XProfan

English

p.specht

How long is a Bogenteil of/ one ellipsis? it comes naturally on The shape the ellipsis on UND on The question, of where To where measured becomes. the arbitrary Relationship the Ellipsenachsen zueinander undo unfortunately each closed Formel.

but: one can The Parameter "Achsenverhältnis" and "Von where To where becomes gemessen" after a of Gauß gefundenene Mittelwerte-relationship ("Arithmetisch-geometrisches Mittel") gegeneinander abtauschen! one attempts then on these point, the Achsenverhältnis 1 go To let (The undertow. disembark-Transformation), then having we it suddenly with a circle To do, and the others Parameter supply then the Result via The for Kreise fine known Umfangsformel. moreover need one but the detailed AGM:

Compile Mark Separation

Window Title "Den Arithmetisch-geometrischen story AGM(a,b) berechnen"
'(CL) CopyLeft 2015-08 by P.woodpecker, Wien (Austria); OHNE EACH GEWÄHR!
'fountain u.a. https://www.math.cornell.edu/~hubbard/RationalLandenTrans.pdf
Window Style 24:Cls:declare a!,b!,sgn!,tmp!,c$:set("decimals",18)
print "\n for Parameterwerte a and b becomes the of  C. F. Gauß  entwickelte"
print " Arithmetisch-geometrische story iterativ errechnet. The hat"
print " The quality, Invarianztransformationen the Elliptischen Funk-"
print " tionskurven (speak Parameter-Abtausch) To make possible, without daß"
print " the Funktionswert self changed becomes. (the ermöglichte später"
print " schrittweise Näherungen for Funktionswerte, for no Formel"
print " existing How zB The Bogenlänge of Ellipsen, Lemniskaten etc. )"
print " ----------------------------------------------------------------\n"
Font 2
running:
print " worth a = ";:input c$:a!=val(c$)
print " worth b = ";:input c$:b!=val(c$)
print " ----------------------------------------------------------------"
print "         a                                     b                 "
print " ";stature$("%g",a!),tab(40);stature$("%g",b!)
tmp!=a!*b!:sgn!=(tmp!>0)-(tmp!<0)

Repeat

    tmp! =(a!+b!)/2
    b!=sgn!*sqrt(abs(a!)*abs(b!))
    a!=tmp!
    print " ";stature$("%g",a!),tab(40);stature$("%g",b!)

until stature$("%g",a!)=stature$("%g",b!)

print " ----------------------------------------------------------------"
locate %csrlin-2,30:print "<=AGM=>\n\n";
waitinput
CLS
print " ----------------------------------------------------------------"
goto "Lauf"