why is a 13" tonearm design really superior?

Here are some pics
http://www.euphonia-audioforum.se/forums/index.php?showtopic=6887&hl=thales&st=45

Mathematical explanation:

The cartridge traces out an arc as the arm moves from the golder to the center of the record. When the arm is short this arc is very curved on the region between the holder spindle, where as if the arm is longer the arc becomes less curves. Now, when the arc is bigger and relatively less curved, it maintains tangency for a brief period just like the short arm, but the error dur to the curvature is minimzed. I suppose you can call it more tangent if that makes any sense.

I promised to report about the 24" tonearm I have seen on a pic - it is a design of German tonearm designer Fuchs. A friend of mine told me that it sounded very good. 24" inches - not too short...

We next aught to work on a 24'long, what say you?
Like a low resonace pool-cleaner tube?
Will like major minimise the tangent error, no?
Got to have some fantasie else things are not moving foreward here, I say.

at the High-End in Munich the Italian designer Horo presented a turntable in the figure of a long Steinway piano. He mounted a tonearm in the form of a violin bow, properly a 30" design... I never listened to it.