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{SECT 0 {SECT 1 {PARA 256 "" 0 "" {TEXT 257 42 "Chapter 15\n\nGraphics
\n\n\nPart C: Specialties" }{TEXT 268 1 "\n" }}{PARA 19 "" 0 "" {TEXT 
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\351 Heck." }}}{SECT 1 {PARA 0 "" 0 "" {TEXT 270 3 "29." }{TEXT -1 41 
" Make an animation of a rotating spiral.\n" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name cha
ngecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 116 "tubeplot([cos(t),sin(t),t], t=0..6*Pi, radius=1/3,\n  style=p
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{TEXT -1 51 " Prove and visualize the Pascal's theorem with the " }
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l's theorem." }{TEXT -1 6 "\n\nLet " }{XPPEDIT 18 0 "A, B, C, D, E" "6
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" {TEXT 273 3 "33." }{TEXT -1 54 " Prove and visualize the following t
heorem of Euler.\n\n" }{TEXT 274 16 "Euler's theorem." }{TEXT -1 189 "
\n\nIn a triangle, the orthocenter (intersection of altitudes), the ce
ntroid (intersection of medians), and the circumcenter (center of the \+
circle circumscribing the triangle) lie on a line.\n" }}{EXCHG {PARA 
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{MPLTEXT 1 0 58 "triangle(T,\n  [point(A,0,0), point(B,1,0), point(C,x
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{TEXT -1 39 "Let us make a drawing of the situation." }}{EXCHG {PARA 
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{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 278 3 "34." }
{TEXT -1 141 " Verify and visualize Feuerbach's nine-point circle. Ver
ify with Maple that Feuerbach's nine-point circle is the same as the E
uler circle,\n\n " }{TEXT 277 30 "Feuerbach's nine-point circle." }
{TEXT -1 22 "\n\nConsider a triangle " }{XPPEDIT 18 0 "T" "6#%\"TG" }
{TEXT -1 15 " with vertices " }{XPPEDIT 18 0 "A, B" "6$%\"AG%\"BG" }
{TEXT -1 6 ", and " }{XPPEDIT 18 0 "C" "6#%\"CG" }{TEXT -1 6 ". Let " 
}{XPPEDIT 18 0 "`A'`, `B'`, `C'`" "6%%#A'G%#B'G%#C'G" }{TEXT -1 36 " b
e the midpoints of the edges, let " }{XPPEDIT 18 0 "D, E, F" "6%%\"DG%
\"EG%\"FG" }{TEXT -1 39 " be the feet of the altitudes, and let " }
{XPPEDIT 18 0 "X, Y, Z" "6%%\"XG%\"YG%\"ZG" }{TEXT -1 57 " be the midp
oints of segments connecting the orthocenter " }{XPPEDIT 18 0 "H" "6#%
\"HG" }{TEXT -1 47 " (intersection of alitudes) to the vertices of " }
{XPPEDIT 18 0 "T" "6#%\"TG" }{TEXT -1 19 ". Then, the points " }
{XPPEDIT 18 0 "`A'`, `B'`, `C'`, D, E, F, X, Y" "6*%#A'G%#B'G%#C'G%\"D
G%\"EG%\"FG%\"XG%\"YG" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "Z" "6#%\"ZG
" }{TEXT -1 30 " lie on a circle whose center " }{XPPEDIT 18 0 "N" "6#
%\"NG" }{TEXT -1 40 " is the midpoint of the segment joining " }
{XPPEDIT 18 0 "H" "6#%\"HG" }{TEXT -1 21 " to the circumcenter " }
{XPPEDIT 18 0 "O" "6#%\"OG" }{TEXT -1 4 " of " }{XPPEDIT 18 0 "T" "6#%
\"TG" }{TEXT -1 47 ", and whose radius is half the circumradius of " }
{XPPEDIT 18 0 "T" "6#%\"TG" }{TEXT -1 2 ".\n" }}{EXCHG {PARA 0 "> " 0 
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triangle(T, [point(A,0,0),point(B,7,0),point(C,5,6)]):   " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "midpoint(`A '`, B, C): \nmidpoint(`
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "altitude(AD, A, T, D): \naltitude(B
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fc" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 214 "IsOnC
ircle(`A '`, fc) and \nIsOnCircle(`B '`, fc) and \nIsOnCircle(`C '`, f
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 `B '`, `C '`,\n  D, E, F, X, Y, Z], symbol=circle, axes=none,\n  scal
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}{SECT 1 {PARA 0 "" 0 "" {TEXT 279 3 "35." }{TEXT -1 9 " Use the " }
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\n  off := min( op(map( x->op(2,x), d)) ):\n  for i in args[2..nargs] \+
do\n    if type(i, 'identical(offset) = numeric') then\n      off := r
hs(i)\n    else \n      ERROR(`bad option `, i)\n    end if\n  end do:
\n  grayshades := map(x->COLOR(RGB,x,x,x), \n    [0.5,0.7,0.9] ):\n  f
or i to n do\n    pies[i] := plots[display](plottools[pieslice](\n    \+
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1+(i mod 3))])):\n    pies[i] := plottools[translate](pies[i], \n     \+
 evalf(off*cos(Pi*(2*i-1)/n)),\n      evalf(off*sin(Pi*(2*i-1)/n))):\n
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-1)/n), \n      (off+1/2*d[i][2])*sin(Pi*(2*i-1)/n), \n      convert( \+
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