The use of the radius instead of diameter is historic and constructive: the circumference was make by turning a rope or a compass a full turn instead of turning a rigid stick half a turn around his center. The former is easier.
2013/7/9 Jason Resch <[email protected]> > > > > > > On Tue, Jul 9, 2013 at 2:20 PM, John Clark <[email protected]> wrote: > >> On Mon, Jul 8, 2013 at 5:16 PM, Jason Resch <[email protected]> wrote: >> >> >>> >> I think the fact that e^i*PI +1 = 0 surprises almost everyone when >>>> they first hear of it. >>> >>> >>> > This one is very interesting, but the fact that Pi was a poor choice >>> for the constant makes the equation considerably more ugly than it should >>> be. There is a growing movement to usurp the number Pi with the much more >>> important constant "2*Pi" (see: http://www.math.utah.edu/~palais/pi.html ). >>> If we call that new number tau (t). Then Euler's identity becomes: >>> e^(t * i) = 1 >>> >> >> There is no disputing matters of taste but I think the original equation >> is more beautiful because it shows a relationship between 5 of the most >> important numbers in all of mathematics. Your new equation only has 4 >> important numbers, it doesn't include zero, it has the multiplicative >> identity but not the additive identity. >> > > If you want to see all the constants at once there is an easy correction: > e^(t*i) - 1 = 0 > > Circles are defined by their radius, not their diameter. The mistake of > using Pi leads to circles being 2*Pi radians, rather than tau radians. The > area formula for circles obscures the fact that an integration took place > (1/2) tau r^2 makes it clearer that there was an integration. The period > of sin and cosine are tau, cos(t) = 1 rather than -1, etc. Pi is simply a > less elegant circle constant than tau. > > Jason > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. > > > -- Alberto. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
