, the ratio of the circumference of a circle to its diameter, should be replaced by 
, the ratio of the circumference to the radius. This replacement, argued by Bob Palais, is much more natural and leads to frequent simplification in many cases. For example, 1/4 of a circle is 
radians not 
. Using 
, the fractions always match making it easier to remember and avoid mistakes. There are also many math and physics equations where 
appears (for example: 
) that are simpler to write and read with this substitution. Euler's equation, 
, becomes 
, a much nicer thing to write.OK. So you are not convinced. Consider this: With this substitution, we have
day instead of (in addition to?) day. this moves the celebration to June 28th. March is cold and we're all in school. June is warm and we're all on the beach (mentally at least) and it is clearly a much better day to be celebrating.If you are still not convinced, give this a look. This is a video of
being set to music. It is really quite nice.Fine. So we we won't be switching to
any time soon. But it is good to know that the mathematicians are thinking about such things and preparing the world for ever more rational thought.I wonder if we can find a way to set Newton's laws or Maxwell's equations to music? The lagrangian for Quantum Chromodynamics (that describes the strong interaction) might just be a delight to hear.
And, lest you think that you'd have to go relearn
in place of and are worried since you've got to 20 or 30 digits, consider the plight of this young woman...