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462Re: [Pythagorean-L] Hi! Homework Help

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  • Larry Rafey
    Sep 18, 2005
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      Most interesting, my dear octobergirl. In fact, I have never heard of a
      number feared by the Pythagoreans, however, my guess is that the number is
      17. I shall make the following argument for this number:
      Let x and y = the sides of a rectangle in integers.
      Let its Area = xy
      Let its Perimeter = 2(x+y)
      Then, create the appropriate polynomial and solve for x:
      xy = 2x + 2y
      xy - 2x - 2y = 0
      x(y-2) = 2y
      x = 2y/(y-2)
      Given that x>0
      y>0
      and both x and y are integers:
      Then,
      When y = 3, x = 6
      When y = 4, x = 4
      The resulting numbers will be 18 and 16, respectively. 17 is half-way
      between !
      Of course.... I could be mistaken. Perhaps someone else on this list is
      better acquainted with the "Pythagorean fear, " as you have indicated.
      Thanks for inquiring........
      LD Rafey






      ----- Original Message -----
      From: "octobergirl1028" <octobergirl1028@...>
      To: <Pythagorean-L@yahoogroups.com>
      Sent: Sunday, September 18, 2005 12:46 PM
      Subject: [Pythagorean-L] Hi! Homework Help


      > Hi! My name is Jane, and I was needing some help with my homework. THe
      > question is "The number feared by the Pythagoreand since it lies
      > halfway between the only two numbers that can be both the perimeter and
      > the area of the same rectanle." can anyone help? thanks!
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      > But before all, thy soul to its faithful duty,Invoke these Gods with
      fervour, that whose aid,Thy work begun, alone can terminate. Instructed by
      them,naught shall then deceive thee: Of diverse beings thou shalt sound the
      essence; And thou shalt know the principle and end of All.
      >
      > Yahoo! Groups Links
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