Fog Creek Software
Discussion Board

  Frustated by (Near) Impossible Mathematical Func

If anyone of you has the time, inclination and the skill to solve complex mathematical probs., here's one I've been banging on for about a year now.

Rectangle/Square PQRS with lengths A & B

          P      ---      Q

          |                  |

          S      ---      R

PQ || SR = A
QR || PS = B
Area = AB = C
Diagonal = SQ
t = Angle PSQ = 45 deg.
tan(t) = A/B = 1
As t reduces to 0, PS increases & PQ decreases. So the function has limits of 45 deg. -> 0.deg.

Problem: Generate the function. And solve for A & B in all N, where N is a Natural number.

Can it be solved? Or can it be _proven_ unsolvable?



Indian Developer in India
Tuesday, January 27, 2004

What function?  Where does N fit in to this?

Unless I misread this, you left out some important details.

BTW, how did you come across this problem?

Tuesday, January 27, 2004

Yes, I did leave out ONE important detail. As mentioned earlier (in another thread), the primary input will be C, the area.

I made this up myself.

Indian Developer in India
Tuesday, January 27, 2004

The eqn. I've come up with is

Sqroot(C*Tan(t))  = N ; Where N is natural number
for a given natural constant "C", with "t" ranging from 0 degrees to 45 degrees

Indian Developer in India
Tuesday, January 27, 2004

I am reading this thread because I like math problems.  But the main problem here is that the problem is described rather poorly.  It has something to do with angles and area but that is about all I can figure out so far.

Looking at your first post it says "solve for A & B in all N" and tells us N is a positive integer, but never says where it fits in to anything else.

In the fourth post you give the equation "Sqroot(C*Tan(t))  = N".

Using tan(t) = A/B and C = AB we reduce this to:
sqr( C * tan(t) ) = N
sqr ( A * B * A / B ) = N
sqr ( A * A ) = N
A = N

And of what use is this?

Tuesday, January 27, 2004

C is the Area. A & B are its factors. N should be a positive integer.

Indian Developer in India
Tuesday, January 27, 2004

So if there can be formally representation (algebraically) of a positive integer, C can be identified as a prime or not.

Indian Developer in India
Tuesday, January 27, 2004

If I understand correctly, you are looking for a function that takes an integer, C, and gives the angle t?

Are you trying by any chance to solve integer factoring?
Tuesday, January 27, 2004

As mentioned earlier, yes ;)

Indian Developer in India
Tuesday, January 27, 2004

I suggest you spend some time looking into number theory.  And if you find the answer, don't tell anyone -- you'll probably get kidnapped or shot by a government agency.

I'm not kidding.

H. Lally Singh
Tuesday, January 27, 2004

The short answers are:

Yes, it can be solved (sort of), and no, you don't need to worry about government agencies coming after you.

The problem is, there's not a quick method to find the value of t (if any) where A and B are natural numbers.  It's a matter of checking values of A and B as t decreases, and if A and B are both natural numbers then A and B are factors of C.  You could basically ignore the trigonometry and just check values of A and B up to C, which could probably be done slightly faster.

Unfortunately, it can't be done fast enough (yet) to be feasible for large values of C.

If anyone has another way of looking at this that's different from what I've said here, please share.  I'm always up for a good math problem.  Speaking of which, I really should get back to my homework.

Wednesday, January 28, 2004

Actually he wants to use this for 2000-bit numbers, which you can't check "one by one."

And yes, after he cracks it, he can collect the $500,000 RSA reward, live well for a couple of months, and then get waxed by Alec Baldwin from Mercury Rising.
Wednesday, January 28, 2004

Money aside, and my (in)competence apart, do any of you think that's a way forward?

The problem is with definitions. What is the function/equation of a positive integer?

Indian Developer in India
Wednesday, January 28, 2004

cos(2*pi*x) == 1

but it doesn't get you anywhere (yes I tried).
Wednesday, January 28, 2004

*  Recent Topics

*  Fog Creek Home