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.

>

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