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.
