XProfan

Window Title upper$("                 E l l i p s e n u m f a n g   Näherungsformeln to steigender Präzision")
'Q: https://www.youtube.com/watch?v=5nW3nJhBHL0
Window Style 24:Font 2
Declare a!,b!,eps!,eh2!,ga!
Set("decimals",8)
rept:
cls $909090
Print "\n  a = ";:Input a!
Print "\n  b = ";:Input b!
:If b!>a!:eps!=a!:a!=b!:b!=eps!:EndIf
Case a!=0:Goto "rept"
Case (a!+b!)=0:Goto "rept"

If b!=0:Print "\n Entartetes levelly the Doppelstrecke = ";4*a!:Goto "wai":EndIf

    eps!=Sqrt(Sqr(a!)-sqr(b!))/a!
    Print "\n  Numer.Exzentrizität epsilon = ";eps!:Print
    :If eps!=0:Print "  Kreisumfang: ";2*Pi()*a!:Goto "wai":EndIf
    ga!=  1 - eps!^2/4 - 3/64*eps!^4 - 5/256*eps!^6 - 175/16384*eps!^8 - 441/65536*eps!^10
    ga!=ga! - 4851/1048576*eps!^12 - 14157/4194304*eps!^14 - 920205/1073741824*eps!^16
    ga!=2*a!*Pi()*ga!
    Print "\n  Subtraktionsreihe: ";ga!
    Print "\n    Grober Schätzer: "; Pi()*(3/2*(a!+b!)-Sqrt(a!*b!))
    Print "\n    Parker-Schätzer: "; Pi()*(53/3*a!+717/35*b!-Sqrt(269*a!*a!+667*a!*b!+371*b!*b!))
    Print "\n        Ramanujan_I: "; Pi()*(3*(a!+b!)-Sqrt((3*a!+b!)*(a!+3*b!)))
    eh2!=Sqr(a!-b!)/Sqr(a!+b!)
    Print "\n        RamanujanII: "; Pi()*(a!+b!)*(1+3*eh2!/(10+Sqrt(4-3*eh2!)))
    Print "\n       Parker-row: "; Pi()*(a!+b!)*(1+eh2!/4+Sqr(eh2!)/64+(eh2!^3)/256+25/16384*Sqr(Sqr(eh2!))),
    Print " with max. Error ";eh2!^4*25/16384
    wai:
    WaitInput
    Goto "rept"