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wu :: forums    riddles    medium (Moderators: Grimbal, towr, william wu, Eigenray, Icarus, ThudnBlunder, SMQ)    Joined Pythagorean Triangles « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Joined Pythagorean Triangles  (Read 587 times) ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Joined Pythagorean Triangles   Pythag.jpg « on: Sep 25th, 2007, 4:38pm » Quote Modify The figure below shows two Pythagorean triangles joined together with a common side. Can you find any more examples where three of the five side-lengths are prime? « Last Edit: Sep 26th, 2007, 5:05am by ThudnBlunder » IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Joined Pythagorean Triangles   Pythag2.jpg « Reply #1 on: Sep 25th, 2007, 4:45pm » Quote Modify Can a fourth triangle be added (as below) such that four of the seven side-lengths are prime? IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Barukh Uberpuzzler     Gender: Posts: 2276 Re: Joined Pythagorean Triangles   « Reply #2 on: Sep 25th, 2007, 11:55pm » Quote Modify For the first: yes, for example: a = 11, c = 61, e = 1861. « Last Edit: Sep 26th, 2007, 8:56am by Barukh » IP Logged Barukh Uberpuzzler     Gender: Posts: 2276 Re: Joined Pythagorean Triangles   « Reply #3 on: Sep 26th, 2007, 12:07am » Quote Modify For the second: yes, a > 100. IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Joined Pythagorean Triangles   « Reply #4 on: Sep 26th, 2007, 3:01am » Quote Modify Are there also examples with two triangles where 4 of the 5 sides are prime? (In which case, obviously, the even sides have to match). IP Logged Wikipedia, Google, Mathworld, Integer sequence DB ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Joined Pythagorean Triangles   « Reply #5 on: Sep 26th, 2007, 4:13am » Quote Modify on Sep 25th, 2007, 11:55pm, Barukh wrote: For the first: yes, for example: a = 11, b = 61, e = 1861. But a and b are not defined in the first problem.     on Sep 26th, 2007, 12:07am, Barukh wrote: For the second: yes, a > 100. a = 101?   IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Barukh Uberpuzzler     Gender: Posts: 2276 Re: Joined Pythagorean Triangles   « Reply #6 on: Sep 26th, 2007, 4:18am » Quote Modify on Sep 26th, 2007, 4:13am, ThudanBlunder wrote: a = 101?   No, a > 101.   IP Logged ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Joined Pythagorean Triangles   « Reply #7 on: Sep 26th, 2007, 6:57am » Quote Modify on Sep 25th, 2007, 11:55pm, Barukh wrote: For the first: yes, for example: a = 11, b = 61, e = 1861. If a is prime, can you express the other sides in terms of it? IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Barukh Uberpuzzler     Gender: Posts: 2276 Re: Joined Pythagorean Triangles   « Reply #8 on: Sep 26th, 2007, 8:58am » Quote Modify on Sep 26th, 2007, 6:57am, ThudanBlunder wrote: If a is prime, can you express the other sides in terms of it? There was a typo in notation.   c = F(a) = (a2+1)/2, e = F(c)   Of course, this is necessary, but not sufficient. IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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