# Tagged Questions

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### How many non-isomorphic Fano planes exist? [on hold]

How many non-isomorphic Fano planes exist? 1 down vote favorite 1 The Fano plane is the finite projective plane of order 2, having the smallest possible number of points and lines, 7 each, with 3 ...
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### Half spaces free of roots of a given polynomial

I thank Loic Teyssier and Emil Jerabek who helped me to revise the two previous version This question is motivated by the following fact in complex variable:(I learned this fact from the book of ...
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### Enclosing a convex plane domain in a disc

The following statement seems obvious to me: Let $\gamma:S^1\to\mathbb R^2$ be a smooth injection such that $\dot\gamma$ and $\ddot\gamma$ never vanish. Then $\gamma$ encloses a strictly convex ...
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### What is the smallest positive integer for which the congruent number problem is unsolved?

The congruent number problem is the problem of figuring out whether a given positive integer $N$ is the area of a right-angled triangle with all side lengths rational. According to Dickson's "History ...
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### Decidability of convex rearrangements of polygons

Triggered by the MO question, "How many convex shapes can be made with the pieces of the Stomachion?," I would like to pose this question: Q. Given $n$ polygons in a set $S$, say each with integer ...
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### What are the central points of a semi-nice region in the plane?

For a convex set in Euclidean space, there is an obvious notion of its center: namely, its center of mass, which by convexity lies in the set. For a nonconvex set there is just as obviously no nice ...
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### A conjecture on six planes [closed]

When I read Cox's Theorem, and Clifford's Circle Theorem and Miquel six circles theorem, I found the conjecture as folowing. And I checked the conjecture by the Geogebra sofware, the conjecture is ...
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### A chain of six circles associated with a conic

I found this problems three years ago. But I never have been a proof. Recently I posted in math.stackexchange.com. I am looking for a solution of the following problems: A chain of six circles ...
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### Conjecture generalization of Feuerbach theorem and somes another theorems

My question: I am looking for a solution of a conjecture generalization of the Feuerbach theorem in the end of the topic. But I think, I should let you know why I found this conjecture. I thank to You ...
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### Dao's theorem on six circumcenters associated with a cyclic hexagon

This questions from Ngo Quang Duong's paper In 2013, O. T. Dao published without proof a theorem with title Another seven circles theorem in Cut the Knot, a free site for popular expositionsof many ...
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### Set of balls which the number of the ball intersects lines on the plane is bounded

Does there exist the set of balls(may be not disjoint) $X=\{B_i\subset\mathbb{R^2};i\in I\}$, satisfing following properties?(Note that the ball has a positive real radius) Let the set of all lines ...
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### Best measure for curve similarity

I would like to measure similarity between two curves represented by two arrays of points. The similarity measure should not depend on the size of these shapes. Two similar shapes but have different ...
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### Why is it so hard to prove Toeplitz' conjecture?

I'm a layman in mathematics, so please excuse me in advance for anything in this question that may be inappropriate :D. Well: Four years ago, I was reading (and working to solve the puzzles on) ...
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### Terminology for polygons

As you may know term "polygon" might mean few different things and its meaning has to guessed from context. By some reason I have to use few of these meaning in one place. So I converge to the ...
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### Maximal opening angle of a polygon from a point [closed]

I'm looking for an algorithm that given a 2D convex polygon and point outside it, returns the two points of the polygon which are the two extremities of the polygon when viewed from that point. One ...
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### Is there a subset of the plane that meets every line in two open intervals?

Using the Axiom of Choice, it is possible to construct a subset of the plane that meets every line in two points (these are called "$2$-point sets"). What if, instead of points, we ask for two open ...
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### Best polygonal approximation to a polynomial $\pm$ c

Let a planar region $R$ be defined by the vertical range bounded by a polynomial $f(x) \pm c$ with $c>0$ a constant, and with $x$ varying between the smallest and largest roots of $f(x)$. For ...
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### Existence of finite set of points in the revolving circles

Let $k$ and $n$ be two fixed integers. Let $C$ denotes the circle with radius $4n$ (in the plane $\mathbb{R}^2$). Suppose $\{C_1,C_2\}$ shows the set of two arbitrary tangent circles with radius $2n$ ...
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### Projecting a convex partition onto a convex set

Say that $X$ and $Y$ are two convex regions in the plane, and suppose that $X \subset Y$. Further suppose that $Y$ is partitioned into disjoint convex subsets $Y_1 ,\dots, Y_n$. Is there a way of ...
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### A (possibly boring) Voronoi Game

The board for this game is a compact convex region $\cal C$ of $\mathbb{R}^2$. Below I illustrate with $\cal C$ an equilateral triangle. Two players, $A$ and $B$, alternate turns. At each turn they ...
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### Complexity of planar scissor congruence

Two (not necessarily convex) poygons of equal area are scissor-congruent, i.e. both can be cut along a finite number of straight lines or segments into isometric pieces. What can be said about the ...
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### Will (general points + small number of arbitrary points) impose independent condtions on plane curves?

It is well known that imposing vanishing at general points of $\mathbb P^2$ gives independent conditions on curves of degree $d$. Also, it is known that a small number ($\le d+1$) points always impose ...
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### Polygons with centroid at origin and vertices on compact codimension one submanifold of $\mathbb{R}^{n}-\{0\}$

Let $M$ be a compact codimension one submanifold of $\mathbb{R}^{n}$ which does not contaion $0$ and the origin lies in the bounded component of$\mathbb{R}^{n}-\{0\}$. Is it true to say that: ...
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### What's the name of this geometric mathematical modeling problem?

There is a right angle corner with width 1 in both directions. One wants to find the largest area shape which can pass through this corner. I know that this is a famous problem, but what is it called?
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### Intersecting balls with convex regions and a bisector thereof

This question is related to my previous posting Angle subtended by the shortest segment that bisects the area of a convex polygon Let $C$ be a convex region in the plane and let $s$ be the shortest ...
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### Perimeter of ellipse: Combination of two geometries

Is there a Riemannian metric $g$ on $\mathbb{R}^{2}$ such that for every ellipse $\gamma$ in the plane we have:$$\text{The Euclidien perimeter of}\; \gamma=\lambda (g\text{-diameter of}\;\gamma)$$...