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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