3 ms·
you cannot stretch a parabola into a circle because a circle is a closed loop, while a parabola is not. any stretching would necessarily have to tear the circle
by dmvaldman 17y ago
you cannot stretch a parabola into a circle because a circle is a closed loop, while a parabola is not. any stretching would necessarily have to tear the circle. a topologist would say they have different fundamental groups.
the author of this article should stick to what she knows...english literature, not algebra.
- cperciva 17y agoa topologist would say they have different fundamental groups In the affine real plane, yes. In the projective real plane, all (non-degenerate) conics have the same fundamental group.
- gambling8nt 17y agoTo elaborate on cperciva's (correct) point: On a projective plane a parabola contains a single point at infinity, connected (both figuratively and topologically) to the two open ends. A hyperbola contains two distinct points at infinity each connected to one end of each of the two usual components.