I am a mathematician by education, computer programmer and financial adviser by profession and a math teacher by inspiration.
Founded an educational Web site UNIZOR.COM - Math4Teens - Creative Mind through Art of Mathematics.
Yes, unfortunately, non-negativity of the #r# is not shared by many authors. In defense of this requirement I'd say that if negative #r# is allowed, any point on a plane, except the origin, would have two different pairs of polar coordinates: #(r, theta)# and #(-r, theta+pi)#. This is not a good property of any coordinate system to have two different numeric representation of the same point.
How do you graph #r=-1#?