1
vote
1answer
90 views

Finding the “differentness” of two point clouds

I would like to reduce the "differentness" of two point clouds $X$ and $Y$ to a single comparable value $\lambda$, which would ideally be $0$ when $X$ and $Y$ are identical upto isometry (rotation, ...
1
vote
1answer
50 views

Motivation and application for stochastic geometry.

I am starting a PhD, and there is a good chance that my project will be oriented in the study of random polytopes or/and random mosaics. I was wondering what are the motivations and applications of ...
2
votes
4answers
312 views

Applications of group theory to geometry

What are the applications of group theory to geometry? Where can I know more about these applications?
2
votes
2answers
2k views

Point on the left or right side of a plane in 3D space

I have an alpha plane determined by 3 points in space. How can I check if another point in space is on the left side of the plane or on the right side of it? I need a fast solution for plug-in ...
1
vote
1answer
407 views

How many feet of rope would be needed to wrap this device?

So here is the problem. My dad designed this umbrella that is to be wrapped with rope. The rope is 1 inch thick, and the umbrella is made of poles that arch away from a center beam extending upward ...
1
vote
1answer
158 views

Maximal color difference

I have a picture consisting of a two-dimensional array of ordered triples (red, green, blue) of real numbers from 0 to 1. I'm looking for something like a norm on pictures which expresses the range of ...
3
votes
1answer
117 views

Geometric reason for 3/4-power growth rate?

It seems pretty well established that organisms grow according to a 3/4-power law. For example, Niklas and Enquist, in their paper "Invariant scaling relationships for interspecific plant biomass ...
9
votes
1answer
2k views

Why does GPS require a minimum of 24 satellites?

From Wikipedia, The GPS design originally called for 24 SVs, eight each in three approximately circular orbits, but this was modified to six orbital planes with four satellites each. [...] The ...
1
vote
3answers
490 views

Distance from a point to a line in vector geometry - real world applications?

In vector geometry it is a standard example how to calculate the distance between a point and a line in space. However are there any interesting real world applications of this. I.e. where one wants ...
5
votes
2answers
994 views

Are there any practical applications of the directrix of a parabola?

I know of many applications for the focus of a parabola (satellite dish, whispering gallery, etc.), but haven't been able to find any for the directrix. An internet search has come up empty. I have ...
0
votes
2answers
376 views

Applications of circumcircles?

Are there examples where the circumcircle of a triangle is useful in everyday life (not unrealistic or far-fetched ones)? Are there other interesting applications (physics, technology, mathematics)?