# Tagged Questions

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### approaches to Apollonius circle problems

I've been looking for solutions to finding the set of circles tangent to two other circles. one circle can be inverted to a line, but two circles can be mapped to a line and a circle or equivalently ...
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### Reference to parabola lemma

I am looking for a previous reference to the following very simple geometric lemma, which I use in my paper [arXiv:1503.03462]: Let $P$ be the parabola $y=x^2$. Let $a,b,c,d$ be four points on $P$ ...
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### Discovery and Study of Conic Sections in Ancient Greece

Is there anything known about what drew the attention of ancient greek mathematicians to conic sections and, what were the models they used to study conic sections? What I would like to know, is ...
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### the paraboloid model for hyperbolic space [closed]

In Thurston's Three-Dimensional Geometry and Topology, he gives a recipe for a non-standard model for hyperbolic space which he calls the paraboloid model. I'd like to use the model to try out ...
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### Empty real conic containing two pairs of conjugate points in the projective plane?

Given two conjugate pairs of points in general position in $\mathbb{CP}^2$, there is a pencil of real conics containing these four points. Is there a real empty conic in this pencil?
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### Does an origin-centered ellipse in the plane intersect each $L^p$-circle at most 8 times?

The question is in the title: Let $E$ be an origin-centered ellipse in ${\mathbb R}^2$ and let $S$ be an "$L^p$-circle": $S = \{(x,y) : |x|^p + |y|^p = \text{const}\}$, where $1 \leq p \leq \infty$. ...
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### Mutually tangent ellipsoids in 3 space

I recently heard a claim that for any n, it is possible to arrange n ellipsoids in 3 space such that each pair of ellipsoids is kissing. Is this true, and if so, how? Edit: By kissing, I mean that I ...
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### Asymptotes of hyperbolic sections of a given cone

A book I'm reading (Companion to Concrete Math Vol. I by Melzak) mentions, "...any ellipse occurs as a plane section of any given cone. This is not the case with hyperbolas: for a fixed cone only ...
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### Minimum distance between two arbitrary circles in space?

What is the minimum distance between two arbitrary circles in space? I am working out the problem with Maxima, but I am surprised by how complicated this rapidly turns out to unfold for such a "...
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### In the classical construction of conic sections, where does the axis of the cone intersect the plane?

Everybody knows that if I take the intersection of a right circular cone with a plane, I get a conic section. My question is, where does the symmetry axis of the cone intersect the plane? Does this ...