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#!/usr/bin/perl
use Modern::Perl;
use bignum qw(e);
use Math::BigFloat;
Math::BigFloat->precision(-50);
# write a script to calculate e https://en.wikipedia.org/wiki/E_(mathematical_constant)
# e, Euler's number, 2.71828182845904523536028747135266249775724709369995
sub factorial {
my $f = 1;
map { $f *= $_ } ( 1 .. shift );
return $f;
}
sub e_factorial {
my $e = 0;
map { $e += 1/factorial($_) } ( 0 .. shift );
return $e;
}
sub brothers {
my $b = 0;
map { $b += (2 * $_ + 2) / factorial(2 * $_ + 1) } ( 0 .. shift );
return $b;
}
sub e_brothers {
my $b = shift;
my $e = brothers($b);
return $e;
}
sub e_limit_n {
my $n = shift;
return ( 1 + 1/$n ) ** $n;
}
sub e_limit_t {
my $t = shift;
return ( 1 + $t ) ** (1/$t);
}
my $e = 2.71828182845904523536028747135266249775724709369995;
say $e, " e constant from wiki";
$e = e();
say $e, " e from perl module bignum";
my $n = 40;
$e = e_factorial($n);
say $e, " e calculated from $n factorial";
$n = 20;
$e = e_brothers($n);
say $e, " e calculated from brothers, $n steps";
$n = 100000;
$e = e_limit_n($n);
say $e, " e calculated as a limit n approaching infinity $n";
$n = .00001;
$e = e_limit_t($n);
say $e, " e calculated as a limit t approaching zero $n";
__END__
./ch1.pl
2.71828182845904523536028747135266249775724709369995 e constant from wiki
2.71828182845904523536028747135266249775700000000000 e from perl module bignum
2.71828182845904523536028747135266249775724709369992 e calculated from 40 factorial
2.71828182845904523536028747135266249775724709369997 e calculated from brothers, 20 steps
2.71826823717448966803506482442604644797444693267782 e calculated as a limit n approaching infinity 100000
2.71826823717448966803506482442604644797444693267782 e calculated as a limit t approaching zero 0.00001
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