Essays/Gauss-Bonnet/Bonnet04
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11 Geodesic Curvature
... McCONNELL Chapter XIV Section 10 ...
... Sokolnikoff Section 63 ...
11.1 V-Coordinate System
NB. ... script (ijs) ... tgnt=:(0,mcv22^_0.5"_)"1
NB. ... script (ijs) ...
tgntdrv1=:((0{1{1{ch2k)%mcv22)"1
tgntdrv2=:((_0.5*(mcv22^_2:)*mcv22v2)+(1{1{1{ch2k)%mcv22)"1
tgntdrv =:(tgntdrv1,tgntdrv2)"1
NB. ... execute (ijx) ... *./@(*./)@(0=])@ts0@:(+/@((<0 1)|:axs@((1;mcv),1;tgnt*/tgntdrv))"1) vpgen'' 1
NB. ... script (ijs) ... geoc=:+/@((<0 1)|:axs@((1;ecv),1;tgnt*/tgntdrv))"1
12 Gauss-Bonnet Theorem
... McCONNELL Chapter XIV EXAMPLES XIV Problem 14 ...
... Sokolnikoff Section 74 ...
12.1 U-Coordinate System
Figure 2: Tangent to Curve
12.2 V-Coordinate System
NB. ... script (ijs) ... dS=:%:@m*((f1-s1)%i1)*(f2-s2)%i2 ds=:%:@mcv22*(f2-s2)%i2
NB. ... script (ijs) ... KSurface=:(+/%2:)@:(+/@(+/)@:((K*dS)"1)"3)@(}.,:}:)@:(}:"2)
NB. ... script (ijs) ...
geocCurve=:-/@:(+/"1)@:((geoc*ds)"1)@(}:"2@({.,:{:))
NB. ... execute (ijx) ... KSurface vpgen'' 1.31588 geocCurve vpgen'' 1.31783
Download: File:LGB0401C.txt
Download: File:LGB0402C.txt
Download: File:LGB0403C.txt
Download: File:LGB0404C.txt
Download: File:LGB0405C.txt
Download: File:LGB0407C.txt
Download: File:LGB0408C.txt
Download: File:LGB0409C.txt
Download: File:LGB0410C.txt
Download: File:LGB0411C.txt
Download: File:LGB0412C.txt
Download: File:LGB0413C.txt
Download: File:LGB0414C.txt
Download MoinMoin source: File:Bonnet04.ijs
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Contributed by Tom Allen