Re: Pi vs its decimal approximation

*To*: mathgroup at smc.vnet.net*Subject*: [mg113170] Re: Pi vs its decimal approximation*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Sat, 16 Oct 2010 13:12:02 -0400 (EDT)

On 10/15/10 at 1:51 PM, accardi at accardi.com (John Accardi) wrote: >In my notebook below, why doesn't cosine2 graph? When I replace the >symbol for Pi with the decimal approx in the definition of cosine3, >it graphs correctly. . Why does Mathematica not interpret Pi >correctly in the first definition of cosine2? >In[29]:= cosine2:= 2/3 Cos[2\[Pi]x - \[Pi]/2 ] +1 You are missing a space. 2\[Pi]x should be 2\[Pi] x. Without the space, Mathematica sees this as a new variable named \[Pi]x which never gets defined. Consequently, there is nothing to plot from Mathematica's perspective. Also, there is no reason to use SetDelayed (:=) here. When you use SetDelayed here, the portion on the right hand side is re-evaluated every time a new x is generated. Since this is a very simple expression, the performance penalty will be too small to be noticed. But defining cosine2 as cosine2= 2/3 Cos[2\[Pi] x - \[Pi]/2 ] +1; is more efficient. >In[30]:= yline:=1 >In[31]:= Plot[Tooltip[{cosine2, yline}], {x, 0, 1.5}, >Ticks -> {{0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 1.0, 1.1, 1.2, >1.3, 1.4, >1.5}, Automatic}] >The plot that appears here only shows the y=1 line, not the cosine2. >But now I replace the symbol Pi with a decimal approximation in the >definition of cosine3 .. and it graphs correctly. >In[20]:= cosine3:= 2/3 Cos[2(3.141592653589793`)x- \[Pi]/2 ] +1 This works not because you have provided a numeric value for Pi, but because you have it clear there is a multiply. Try cosine3= 2/3 Cos[2(\[Pi])x- \[Pi]/2 ] +1; or adding the space suggested above and you will get what you were expecting.