Re:non-integer dimensions of physical or non-physical quantities

Posted by Ramanujan12 on October 11, 2003 at 22:02:40:

In Reply to: non-integer dimensions of physical or non-physical quantities posted by ceco on October 08, 2003 at 08:42:44:

ceco

In Dimensional Analysis there is something reffered to as a dimensionless or nondimensional physical quantity (a parameter, constant, or variable that is 1-dimensional.) However this treatment of dimensionless physical quantities is redirected by Thomas Szirtes in his book 'Applied Dimensional Analysis and Modeling' to be only a charectaristic of variables that are less than 1-dimensional yet have dimension. Szirtes' vision is basically the same as non-integer dimension except he develops them along the lines of dimensionless variability. I haven't heard of anything aside from fractals concerning non-integer dimensions; 'The Geometry of Fractal Sets' by Falconer has these integerial and non-integerial relations. Non-physical quantities perhaps relating to infinitesimal numbers and evanescence in Infinitesimal Analysis; 'A Primer of Infinitesimal Anlysis' by John Bell is a very entertaining and thought provoking mathematics text. Dimensional Analysis and Infinitesimal Analysis together have lot's on this subject of quasi-dimensionality and quasi-zero quantities. For physical quantities Dimensional Analysis in the context of asymptotics may be a bridge between the fractal and the physical domains for non-integer dimensions. This is a subject well worth investigation and developing ideas, good luck in your quest.

Ramanujan12

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