# Circle problem

• May 20th 2011, 03:00 AM
Circle problem
I need to write this:

f(x,y) = hardlim(sqrt(x^2+y^2)-1) (hardlim(x) = 0 if x <= 0 and 1 otherwise)

but without using any multiplication or the square root. Only thing I can use is summation, multiplication by a value (x*5), and the hardlim or hyperbolic tangent functions.

(I basically need to build a neural net classifier thingie that will return 1 if a point is in the unit circle and 0 otherwise.)
• May 20th 2011, 07:37 AM
Opalg
Quote:

I need to write this:

f(x,y) = hardlim(sqrt(x^2+y^2)) (hardlim(x) = 0 if x <= 0 and 1 otherwise)

but without using any multiplication or the square root. Only thing I can use is summation, multiplication by a value (x*5), and the hardlim or hyperbolic tangent functions.

(I basically need to build a neural net classifier thingie that will return 1 if a point is in the unit circle and 0 otherwise.)

I'm not sure that I understand the question. That function f(x,y) is always 1 except at the origin. I don't see what that has to do with a function that will return 1 if a point is in the unit circle and 0 otherwise.

You can define the given function f(x,y) in terms of the hardlim function by

f(x,y) = hardlim( hardlim(x) + hardlim((–1)*x) + hardlim(y) + hardlim((–1)*y) ).
• May 20th 2011, 07:48 AM