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Pi vs its decimal approximation
*To*: mathgroup at smc.vnet.net
*Subject*: [mg113149] Pi vs its decimal approximation
*From*: John Accardi <accardi at accardi.com>
*Date*: Fri, 15 Oct 2010 13:51:59 -0400 (EDT)
Thanks in advance for any insights ...
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
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
In[14]:= yline:=1
In[15]:= Plot[Tooltip[{cosine3, 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 shows here is correct. It contains both y=1 and
cosine3. The only difference is the use of Pi vs 3.14159265...
(I inputted Pi using the Greek letter on the Classroom Assistant.)
*.nb file here:
http://www.accardi.com/PiQuery.nb
Gianni
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