# Tagged Questions

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### How can the R3 vertices of a 4-dimensional object be generated?

After learning a bit of OpenGL, I was hoping to find a way to project a 4-dimensional object into 3-space to visually study them. However, I'm not even sure how I would begin to do this. What kind ...
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### Calculate remaining space of a box/cube

Im developing an eCommerce system where items are 'logically' placed into boxes. Rather than the shipping system calculating the shipping of each item individually. The shipping will be calculated by ...
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### Find the direction of the clock arrow [closed]

A clock is placed such that at 12 noon its small arrow points towards north-east. In which direction does its large arrow point at 1.30 p.m? (A) North (B) South (C) East (D) West (E) None of these
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### 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, ...
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### 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 ...
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### Applications of group theory to geometry

What are the applications of group theory to geometry? Where can I know more about these applications?
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### 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 ...
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### 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 ...
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### 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 ...
120 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 ...
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### 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 ...
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### 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 ...