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Her exposition of math concepts is ridiculous. "De Morgan had proposed a more modern approach to algebra, which held that any procedure was valid as long as it
by georgecmu 17y ago
Her exposition of math concepts is ridiculous.
"De Morgan had proposed a more modern approach to algebra, which held that any procedure was valid as long as it followed an internal logic. This allowed for results like the square root of a negative number"
Imaginary numbers were introduced by Descartes in 17th century and were widely accepted by the middle of 18th (think Euler: e^(i \pi) + 1 = 0).
"This principle (now an important aspect of modern topology) involves the idea that one shape can bend and stretch into another, provided it retains the same basic properties — a circle is the same as an ellipse or a parabola (the curve of the Cheshire cat’s grin)."
Huh? You can bend or stretch a circle into a parabola?
- cperciva 17y agoHuh? You can bend or stretch a circle into a parabola? In a sense, yes. A parabola is simply an ellipse with one of the foci at infinity.
- dmvaldman 17y agoyou 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.
- georgecmu 17y agoNot in the topological sense, which is what she is appealing to.