from the “handbook of mathematical tables and...
TRANSCRIPT
In[6]:= Clear@"Global`*"D; $Line = 0;
From the “Handbook of Mathematical Tables and Formulas” by Burington, 1950, page 12, the area, A,
of an inscribed regular polygon of n sides into a circle of radius r is:
In[1]:= A =
1
2
n r2
SinB2 Π
n
F
Out[1]=
1
2
n r2
SinB2 Π
n
F
Evaluate the above when n = 5 and r = 1. %1 refers to Out[1]. /. is the Mathematica replacement
operator and { n®5, r®1} is a set of replacement rules. Mathematica automatically simplifies prior to
posting a result.
In[2]:= %1 �. 8 n ® 5, r ® 1<
Out[2]=
5
2
5
8
+
5
8
Divide the above by the area of a circle with radius 1.
In[3]:= %2 � Π r2 �. 8r ® 1<
Out[3]=
55
8+
5
8
2 Π
Convert the above to a decimal number.
In[4]:= %3 �� N
Out[4]= 0.756827
The percentage of the area of the circle inside the pentagon is: 75.6827 %.