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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