# Tagged Questions

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### What is the Hilbert curve's equation?!

The Hilbert curve has always bugged me because it had no closed equation or function that I could find. What is its equation or function? For example, if I wanted to find the Hilbert's curve point at ...
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### Intersections of two exponential curves in a plane

I am struggling to show that two exponential curves in $\mathbb{R}^n$ do not overlap except finite distinct points. Could anyone help me? Let $A\in\mathbb{R}^{n\times n}$ and ...
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### Birrational curves and singularities [closed]

If $C$ and $D$ are two birrational plane curves. Is there some relation between their singular points?
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### Harris Exercise 5.13 (points in general position)

I have a question about the second part of Exercise 5.13 in Harris' Algebraic Geometry: A First Course: Given $n \leq 2d + 1$ points in $\mathbb{P}^2$, characterize the subset of $(\mathbb{P}^2)^n$ ...
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### Equation for the Maximum-Area Rotor in a Wankel Engine

I am attempting to construct a specialized Wankel Engine in Autodesk Inventor. For my particular project, the rotor must take up the maximum area, in order to separate the air spaces of the top and ...
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### Components of algebraic varieties

Sorry, but I have to ask a dumb question: Algebraically, a hyperbola has only one irreducible component (given by an irreducible polynomial). Why, then, does the real image of a hyperbola show two ...
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### how can I graph a bicorn given only its equation?

what are the parts or the variables present in the bicorn equation?
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### every divisor of degree $0$ on a smooth cubic curve $\mathcal{C}\subseteq\mathbb{P}^2$ is equivalent to $A-A_0$ for a fixed $A_0\in\!\mathcal{C}$

NOTATION: Let $\mathcal{C}=\mathcal{V}(F)\subseteq\mathbb{P}^2$ be a curve of degree $3\!=\!deg(F)$ with no singularities and let $A_0\!\!\in\!\mathcal{C}$ be fixed. Let $Div(\mathcal{C})$ denote the ...
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### How many cubic curves are there?

It is well-known that there is only one "kind" of line, and that there are three "kinds" of quadratic curves (the nature of which depends on the sign of a so-called "discriminant"). It is noteworthy ...
This is a bit of a silly question, but I've been puzzled on how this can be done, so I ask here. You are given an implicit Cartesian equation like 4 x^4-4 x^3+8 y^2 x^2-27 x^2+12 y^2 x+4 y^4-27 ...