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| Photo by Gavin Keefe Schaefer |
As we've been studying vector addition in class, I've been coming up with examples to use on the board. I usually deliberately choose the addends so that the magnitude of the resultant will be a whole number. How do I do this?
I choose the addends so they are two members of a pythagorean triple--three integers that are sides of a right triangle. Have you memorized any pythagorean triples?
- Is there a pattern or formula that can be used to generate pythagorean triples?
- Is there a size limitation? Is there such a thing as the largest phythagorean triple or the last pythagorean triple?
- Do you think there are any pythagorean triples in the photo at the top of the post?
I believe that there is a formula for phythagorean triples. i don't know what it is but i can imagine that it's a hard formula. Also I don't think that theres a last triple. Numbers keep going I don't see why they would just stop. You can take a 3,4,5 triangle and keep adding zeros to those nmbers and it will continue to work.
ReplyDeleteThanks for all the comments this week!
ReplyDeleteBecause there are a large amounts of right angles in the photo above, I would imagine there is a good chance that there would be a Pythagorean Triplet.
ReplyDeleteYes, I think there are pythagorean triplets in the photo above. The triangles do have right angles which suggest a pythagorean triplet.
ReplyDeletei agree with the previous thoughts, since there are so many right angles there must be a pythagorean triplet present, a size limitation i would think so since everything has its limits n i dont think so for the last pythagorean triple/largest.
ReplyDeleteThe quadratic expression (p+q)^2-(p-q)^2 has an integer square root if p and q have integer square roots. Submitted by Peter L. Griffiths.
ReplyDelete