Geometry for pivot tonearms - calculation errors??

During several threads in Audiogon's Analog forum the question of pivot tonearm geometry was discussed widely and wildly the past weeks. There seems to be a great confusion about the interelation - and interaction - between overhang, offset, effective length, mounting distance and the position of the 2 zero-error points on the arc over the LP's grooved area.
However - the correct tonearm geometry is paramount for the performance of any analog sourced High-end system.

Do we need a new calculation of these parameters?
Is mounting distance a variable factor in a given pivot tonearms geometry?
Can overhang serve as the fixed parameter for a pivot tonearm?
Is effective length a variable or a fixed parameter in pivot tonearm geometry?
Is there anything like an optimum geometry for a given cartridge/pivot tonearm set-up?

I invite all interested in this complex and very important topic to contribute their thoughts. If possible please do include the geometrical derivation for any given theory and opinion.
This might be difficult in some examples, but please try.
By doing so, - this will keep this thread on terms and will make it more valueable for all.