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Arnold's Trivium
1991 Arnold's Trivium
36
Problem 36
Problem 36
Source:
July 1, 2010
conics
parabola
Problem Statement
Sketch the evolvent of the cubic parabola
y
=
x
3
y=x^3
y
=
x
3
(the evolvent is the locus of the points
r
→
(
s
)
+
(
c
−
s
)
r
→
˙
(
s
)
\overrightarrow{r}(s)+(c-s)\dot{\overrightarrow{r}}(s)
r
(
s
)
+
(
c
−
s
)
r
˙
(
s
)
, where
s
s
s
is the arc-length of the curve
r
→
(
s
)
\overrightarrow{r}(s)
r
(
s
)
and
c
c
c
is a constant).
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