[PW] circumference question

[Richard Wolf]

Hello Nancy:

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. I think there may be a quicker way to do this but I can't remember
it. We would have to check a reference.

As far as patterns go, I thought of the bowling pin arrangement, the Olympic
symbol if five circles and a star wheel made with all 17 arcs.

I have a few questions for you and fellow posters.

Is there a simpler solution to find r and T?

What is the best mathematical subject heading for this problem?

What is the best mathematical subject heading for the solution?

 Who was the roundest knight of the Knights of the Round Table?

Regards,

Richard