[PW] circumference question

[Andrew Warren]

Richard Wolf wrote:

> The diameter of the circle is 23 * the square root of 2. This equals
> 32.53". The arc is a quarter-circle and four arcs would make a full
> circle. Formulas I used are: C=2 Pi r, C' = 25.5, 2rT = 25.5, sin T =
> 11.5 / r. There are two unknowns, r and T and two equations. r is the
> radius and T is half the angle of the full arc. T is in radians and
not
> degrees. r * T = 12.75, r * sin T = 11.5. From this, T / sin T =
1.109.
> To convert this equation from radians to degrees it is T / sin T =
> 1.109 * 360 / 2Pi. T = 45 degrees agrees with this equation.
> ....
> Is there a simpler solution to find r and T?

    I don't think so; T/sin(T) = 23/25.5 seems pretty simple, even
though
    it unfortunately requires a numerical solution.  An analytic
solution
    might be "better", but I can't think of a simple one.

> What is the best mathematical subject heading for this problem?

    Maybe something like "Find the central angle subtending an arc
    given only the arc length and chord length".

> What is the best mathematical subject heading for the solution?

    "The Wolf Method Revealed: I Did It, and So Can You!"

    -Andrew
    
=== Andrew Warren  - awarren at synaptics.com
=== Synaptics, Inc - Santa Clara, CA