3.8
Important constants
In applications we often encounter the need to use Euler's number $\ee$ and Ludolph's number $\pi$. Approximate values
of these constants with precision of one thousand decimal places are given below.
\begin{equation*}
\begin{aligned}
\pi \approx 3.&14159265358979323846264338327950288419716939937510582097494459230781 \\
&64062862089986280348253421170679821480865132823066470938446095505822 \\
&31725359408128481117450284102701938521105559644622948954930381964428 \\
&81097566593344612847564823378678316527120190914564856692346034861045 \\
&43266482133936072602491412737245870066063155881748815209209628292540 \\
&91715364367892590360011330530548820466521384146951941511609433057270 \\
&36575959195309218611738193261179310511854807446237996274956735188575 \\
&27248912279381830119491298336733624406566430860213949463952247371907 \\
&02179860943702770539217176293176752384674818467669405132000568127145 \\
&26356082778577134275778960917363717872146844090122495343014654958537 \\
&10507922796892589235420199561121290219608640344181598136297747713099 \\
&60518707211349999998372978049951059731732816096318595024459455346908 \\
&30264252230825334468503526193118817101000313783875288658753320838142 \\
&06171776691473035982534904287554687311595628638823537875937519577818 \\
&57780532171226806613001927876611195909216420199\ldots
\end{aligned}
\end{equation*}
\begin{equation*}
\begin{aligned}
\ee \approx 2.&71828182845904523536028747135266249775724709369995957496696762772407 \\
&66303535475945713821785251664274274663919320030599218174135966290435 \\
&72900334295260595630738132328627943490763233829880753195251019011573 \\
&83418793070215408914993488416750924476146066808226480016847741185374 \\
&23454424371075390777449920695517027618386062613313845830007520449338 \\
&26560297606737113200709328709127443747047230696977209310141692836819 \\
&02551510865746377211125238978442505695369677078544996996794686445490 \\
&59879316368892300987931277361782154249992295763514822082698951936680 \\
&33182528869398496465105820939239829488793320362509443117301238197068 \\
&41614039701983767932068328237646480429531180232878250981945581530175 \\
&67173613320698112509961818815930416903515988885193458072738667385894 \\
&22879228499892086805825749279610484198444363463244968487560233624827 \\
&04197862320900216099023530436994184914631409343173814364054625315209 \\
&61836908887070167683964243781405927145635490613031072085103837505101 \\
&15747704171898610687396965521267154688957035035\ldots
\end{aligned}
\end{equation*}
The definition of Euler's number will be discussed in detail in BIE-ZMA. It is not necessary
to stress out the importance of $\pi$. One application of $\ee$ is related to its being used as
the base of the natural logarithm that we will be discussing in section 4.10.