tag:blogger.com,1999:blog-2433841880619171855.comments2022-12-06T15:03:16.008+00:00Pat'sBlogUnknownnoreply@blogger.comBlogger1312125tag: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.comtag:blogger.com,1999:blog-2433841880619171855.post-48421743128522654832022-08-10T19:12:22.452+01:002022-08-10T19:12:22.452+01:00Hello Pat. My name is cheryl holland and i came ac...Hello Pat. My name is cheryl holland and i came across your blog when i was looking for information about my high school mentor, Hector Hirigoyen. He was my high school math teacher. I know he died in 2003 but I was wondering if you were a friend of his and could tell me more about him. I graduated high school in 1979ðŸ˜³ and I am filling out an application to a graduate degree program and it asked me to name some of my intellectual influences and he was oneâ€¦Anyway, if you have any information about him after about 1980, i would love to hear it. Thank you, my email is hollandc@me.comAnonymoushttps://www.blogger.com/profile/10232188860052695054noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-91343945486566391562022-05-02T15:49:28.543+01:002022-05-02T15:49:28.543+01:00Thank you, hopefully correctedThank you, hopefully correctedPat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-49229670379067414702022-05-02T07:33:54.198+01:002022-05-02T07:33:54.198+01:00In birth of Etienne Pascal, you wrote: "an Ac...In birth of Etienne Pascal, you wrote: "an AcadÃ©mie Libre or ACADÃ‰MIE FRANÃ‡AIS". In French, the word acadÃ©mie is feminine, hence it should read (note the final "E"): "an AcadÃ©mie Libre or ACADÃ‰MIE FRANÃ‡AISE".Unknownhttps://www.blogger.com/profile/02670765110725430103noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-21505648624168549382022-04-29T19:41:35.179+01:002022-04-29T19:41:35.179+01:00And thank you sir, for the kind words. And thank you sir, for the kind words. Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-37613859558313739382022-04-25T15:13:31.806+01:002022-04-25T15:13:31.806+01:00Wonderful article. very nicely done, Pat. Thank yo...Wonderful article. very nicely done, Pat. Thank you.SIDDHARTHA MISRAhttps://www.blogger.com/profile/08846056833260395680noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-38418649634654996052022-04-05T11:57:08.108+01:002022-04-05T11:57:08.108+01:00The 95th day of the year; 95^0 + 95^1 + 95^2 + 95^...The 95th day of the year; 95^0 + 95^1 + 95^2 + 95^3 + 95^4 + 95^5 + 95^6 is prime.<br /><br />I wrote a small python program to check the numbers from 2 to 366, with the sum of their powers from 0 to 200. Here are the coming days:<br />97 16 6.20652E+31 --> 97^0 + 97^1 + 97^2 + ... + 97^16 is about 6.20652E+31 and is prime<br />97 36 3.37507E+71<br />98 12 7.92807E+23<br />98 46 3.98891E+91<br />99 2 9901<br />99 4 97039801<br />99 36 7.03519E+71<br />99 46 6.3625E+91<br /><br />Unknownhttps://www.blogger.com/profile/02670765110725430103noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-63716782945012323002022-03-29T14:23:23.000+01:002022-03-29T14:23:23.000+01:00Thank you for the correction.Thank you for the correction.Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-90628812973298894432022-03-29T13:26:44.574+01:002022-03-29T13:26:44.574+01:00I noticed three typos in the title of the article ...I noticed three typos in the title of the article mentioned in the birth of Tullio Levi-Civita (29 Mar 1873, 29 Dec 1941). The exact title is: <b>MÃ©thodes de calcul diffÃ©rentiel absolu et leurs applications</b>. Here is a link that mentions this article: https://link.springer.com/article/10.1007/BF01454201Unknownhttps://www.blogger.com/profile/02670765110725430103noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-12084754416136060922022-03-27T23:37:00.279+01:002022-03-27T23:37:00.279+01:00Thanks, So there is only one n digit number for wh...Thanks, So there is only one n digit number for which cube of prime has more than one solution below n=6.Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-14434384069091384252022-03-27T12:53:05.356+01:002022-03-27T12:53:05.356+01:00You wrote: "The 86th prime is 443, and 443^3 ...You wrote: "<i>The 86th prime is 443, and 443^3 = 86,938,307. There is no other two digit n, such that the nth prime [cubed] starts with n.</i>"<br /><br />I have found a few more with primes below 10^8:<br />The 2nd prime is 3, its cube is 27 which starts with 2<br />The 86th prime is 443, its cube is 86,938,307 which starts with 86<br />The 522nd prime is 3,739, its cube is 52,271,672,419 which starts with 522<br />The 3,512th prime is 32,749, its cube is 35,123,204,285,749 which starts with 3,512<br />The 196,569th prime is 2,698,807, its cube is 19,656,920,616,618,963,943 which starts with 196,569<br />The 552,758th prime is 8,206,889, its cube is 552,758,816,881,636,973,369 which starts with 552,758<br />The 1,567,534th prime is 25,026,821, its cube is 15,675,343,346,747,191,585,661 which starts with 1,567,534<br />The 4,477,045th prime is 76,500,421, its cube is 447,704,516,432,426,884,118,461 which starts with 4,477,045.Unknownhttps://www.blogger.com/profile/02670765110725430103noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-69395322566738594272022-03-24T00:20:26.915+00:002022-03-24T00:20:26.915+00:00Thanks for adding this. Much appreciated.Thanks for adding this. Much appreciated.Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-50683389946523690102022-03-22T08:56:37.879+00:002022-03-22T08:56:37.879+00:0081 is a square number(9^2) and the sum of irs divi...81 is a square number(9^2) and the sum of irs divisors is also a square, 1 + 3 + 9 + 27 + 81= 121 = 11^2.<br />There are no other year dates with this property. I can find no record of any other of any size....anyone?<br /><br />I calculated a few below 10**8:<br />1 1 [1]<br />81 121 [1, 3, 9, 27, 81]<br />400 961 [1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400]<br />32400 116281 [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200, 32400]<br />1705636 2989441 [1, 2, 4, 653, 1306, 2612, 426409, 852818, 1705636]<br />3648100 7958041 [1, 2, 4, 5, 10, 20, 25, 50, 100, 191, 382, 764, 955, 1910, 3820, 4775, 9550, 19100, 36481, 72962, 145924, 182405, 364810, 729620, 912025, 1824050, 3648100]<br />Unknownhttps://www.blogger.com/profile/02670765110725430103noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-69979395964116710452022-03-21T18:48:52.985+00:002022-03-21T18:48:52.985+00:00Thanks for adding this. Thanks for adding this. Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-54071187536571114102022-03-21T16:16:33.249+00:002022-03-21T16:16:33.249+00:00For those who care, the 80 primes made by the conc...For those who care, the 80 primes made by the concatenation of primes with two digits are:<br />1117, 1123, 1129, 1153, 1171, 1319, 1361, 1367, 1373, 1723, 1741, 1747, 1753, 1759, 1783, 1789, 1913, 1931, 1973, 1979, 1997, 2311, 2341, 2347, 2371, 2383, 2389, 2917, 2953, 2971, 3119, 3137, 3167, 3719, 3761, 3767, 3779, 3797, 4111, 4129, 4153, 4159, 4337, 4373, 4397, 4723, 4729, 4759, 4783, 4789, 5323, 5347, 5923, 5953, 6113, 6131, 6143, 6173, 6197, 6719, 6737, 6761, 6779, 7129, 7159, 7331, 7919, 7937, 8311, 8317, 8329, 8353, 8389, 8923, 8929, 8941, 8971, 9719, 9743 and 9767Unknownhttps://www.blogger.com/profile/02670765110725430103noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-10877020273802630812022-03-21T13:26:17.083+00:002022-03-21T13:26:17.083+00:00This comment has been removed by the author.Unknownhttps://www.blogger.com/profile/02670765110725430103noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-25868996995115012562022-03-05T17:55:22.745+00:002022-03-05T17:55:22.745+00:00What about a hint. It is more than 63, but less th...What about a hint. It is more than 63, but less than 100. Good Luck.Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-72725490980611677482022-03-03T14:46:02.831+00:002022-03-03T14:46:02.831+00:00What is the other number beside 63 with that pecul...What is the other number beside 63 with that peculiar Roman numeral property? Thanks!Anonymoushttps://www.blogger.com/profile/08629763047619668343noreply@blogger.com