# Tagged Questions

243 views

### Diameter and Hausdorff Distance

Let $A,B \subset \mathbb R^n$ be non empty compact sets and $d_H$ be Hausdorff distance. I'm thinking that if we know the distance between two sets, the difference between their diameters is bounded. ...
27 views

### Paramertrization of intersection between spehere and plane.

I have the normal $n = (a,b,c)$ for a plane through origo,and want to find the paramertrization of the unit circle. How can I do this? I guess I should eliminate one coordinate from the plane and ...
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### $\tan{\frac{a}{2}}\cdot \tan{\frac{b}{2}}\cdot \tan{\frac{c}{2}}\leq \frac{1}{3\sqrt{3}}$, Where a,b,c are angles of triangle

As in title $$\tan{\frac{a}{2}}\cdot \tan{\frac{b}{2}}\cdot \tan{\frac{c}{2}}\leq \frac{1}{3\sqrt{3}}$$whats more, is that this is acute triangle. I think it should be doable somehow with Jensen ...
328 views

### Pattern matching circle, square or triangle

I have a set of x, y co-ordinates that are actually taken from hand drawings of a circle, square or a triangle. Using the set of points, I need to mathematically find if the points approximately fit a ...
231 views

### Why it is sufficient to show $|f'(z)-1|<1$?

According to an article entitled "On the Univalency of Certain Analytic Functions" by Wang et al. (2006), we have to show that $|f'(z)-1|<1$ in order to find the radius of univalency for the class ...
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### Relationship between Number of circles required to surround a circles and the distance function?

In Why is a circle in a plane surrounded by 6 other circles, the implicit assupmtion is the distance is Euclidean, my question is: Are there any relation between the distance function being used and ...
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### Distribution or bounds for maximum Cartesian coordinate sampled from the sufarce of an n-sphere

It's been said that for high dimensions a hypersphere is "nearly all equator". The amount of space near the poles is just ridiculously small. This of course means that from a uniformly random sample ...
### What does it mean for a sequence of self-homeomorphism of $\mathbb{R}^n$ to converge to a point?
Let $\{f_j\}$ be a family of self-homeomorphisms of $\overline{\mathbb{R}}^n$ and $x,y\in\overline{\mathbb{R}}^n$, where $\overline{\mathbb{R}}^n$ is the one-point compactification of $\mathbb{R}^n$. ...