.post-81372296098910078932023-01-05T21:59:03.943+00:002023-01-05T21:59:03.943+00:00Good day Sir,
There is a typo in the title of the...Good day Sir,<br /><br />There is a typo in the title of the book from Jean-André Lepaute: it is "Traité d'horlogerie" (and not horologerie). Here is a link to it:<br />https://gallica.bnf.fr/ark:/12148/bpt6k6292970j.texteImage<br />Kind regards,<br />Stéphane QuensonUnknownhttps://www.blogger.com/profile/02670765110725430103noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-35618810234720459482022-12-09T08:40:34.752+00:002022-12-09T08:40:34.752+00:00the middle daughter, Alica?the middle daughter, Alica?Unknownhttps://www.blogger.com/profile/07659270566129809287noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-50385654035225633222022-11-10T19:14:55.747+00:002022-11-10T19:14:55.747+00:00Well, actually those of us who were close to him s...Well, actually those of us who were close to him sometimes use his nickname Car.... OK, actually I'm busted. It was a typo. Thanks for pointing it out. Be well.Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-57612653246052703372022-11-09T15:58:01.683+00:002022-11-09T15:58:01.683+00:00Typo: I suspect the opening quote is supposed to b...Typo: I suspect the opening quote is supposed to be from Carl Sagan, not Car Sagan.Nhttps://www.blogger.com/profile/13714764990968576130noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-37922081567069198452022-10-03T14:34:25.108+01:002022-10-03T14:34:25.108+01:00excellent! the best...
excellent! the best...<br />Anonymoushttps://www.blogger.com/profile/00812856153188042635noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-46970352203465664232022-09-09T19:45:12.717+01:002022-09-09T19:45:12.717+01:00triangles abc and cde are mathematically similar. ...triangles abc and cde are mathematically similar. This means that they have the same shape, but possibly different sizes. triangles abc and cde are both triangles, so they have three sides and three angles. The sides of triangles abc and cde are in the same ratio, so their angles must be in the same ratio as well. This means that triangles abc and cde are similar.Read another amazing blog: https://lead-academy.org/blog/triangles-abc-and-cde-are-mathematically-similar/<br />Torreshttps://www.blogger.com/profile/02657210351999026844noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-75277127769219745642022-09-05T21:34:38.294+01:002022-09-05T21:34:38.294+01:00wgisa Sadly, too true. Send me a link to your rev...wgisa Sadly, too true. Send me a link to your revision, always more to learnPat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-53030585772612183022022-09-05T16:38:40.552+01:002022-09-05T16:38:40.552+01:00Oh Pat... I was revisiting this post to share with...Oh Pat... I was revisiting this post to share with others. I had to chuckle because I read the last the last comment out of context. Ha! Then I went back and read the comments above it. Phew! You weren't attacking Liam, you were telling him not to worry about his typo in the previous comment. ;) Sad that the internet has definitely changed since you first posted this. People are much more quick to attack...wgisahttps://www.blogger.com/profile/12905892779308099279noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-69911044853318753492022-08-17T22:46:27.080+01:002022-08-17T22:46:27.080+01:00Thanks Heaps John. Thanks Heaps John. Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-12912834864964042112022-08-16T23:29:30.082+01:002022-08-16T23:29:30.082+01:00Found it! https://pages.uoregon.edu/koch/Pentagona...Found it! https://pages.uoregon.edu/koch/PentagonalNumbers.pdfJohn Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.com