Notices
Results 1 to 17 of 17

Thread: Pythagorean Theorem Question Problem

  1. #1 Pythagorean Theorem Question Problem 
    Forum Bachelors Degree The P-manator's Avatar
    Join Date
    Nov 2005
    Location
    Toronto
    Posts
    474
    So we have been working on the Pythagorean Theorem and in this weekend's homework the following question was on the sheet.

    "The lengths of the three sides of a right triangle are consecutive integers. Find them."

    There was no other info. What does the question mean? What are "consecutive integers"?

    I don't want anyone to do my homework, I just want help figuring out what this question means.


    Pierre

    Fight for our environment and our habitat at www.wearesmartpeople.com.
    Reply With Quote  
     

  2.  
     

  3. #2  
    Forum Professor wallaby's Avatar
    Join Date
    Jul 2005
    Location
    Australia
    Posts
    1,521
    consecutive integers is any set of three numbers where the difference between each sucessive element is equal to one.

    ie (1,2,3) or (4,5,6) or (21000 ,21001 ,21002) etc.

    hence they want you to work out the lengths of the three sides of your triangle such that the lengths of the sides is one unit longer, or possibly shorter, than the previous length you used.

    and of course the Pythagorean Theorem must still apply.


    Reply With Quote  
     

  4. #3  
    Forum Professor river_rat's Avatar
    Join Date
    Jun 2006
    Location
    South Africa
    Posts
    1,517
    And a big hint is that there is only one Pythagorean triple made up of consecutive integers. mmm, so what is the standard pythagorean triple everyone knows?
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
    Reply With Quote  
     

  5. #4  
    Guest
    Obviously not everyone knows...

    I'll help narrow it down, the highest of the three numbers is less than 25.

    It's always ued as an example so if you were to use a search engine.....
    Reply With Quote  
     

  6. #5  
    Forum Professor river_rat's Avatar
    Join Date
    Jun 2006
    Location
    South Africa
    Posts
    1,517
    And my pythagorean triple of the day is (21, 220, 221)
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
    Reply With Quote  
     

  7. #6  
    New Member
    Join Date
    Nov 2006
    Posts
    4
    interesting... let me think first
    Reply With Quote  
     

  8. #7  
    Forum Professor river_rat's Avatar
    Join Date
    Jun 2006
    Location
    South Africa
    Posts
    1,517
    and todays pythagorean triple is (231, 520, 569)
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
    Reply With Quote  
     

  9. #8  
    Guest
    There's also 33 44 55 - 333, 444, 555 - 3333,4444,5555 - etc etc.. :wink:
    Reply With Quote  
     

  10. #9  
    Moderator Moderator
    Join Date
    Jun 2005
    Posts
    1,620
    Quote Originally Posted by river_rat
    And a big hint is that there is only one Pythagorean triple made up of consecutive integers. mmm, so what is the standard pythagorean triple everyone knows?
    Ya, well, I think you are being a bit unfair to the OP. Suppose, for example, you dont know the obvious Pythogorean triple referred to (most house builders do, by the way), how would one deduce it?

    Other than trial and error, I cannot see how it could be done. Is there a way? I don't see it yet.
    Reply With Quote  
     

  11. #10  
    Forum Sophomore
    Join Date
    Jul 2005
    Posts
    121
    You don't need trial and error. Three consecutive integers look like n, n+1, n+2 for some integer n. Use the condition these are a Pythagorean triple.
    Reply With Quote  
     

  12. #11  
    Moderator Moderator
    Join Date
    Jun 2005
    Posts
    1,620
    Jeez, that was dumb of me, just get it in quadratic form, thus:

    n<sup>2</sup> + (n + 1) <sup>2</sup> = (n + 2)<sup>2</sup>

    2n<sup>2</sup> + 2n + 1 = n<sup>2</sup> + 4n + 4

    n<sup>2</sup> - 2n - 3 = 0

    and solve for n using the quadratic equation formula we learned in school
    Reply With Quote  
     

  13. #12  
    Forum Professor river_rat's Avatar
    Join Date
    Jun 2006
    Location
    South Africa
    Posts
    1,517
    The same trick shows that there is only one triple consisting of consecutive integers
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
    Reply With Quote  
     

  14. #13  
    Moderator Moderator
    Join Date
    Jun 2005
    Posts
    1,620
    Well, technically, there are 2 roots to the quadratic, but of course only one of them yields a right triangle, which is what the OP was concerned with.
    Reply With Quote  
     

  15. #14  
    Guest
    Does anybody think there might be another universe out there where you can make a rightangled triangle with sides 5,5,5 ? :-D
    Reply With Quote  
     

  16. #15  
    Moderator Moderator
    Join Date
    Jun 2005
    Posts
    1,620
    What on Earth are you talking about? The roots of n<sup>2</sup> - 2n - 3 = 0 are 3 and -1. Where does 5 come into it? Have I missed your point?
    Reply With Quote  
     

  17. #16  
    Guest
    Yes you have missed it, pythagorus works in our universe but is there another where a perfect r.a.t. might be 5,5,5 ?

    it was err... humor..
    Reply With Quote  
     

  18. #17  
    Moderator Moderator
    Join Date
    Jun 2005
    Posts
    1,620
    Ya, not feeling humourous today, sorry old bean.

    In fact there is a universe where 5, 5, 5 makes a right triangle, it's called a non-Euclidean manifold. Here, the internal angles of a triangle sum to more than 180 degrees, so I'm not sure what a right triangle means here. But. It just so happens we inhabit such a manifold, it's called space-time.
    Reply With Quote  
     

Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •