Mathematica returns empty set when I expect two different values

*To*: mathgroup at smc.vnet.net*Subject*: [mg32329] Mathematica returns empty set when I expect two different values*From*: "spiraltooth" <spiraltooth at netzero.net>*Date*: Tue, 15 Jan 2002 02:30:06 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

The following is a Mathematica file in which a spiral is described in polar coordinates. I am trying to find a point Ttheta,theta on the spiral given another point Tt,t . These two points are separated by the straight line distance Mtheta. Both Ttheta and Mtheta are functions of theta and are the unknowns. Thank you for helping me. Alan Notis In(1)= S=6Pi Out(1)= 6Pi In(2)= MR=.7 Out(2)= .7 In(3)= t=Pi Out(3)= Pi In(4)= Itheta=MR+(theta / S) Out(4)= 0.7+(theta / 6Pi) In(5)= It=MR+(t / S) Out(5)= 0.8666667 In(6)= CM=.025 Out(6)= .025 In(7)= CX=.275 Out(7)= .275 In(8)= Mtheta=CX-(((CX-CM)theta) / S) Out(8)= 0.275-0.0132629theta In(9)= Ttheta=Itheta+Mtheta (* This describes a radius Ttheta given theta as a point on a spiral from ~-.1Pi to ~6.1Pi *) Out(9)= 0.975+0.0397887theta In(10)= Mt=CX-(((CX-CM)t) / S) Out(10)= 0.233333 In(11)= Tt=It+Mtheta (* This describes a radius Tt given t as a point on the same spiral as Ttheta,theta; Again t is demonstrated at Pi here but in reality will vary from 0 to 6Pi *) Out(11)= 1.14167-0.0132629theta In(12)= alpha=ArcCos[((Ttheta^2)+(Tt^2)-(Mtheta^2))/(2(Ttheta)(Tt))] Out(12)= ArcCos[(-(0.275-0.0132629theta)^2+(1.14167-0.0132629theta)^2+(0.975+0.0397887theta)^2) / 2(1.14167-0.0132629theta)(0.975+0.0397887theta)] In(13)= Solve[alpha==ArcCos[(Ttheta^2+Tt^2-Mtheta^2) / (2(Ttheta(Tt)))] , theta ] (* Here I'm Using the law of cosines to find theta where alpha is the angle between t and theta . I'm expecting two values for theta one where theta < t and one where theta > t . Mathematica seems unable to do this as it returns the null set. *) Out(13)= {{}} In(14)= Solve[2X^2 + 14X +12 == 0 , X] (* But Mathematica of course has no problem solving an equation in a quadratic form. Do I need to load a certain package? Am I doing something mathematically wrong? Do I need to use ( and learn ) vector calculus? *) Out(14)= {{X -> -6},{X -> -1}}