Greetings,
Dr. Nelson Beebe of TUG suggested I contact the unicode discussion
forums regarding the need to clarify mathematical and physical
notation with a symbol for 2*\pi. This was pointed out in my paper
in The Mathematical Intelligencer v. 23, vol.3 2001 pp. 7-8 Springer-NY
which may be viewed online at
http://www.math.utah.edu/~palais/pi.html
in which a character which is the concatenation of two "\pi"s is
proposed. All responses were in agreement. There is no purpose for
a 2 in Planck's constant, in the relationship between the period
and frequency of an oscillation. A quarter of an hour and
a quadrant should be indicated by a 4, not a 2! See the figure in the
article for further examples which eliminate unnatural 2s and/or minus
signs from Fourier, Cauchy, Stirling, and Gauss! We don't speak of
3/4 of an hour as "3/2 of half an hour" :-) The pi problem turns
something which should be natural into memorization for many students,
and Unicode could allow an alternative to eventually correct it.
I would appreciate your opinions after seeing how much more natural
this symbol makes basic math and science, and how the supplementary
symbol chosen makes its meaning immediately apparent. The advantage
being that the 2 can no longer be separated from the pi, and the
natural meaning as "one revolution" or "a circle" rather than
"a half revolution" and "a half circle" is much simpler.
Best regards,
Dr. Bob Palais
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