Solve / Reduce for 2 missing values

*To*: mathgroup at smc.vnet.net*Subject*: [mg114941] Solve / Reduce for 2 missing values*From*: "Lea Rebanks" <lrebanks at netvigator.com>*Date*: Thu, 23 Dec 2010 03:55:29 -0500 (EST)

Dear All, Given the enclosed code for 2 spiral functions with mutually missing values of (i) value AND (ii) rotation in each function. Please could someone help me setup the code to Solve / Reduce for these 2 missing values. I have tried many approaches & can not solve for both. ( I can get either value (i) OR (ii), but not both.) Been trying for quite sometime. - Both spirals must equal = 32400 after the Correct number of rotations X the value. - I have tried adjusting the orientation angle M of the spiral. - I have tried to setup calculus rate of change of area of square with respect to time as degree progress inwards from the outer perimeter. - I feel that my methods are not correct. Any suggestions welcome. This question is as much a Math question as it is an exercise in writing Mathematica code. Many thanks for your help & attention, really appreciated. Please see below. Best regards, Lea... ............................................................................ ..................... Clear[value] value = 180; Clear[rotation] rotation = 15; Clear[M1] M1 = N[(45) - ArcTan[(Sqrt[4 - Pi])/Sqrt[Pi]]/Degree, 20]; Clear[M2] M2 = 0*Degree; Clear[spiral1Yaxis] spiral1Yaxis[\[Theta]_] := ((1/360)*\[Theta])*(((value)/Sqrt[Pi])/ rotation)*Sin[(\[Theta] + M1)*Degree] Clear[spiral1Xaxis] spiral1Xaxis[\[Theta]_] := ((1/360)*\[Theta])*(((value)/Sqrt[Pi])/ rotation)*Cos[(\[Theta] + M1)*Degree] Sqrt[spiral1Yaxis[15*360]^2 + spiral1Xaxis[15*360]^2]^2*Pi == 32400 True Clear[spiral2Yaxis] spiral2Yaxis[\[Theta]_] := ((1/360)*\[Theta])*(value/(2*rotation))* Sin[(\[Theta] + M2)*Degree] Clear[spiral2Xaxis] spiral2Xaxis[\[Theta]_] := ((1/360)*\[Theta])*(value/(2*rotation))* Cos[(\[Theta] + M2)*Degree] (Sqrt[spiral2Yaxis[15*360]^2 + spiral2Xaxis[15*360]^2]*2)^2 == 32400 True ...............................