Another [irrational] number. Available in [expr] as ''exp(1)''.

base of natural logarithms; useful since d/dx(e^x) = e^x.

And Integral(1/x) = ln(x)  Integral(1/x) from 1 to e is ln(e) = 1.

2.718281828459... (see http://mathworld.wolfram.com/e.html) Note it does not recur, despite repeating 1828 twice in the first 10 digits.

A spigot algorithm for calculating e:

# spigot algorithm for E from /*paasivir@jyu.fi*/ 
#in http://www1.physik.tu-muenchen.de/~gammel/matpack/html/Mathematics/Pi.html
#int a[3302],b=3301,*c=a,d,e,f;main(){for(e=b;--e;*c++=1);*c=2;
#for(d=2001;d--;printf("%05d",f))for(c=a,e=b;e;f/=e--){f+=*c*1e5;*c++=f%e;}}
# translated into Tcl:

   proc calce {} {
	list a
	set b 3301;	set c 0; set f 0

	for {set e [expr $b-1]} {$e>0} {incr e -1} {  lappend a 1 } ;# fill array with 1 for(e=b;--e;*c++=1);
	lappend a 2 ;#*c=2;
	puts "Should be e =\n2.71828182845904523536028747135266249775724709369995... "
	for {set d 2001} {$d>0 } {puts -nonewline [format "%.5i" [expr int($f)] ] } { ;#for(d=2001;d--;printf("%05d",f))
		incr d -1
		for {set c 0; set e $b} {$e>0} {flush stdout} {;# for(c=a,e=b;e;f/=e--){f+=*c*1e5;*c++=f%e;}
			set f [expr int($f + [lindex $a $c]*100000)]  ;#f+=*c*1e5;
			lset a $c [expr round(fmod($f,$e))];# *c = f%e
			incr c ;# c++
			set f [expr int($f/$e)] ;# f/=e
			incr e -1 ;#e--
		}
	}
   } 
   calce



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[Category Mathematics]