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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG 
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{PARA 4 "" 0 "" {TEXT -1 10 "ellissoide" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 94 "implicitplot3d(x^2+2*y^2+3*z^2=1,x=-1..1,y=-1..1, z=-
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}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 11 "iperboloidi" }}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 91 "implicitplot3d(x^2+y^2-z^2=1,x=-3..3,y=-3..
3,z=-2..2,grid=[20,20,20], orientation=[45,60]);" }{TEXT -1 36 "iperbo
loide a una falda (iperbolico)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 
"per ogni t reale, i punti sulla retta intersezione dei due piani  " }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 257 50 "x - z
 = t (1 - y)       e        t (x + z) = 1 + y" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 156 "stanno sull'iperboloide \+
a una falda di equazione x^2-z^2=1-y^2. Dunque l'iperboloide a una fal
da \350 una superficie rigata: \350 unione di una famiglia di rette." 
}}{PARA 0 "" 0 "" {TEXT -1 51 "(Ci sono altre famiglie di rette sulla \+
superficie?)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "solve(\{x-z
=t*(1-y),t*(x+z)=1+y\},\{x,y\});" }{TEXT -1 84 " calcoliamo equazioni \+
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "plot3d(\{[(2*t+(1-t^2)*z)/(
t^2+1),(t^2-1+2*t*z)/(t^2+1),z]\},z=-2..2,t=-1..2,orientation=[60,60],
grid=[50,50]); " }{TEXT -1 49 "l'iperboloide a una falda \350 una supe
rficie rigata" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "implicitp
lot3d(x^2-y^2-z^2=1,x=-4..4,y=-4..4,z=-4..4,grid=[20,20,20],orientatio
n=[70,50],tickmarks=[3,3,3]);" }}{PARA 0 "" 0 "" {TEXT -1 41 "      ip
erboloide a due falde (ellittico)" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 
-1 11 "paraboloidi" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "implic
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n=[70,50]);" }}{PARA 0 "" 0 "" {TEXT -1 27 "      paraboloide ellittic
o" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "implicitplot3d(x^2-y^2
-z=0,x=-1..1,y=-1..1,z=-1..1,grid=[20,20,20], orientation=[60,60]);" }
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 37 "     paraboloide iperboli
co (a sella)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "solve(\{t*(
x-y)=z,x+y=t\},\{y,z\}); " }{TEXT -1 140 "anche il paraboloide iperbol
ico \350 una superficie rigata. Calcoliamo equazioni parametriche dell
e rette (x=parametro lungo una retta fissata)" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 91 "plot3d(\{[x,-x+t,2*t*x-t^2]\},x=-1..1,t=-1..1,st
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "implicitplot3d(x*y-z=0,x=-1.
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" 0 "" {TEXT -1 80 "     paraboloide iperbolico  xy=z (con assi di sim
metria le rette x+y=0 e x-y=0)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 82 "plot3d(\{[x,t,t*x]\},x=-1..1,t=-1..1,style=PATCH,orientation=[
60,60],grid=[20,20]); " }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 15 "coni \+
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(x^2+y^2-z^2=0,x=-1..1,y=-1..1,z=-1..1,grid=[20,20,20], orientation=[6
0,60]);" }}{PARA 0 "" 0 "" {TEXT -1 9 "     cono" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 83 "plot3d(\{[z*cos(t),z*sin(t),z]\},z=-2..2,t=-P
i..Pi,orientation=[60,60],grid=[50,50]);" }{TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 23 "     cono (parametrico)" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 66 "implicitplot3d(x^2+y^2=1,x=-2..2,y=-2..2,z=-2..2,gr
id=[20,20,20]);" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 23 "     ci
lindro ellittico" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "implici
tplot3d(x^2-y^2=1,x=-2..2,y=-2..2,z=-2..2,grid=[20,20,20]);" }{TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "     cilindro iperbolico" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "implicitplot3d(x^2-z=0,x=-2.
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