diff --git a/books/bookvol8.1.pamphlet b/books/bookvol8.1.pamphlet index b7d5204..4a59983 100644 --- a/books/bookvol8.1.pamphlet +++ b/books/bookvol8.1.pamphlet @@ -405,6 +405,27 @@ draw(curve(j1,j2,j2),-9..9,coordinates == cylindrical) \section{Three dimensional surfaces} \newpage +\subsection{A 3D figure 8 immersion (Klein bagel)} +{\center{\includegraphics[scale=0.50]{ps/v81kleinbagel.eps}}} +\begin{chunk}{kleinbagel} +r := 1 +X(u,v) == (r+cos(u/2)*sin(v)-sin(u/2)*sin(2*v))*cos(u) +Y(u,v) == (r+cos(u/2)*sin(v)-sin(u/2)*sin(2*v))*sin(u) +Z(u,v) == sin(u/2)*sin(v)+cos(u/2)*sin(2*v) +v3d:=draw(surface(X(u,v),Y(u,v),Z(u,v)),u=0..2*%pi,v=0..2*%pi,_ + style=="solid",title=="Figure 8 Klein") +colorDef(v3d,blue(),blue()) +axes(v3d,"off") +\end{chunk} +From \verb|en.wikipedia.org/wiki/Klein_bottle|. The ``figure 8'' immersion +(Klein bagel) of the Klein bottle has a particularly simple parameterization. +It is that of a ``figure 8'' torus with a 180 degree ``M\"obius'' twist +inserted. In this immersion, the self-intersection circle is a geometric +circle in the x-y plane. The positive constant $r$ is the radius of this +circle. The parameter $u$ gives the angle in the x-y plane, and $v$ specifies +the position around the 8-shaped cross section. With the above parameterization +the cross section is a 2:1 Lissajous curve. + \subsection{A 2-Equation bipolarCylindrical Surface} {\center{\includegraphics[scale=0.50]{ps/v81equation108.eps}}} \begin{chunk}{equation108} diff --git a/books/ps/v81kleinbagel.eps b/books/ps/v81kleinbagel.eps new file mode 100644 index 0000000..be511d3 --- /dev/null +++ b/books/ps/v81kleinbagel.eps @@ -0,0 +1,1574 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: GIMP PostScript file plugin V 1.17 by Peter Kirchgessner +%%Title: v81kleinbagel.eps +%%CreationDate: Thu Feb 23 16:05:26 2012 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%Pages: 1 +%%BoundingBox: 14 14 415 415 +%%EndComments +%%BeginProlog +% Use own dictionary to avoid conflicts +10 dict begin +%%EndProlog +%%Page: 1 1 +% Translate for offset +14.173228346456693 14.173228346456693 translate +% Translate to begin of first scanline +0 399.99685039370081 translate +399.99685039370081 -399.99685039370081 scale +% Image geometry +400 400 8 +% 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20120223.01.tpd.patch +20120223 tpd books/ps/v81kleinbagel.eps Klein bagel image +20120223 tpd books/bookvol8.1 add Klein bagel example 20120218 tpd src/axiom-website/patches.html 20120218.02.tpd.patch 20120218 tpd buglist 7225: Lasagna Larga Doppia Riccia does not plot 0.0 20120218 tpd src/axiom-website/patches.html 20120218.01.tpd.patch diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 0294c5d..c28f1ea 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -3822,5 +3822,7 @@ buglist add additional graphics bugs
books/bookvol8.1 fix galletti equations and image
20120218.02.tpd.patch buglist 7225: Lasagna Larga Doppia Riccia does not plot 0.0
+20120223.01.tpd.patch +books/bookvol8.1 add Klein bagel example