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Apr
13
asked Torus-like Riemann surface for a genus 1 Cassini oval
Apr
1
comment Visual understanding for “the genus” of a plane algebraic curve
Your first sentence is rather complex, how on earth may that be visualised, or: is there any connection of that remark to the Riemann sphere?
Apr
1
comment Visual understanding for “the genus” of a plane algebraic curve
How about the relation of the other Cassini curves to the Riemann sphere? Apparatnly they cannot be parametrized - or?
Apr
1
comment Visual understanding for “the genus” of a plane algebraic curve
This explains why the lemniscate is of genus 0, while the others are of genus 1.
Apr
1
asked Visual understanding for “the genus” of a plane algebraic curve
Mar
30
asked Relation between curvature of curve and dual curve?
Mar
28
comment A 4th grade curve meets a line in one point with multiplicity 4
The curve $x^3=y^2$ and line $y=0$ has a multiplicity of intersection 3. But the origin $(0,0)$ is a cusp.
Mar
28
asked A 4th grade curve meets a line in one point with multiplicity 4
Mar
27
revised Dual curve of the lemniscate of Bernoulli?
deleted 58 characters in body
Mar
25
revised Dual curve of the lemniscate of Bernoulli?
added 95 characters in body
Mar
23
revised Dual curve of the lemniscate of Bernoulli?
Expanded the answer
Mar
23
accepted Dual curve of the lemniscate of Bernoulli?
Mar
23
revised Dual curve of the lemniscate of Bernoulli?
Expanded the answer
Mar
23
revised Dual curve of the lemniscate of Bernoulli?
Expanded the answer
Mar
23
revised Dual curve of the lemniscate of Bernoulli?
added 5 characters in body
Mar
22
comment Dual curve of the lemniscate of Bernoulli?
I use homogeneous coordinates. So by putting $x'=x/z, y'=y/z, z'=z/z = 1$ one gets the normal (affine) equation. Or just by putting $z=1$. Also $[u,v,w]$ are homogeneous line coordinates.
Mar
22
answered Bitangents corresponds to nodal points in the dual space
Mar
22
revised Dual curve of the lemniscate of Bernoulli?
added 131 characters in body
Mar
22
answered Dual curve of the lemniscate of Bernoulli?
Mar
19
revised Dual curve of the lemniscate of Bernoulli?
added 73 characters in body; edited tags