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This is probably a good place to mention the mathematical background of center finders.
There's a provable theorem from geometry that says:
The perpendicular divisor of the chord of a circle passes through the center of the circle.
When you use a center head, the two tangent points where the head touches the circular object define a chord on that circle. The blade is mechanically set to bisect the angle between the arms of the head so it automatically provides the perpendicular bisector of the chord. When two of these chord bisectors are drawn, the point where they cross must be the center.
The technique is extendable to circles or circular segments too large for any sort of hand-held tool. Simply draw two chords (as nearly perpendicular as possible), construct their bisectors and the point where they cross is the center. Surveyors employ this technique, using their transits to establish the perpendicular bisectors.
The diameter of a circle is a chord itself. Thus its perpendicular bisector must pass through the diameter at the center of the circle.
It should also be apparent that this math insight can be used to construct a circle that passes through any three non-colinear points. Construct two chords using the three points. The center of the circle is then the point where their bisectors cross and the radius is the distance from the center to any of the points.
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Originally Posted by mklotz
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