pythagorean

  1. D

    Pretty basic Pythagorean & Trigonometry

    Hi, It's probably gonna be a pretty simple thing to solve for you but I'm not that good in math so I'm really thankful for any help that you can bring me. Long story short (refer picture below): As you can see we have two circles forming two right angled triangles with a third one. The...
  2. L

    Pythagorean triple integers' occurrence

    Is there a limit to how many times a particular integer may appear in different Pythagorean triples?
  3. E

    Algebra Pythagorean Theorem

    Hello all. I was wondering how to solve this particular problem. I am not certain I am setting it up correctly, and I think it's likely I don't have it quite right. Any help is deeply appreciated. (from textbook) "Use the Pythagorean Theorem to find the missing side length. Leave answer in...
  4. J

    Pythagorean theorem/Lesson Learned

    Hello, I learned something interesting that I want to share. So, me and my brother were talking about math, and he told me that, "The Pythagorean Theorem only works for right triangles." I then thought to myself, "How would I find side length of a triangle like an isosceles from the two side...
  5. L

    Pythagorean n-tuples' tendency

    The following Pythagorean n-tuples determine the set of every value for the exclusive sums of n terms in Pythagorean equations: For instance, One-tuples: x^2; 1, 4, 9, 16, 25, 36... Two-tuples: x^2+y^2; 2, 5, 8, 10, 13, 18... Three-tuples: x^2+y^2+ z^2; 3, 6, 9, 11, 12, 14... etc. Do these...
  6. H

    Generalized Pythagorean theorem

    Hi, let S be bounded piece of a plane in the space E3 and let's note Si an orthogonal projection of S into xy, xz and yz planes respectively. Then it can be proved that (1) area(S)^2=area(S1)^2+area(S2)^2+area(S3)^2. But there is also a general theorem, that in a vector space with dot product...
  7. G

    Primality Test and Factorization with Pythagorean triples and quadratic diophantine

    A Pythagorean triple (A,b,c) with a minor cateto A odd always admits a solution (A,b,b+1) where 2*b+1=A^2 For example, let N be a semiprimo N=p*q then N/1, N/N, N/p, N/q will be our four paths Suppose we follow the N/q road then (N/q+1)/2 or (N/q-1)/2 will be odd then...
  8. R

    Proving the Pythagorean theorem

    Most of us are very familiar with the Pythagorean theorem, so familiar that we just take it for granted, but would you know how to prove it? If you would like to take a look I made a short lesson where I describe a neat proof of the theorem. aHtVuNZ3khk
  9. L

    # of Pythagorean n-tuples

    For n > 1, what count of Pythagorean n-tuples tends to be greatest?
  10. L

    All prime Pythagorean triple

    Does there exist a Pythagorean triple consisting only of prime numbers?
  11. B

    Pythagorean prime in every prime twin

    Hi, I have a thread to understand, but I have some problem with it. I must prove that in every prime twin there is one and only one Pythagorean prime. I found something about it on 5 page of: www.fq.math.ca/Scanned/24-2/sternheimer.pdf Can anyone explain it a bit easier? Thank you a lot.
  12. L

    Exclusive Pythagorean singles

    Do there exist Pythagorean triples that do not share a member with any other triple? Or those that share two?
  13. A

    A new way to Pythagorean Theorem numbers

    Choos A > 1 Find B by the formula B = 0.5( AA - 1 ) Find C by the formula C = B + 1 the result .... AA + BB = CC Examples A1.4 B0.48 C1.48 = (A140 B48 C148) = ( A35 B12 C37 ) A1.8 B1.12 C2.12 = (A180 B112 C212 )=( A45 B28 C53 ) A2 B1.5 C2.5 = (A20 B15...
  14. S

    Pythagorean Theorem

    To get from one corner of a rectangular court to the diagonally opposite corner by walking along two sides, a distance of 160 meters must be covered. By going diagonally across the court, 40 meters are saved. Find the dimensions of the court, to the nearest cm. I'm using the pythagorean theorem...
  15. C

    Finding a formula which generates (produces) Pythagorean Triplets/triples,

    I have an oral exam on Monday. I need to explain to my professor where the s and t came from the formula, why the rules are what they are (in our case, odds numbers and s>t>0) and why why each a = st, b = (s2 - t2)/2 and Let c = (s2 + t2)/2? Basically, I need to explain how I derived the...
  16. C

    Can you all help with with this Pythagorean Triplets/triples question

    I have an oral exam next week. I need to be able to explain this to my professor b^2 = [(s^2 - t^2)/2]^2 and b^2 = [(s^2 + t^2)/2]^2 Can you all please show me how to distribute these the long way? If this is in the wrong area, can someone move it to the correct area, thanks.
  17. E

    Special Pythagorean triple?

    Is there a Pythagorean triple $(a,b,c)$ such that $a^2 -c$ and $b^2 -c$ are both perfect squares?
  18. T

    Pythagorean theorem

    Mike is standing 200m east of a pole. Sasi is standing directly north of Mike. Starting at the same time, Mike and Sasi race to the pole and reach it at the same moment. Sasi runs three times faster than Mike. How far north of Mike was Sasi standing at the start of race, to the nearest metre?
  19. L

    Another Pythagorean Theorem question

    Use the Pythagorean Theorem to fine what b equals. I'm confused about the square root, I know the square root of something squared is just the number, but what about when there's a number and then the square root. Please help. Thanks in advance.
  20. L

    Pythagorean Theorem Question

    Julian jogs 2 kilometers east, 4 kilometers north, and then 7 kilometers west. How far is Julian from his starting position, to the nearest tenth of a kilometer? --------------------------------------- I don't know if I'm burnt from studying all day and can't see whether or not this is...