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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
...............................
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