tag:blogger.com,1999:blog-28172905.post500779061740027354..comments2024-03-03T17:53:46.947-05:00Comments on (x, why?): List of Pythagorean Triples (3-50)(x, why?)http://www.blogger.com/profile/17499160002806879025noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-28172905.post-77248964804580136212019-04-25T18:47:47.873-04:002019-04-25T18:47:47.873-04:00Thank you for your kind & constructive respons...Thank you for your kind & constructive response. We're happy to help, and have shared this thread with other classes at our school.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-28172905.post-88852610076557695602019-04-25T17:38:46.484-04:002019-04-25T17:38:46.484-04:00I just ran a short BASIC program to find Triples i...I just ran a short BASIC program to find Triples in the form of a, a+1, c (boring, but I got to practice coding for five minutes), and I got the following:<br /><br /> 3 4 5<br /> 20 21 29<br /> 119 120 169<br /> 696 697 985<br /> 4059 4060 5741<br /> 6437 6438 9104<br /> 7422 7423 10497<br /> 8815 8816 12467<br /> 9800 9801 13860(x, why?)https://www.blogger.com/profile/17499160002806879025noreply@blogger.comtag:blogger.com,1999:blog-28172905.post-82399201936876190412019-04-25T10:14:20.032-04:002019-04-25T10:14:20.032-04:00Also 44 - 117 - 125.
Also 44 - 117 - 125.<br />(x, why?)https://www.blogger.com/profile/17499160002806879025noreply@blogger.comtag:blogger.com,1999:blog-28172905.post-46408652601485368992019-04-25T09:43:12.965-04:002019-04-25T09:43:12.965-04:00Thanks for that addition, to which I'll add 36...Thanks for that addition, to which I'll add 36 - 77 - 85.<br /><br />I haven't thought about this post in years, and it started just from my musings on the subject. I never wanted to write a program to find them all (and I used to be a programmer, so it would be somewhat trivial), and I was doing some exploration of my own into the topic to get my own insights, but I was reluctant to read others' notes on the subject. I realize that this was been done to death by so many others. <br /><br />Formulas for generating them are out there, and they don't interest me as much. (It becomes a computer problem instead of a math problem at that point.)<br /><br />My original thinking was much too limited, and had I continued, I would've seen (which I eventually did) that I could search for examples where, say, c = b + 2n^2, where n is an whole number. The fault in my logic was assuming that a should be the smallest number in the triple.<br /><br />In cases like 3-4-5 or 7-24-25, it's not that c is one more than b, it's that 5 = 3 + 2(1) or 25 = 7 + 2(9).<br />(x, why?)https://www.blogger.com/profile/17499160002806879025noreply@blogger.comtag:blogger.com,1999:blog-28172905.post-29126520768286846142019-04-23T18:40:11.058-04:002019-04-23T18:40:11.058-04:0028-45-53 is missing?
28^2 = 784
45^2 =2025
=======...28-45-53 is missing?<br />28^2 = 784<br />45^2 =2025<br />==========<br />53^2 =2809<br /><br />Found in a CAASPP practice problem by a talented MS Geometry class...Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-28172905.post-59426248070076296722019-02-21T05:16:14.074-05:002019-02-21T05:16:14.074-05:00Pythagorean triples can be generated as function o...Pythagorean triples can be generated as function of x (x>=3) according to Mir's Generalized Pythagorean triple generation theorem (MGPTGT) which states "let (x, y, z) be a Pythagorean integral triple (base, perpendicular, hypotenuse in that order) then there exist triple(s) for every x (x>=3) because of existence of two integers (j, k) with parity that of x (3 <=j =3<br />More extensive tables are currently being generated with python.<br />Dr. (Prof.) Shabir Ahmad Mir, AuthorDr.(Prof.) Shabir Ahmad Mirhttps://www.blogger.com/profile/12344010689983736692noreply@blogger.comtag:blogger.com,1999:blog-28172905.post-29173798892686458492012-06-08T23:15:31.365-04:002012-06-08T23:15:31.365-04:00Can't make it too easy for you, can I?
42 is...Can't make it too easy for you, can I? <br /><br />42 is a typo. "Obviously", it should've been 52.(x, why?)https://www.blogger.com/profile/17499160002806879025noreply@blogger.comtag:blogger.com,1999:blog-28172905.post-42607347324075799612012-06-08T21:08:50.090-04:002012-06-08T21:08:50.090-04:0039-42-65 is wrong
Thanks anyway You almost do my ...39-42-65 is wrong <br />Thanks anyway You almost do my homework for me...Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-28172905.post-54063724068935970412009-06-24T17:51:35.786-04:002009-06-24T17:51:35.786-04:00Proofreading was also a consideration for stopping...Proofreading was also a consideration for stopping at 50.<br /><br />That, and some of the numbers were getting extremely large.(x, why?)https://www.blogger.com/profile/17499160002806879025noreply@blogger.comtag:blogger.com,1999:blog-28172905.post-43200202021820612032009-06-24T17:50:18.135-04:002009-06-24T17:50:18.135-04:00Thanks.
27,120,123 is correct. All the numbers are...Thanks.<br />27,120,123 is correct. All the numbers are multiples of 3, so 121 is obviously wrong.<br /><br />Proofreading this was a pain, and I'm sure I missed a couple.(x, why?)https://www.blogger.com/profile/17499160002806879025noreply@blogger.comtag:blogger.com,1999:blog-28172905.post-12603340787374651892009-06-24T07:49:42.562-04:002009-06-24T07:49:42.562-04:0027,120,121 i think should be 17,120,123 becasue th...27,120,121 i think should be 17,120,123 becasue that goes into the a, b, b+3 set and the one for line 27 is missingmarskellhttps://www.blogger.com/profile/01787001244354865006noreply@blogger.com