Expert: Abe Mantell - 8/17/2011

Question
Dear Prof Abe

Referring to the Wikipedia Link for Mathematical Constants

http://en.wikipedia.org/wiki/Mathematical_constant

Can we also Add Acceleration due to Gravity g=9.80665 m/s2 as a Mathematical Constant in the Table of selected mathematical constants ?

http://en.wikipedia.org/wiki/Standard_gravity

Another example is Gravitational constant

http://en.wikipedia.org/wiki/Gravitational_constant

This are the constants used in Physics, so can they be also considered mathematical constants or it will be classified only as
physical constants ?

Comparison between Mathematical and Physical Constants
---------------------------------------------------------------------

http://en.wikipedia.org/wiki/Physical_constant

Though both are constants, A physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement.

Mathematical Constants used in Physics
----------------------------------------

http://www.desy.de/user/projects/Physic ... GR/pi.html

For the types of non-Euclidean geometry used in physics, the ratio is very nearly π over small distances so we do not notice the difference in ordinary measurements. This does not mean that π changes, because our definition of π specified a Euclidean geometry, not physical geometry. No new theory or experiment in physics can change the value of mathematically defined constants.

This are the Definitions of Mathematical and Physical Constants in Wikipedia.

Is there a thin line between the two comparisons i.e Mathematical and Physical Constants ?

Note : Physical Constants value remain the same, they measure a physical quantity, so then does it implies that they can be also considered as mathematical constants but used in Applications of Physics viz Newton's Laws of Motion, Newton's Law of Gravity etc.

Thanks & Regards,
Prashant S Akerkar

Answer
Hello,

I would not add g to the list of mathematical constants.  A mathematical constant IS CONSTANT
everywhere, independent of the environment.  g=9.8066... is the gravitational acceleration on earth only at a given distance from the center of the planet (I think at sea level).  Move to
higher or lower ground, or to another plant, and g changes!  Maybe it should be listed as
physical constant relevant to us.

Sure, perhaps there is a thin line between mathematical & physical constants.  I think, generally, mathematical constants do not have to a have a physical analog.

My opinions...

Abe