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Parametric curves - UNSA MP 2001
plane curves: graphic recognization, tangent, etc.
180 2001
3
U1
geometry
normal, function, graphic, Lissajous


This is the translation of a sheet designed for first year students of mathematics and physics at Université de Nice - Sophia Antipolis, of year 2000-2001.  Each student has had 3 hours to work on this sheet.

:U1/geometry/paramcomp.en
asktype=1&level=2&repeat=2
10
1
Parametric composition I
recognize a parametric curve by the graphs of its coordinate functions. 
:U1/geometry/paramcomp.en
asktype=2&level=2&repeat=2
10
1
Parametric composition II
recognize a parametric curve by the graphs of its coordinate functions. 
:U1/geometry/paramcomp.en
asktype=2&level=4&repeat=2
20
1.5
Parametric composition III
recognize a parametric curve by the graphs of its coordinate functions. 
:U1/geometry/paramchoice.en
type=point&type=deriv&choices=6&miss=no&repeat=3
10
0.6
Parametric choice I
from a parametric curve, recognize values or derivatives of functions. Animated graphics.
:U1/geometry/paramchoice.en
repeat=8&type=point,deriv&choices=6&miss=yes
20
1
Parametric choice II
from a parametric curve, recognize values or derivatives of functions. Animated graphics.
:U1/geometry/lisschoice.en
atype=1&style=1&repeat=4
10
1
Lissajous choice I
recognize a Lissajous curve according to its equations, or vice versa.
:U1/geometry/lisschoice.en
atype=2&style=1&repeat=4
20
1
Lissajous choice II
recognize a Lissajous curve according to its equations, or vice versa.
:U1/geometry/coincparam.en
Degree=1&maxsize=25&maxreply=12
20
1
Coincidence Param I
find the best approximation of a parametric curve.
:H6/geometry/tangent2d.en
curvetype=explicit&fundif=2&linetype=tangent&precision=0.001
10
0.7
Tangent 2D I
find the tangent of an explicit plane curve.
:H6/geometry/tangent2d.en
curvetype=parametric&fundif=2&linetype=tangent&precision=0.001
20
1
Tangent 2D II
find the tangent of a parametric curve.
:U1/geometry/parmtangent.en
curvetype=cubic&level=2&precision=0.001
10
1
Tangent parameters I
find a curve having a given tangent.
:U1/geometry/parmtangent.en
curvetype=parametric&level=2&precision=0.001
20
1.3
Tangent parameters II
find a parametric curve having a given tangent.
:U1/geometry/parmtangent.en
curvetype=cubic&level=4&precision=0.001
10
1.7
Tangent parameters III*
find a curve having a given tangent.
:U1/geometry/paramcusp.en
level=2&precision=0.001
10
1
Parametric cusp
parametrize a parametric curve so that it has a cusp.
:U1/geometry/coincparam.en
Degree=3&maxsize=30&maxreply=10
16
2
Coincidence Param II*
find the best approximation of a parametric curve.