The Boundary of a Wheel

For the Wheelwrights of the Reunited Kingdom, they often have trouble in deciding how long a piece of metal is required to form the metal rim to the wooden wheels used on the most heavy-duty of wagons. Presently they rely on a question of instinct, passed down through their Guild from Master to Journeyman and hence to Apprentice. However they recently applied to the Mathematically minded Scribes to come up with a solution, and this work is the result.

First all the measurements of exsisting wheels were taking into consideration - their width, the lenght of the spokes, the height of the wheel, the lenght of the boundary and the curvature of the whole. With these results from a number of wheels the information was tabulated to enable us to seek comparisons. It was noted that the boundary was close to three times greater than the height of the wheel. Using this idea, various numbers were tried to see whether they would suit the requirements needed to match exactly the data collected.

One of the First approximations we attempted was to use the value of 22 divided into 7 parts - this produced an answer which was close to, but not exact enough for the purposes of the Wheelwrights. In each case there was a subtle difference of only a few short units, but this was more than suffienct to cause inperfect lenghts to be used.

The next attempt was to approximate that number produced by splitting 22 in 7 parts to a greater degree. With each number past the crown-point we discovered that the lenght required was getting closer, and in most cases, was more than suffienct to produce the desired result. This number, here written to 20 numbers past the crown point, appears to be as endless as the One is ultimate - I firmly believe that in the future this number will continue to grow.

The Numerical Value for the King’s Patience - called Pi for short - is 3.14159265358979323846

Initiate Scribe
18th May 2005

Back to MT