462Re: [Pythagorean-L] Hi! Homework Help
- Sep 18, 2005Most 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
and both x and y are integers:
When y = 3, x = 6
When y = 4, x = 4
The resulting numbers will be 18 and 16, respectively. 17 is half-way
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........
----- Original Message -----
From: "octobergirl1028" <octobergirl1028@...>
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!
> 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.
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