# Questions tagged [geometry]

To be used for questions on geometry closely pertaining to physics. Includes differential geometry and euclidean geometry.

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### What is Snell's law's main formula?

My book states it as $(\sin i)/(\sin r)=n$. However, University Physics has a different say. It says, $n_{a} \sin a =n_{b} \sin b$. Which of the following is correct?
401 views

### New direction vector after collision of spheres [closed]

I have a volume in 3-space in which random spheres are spawned in motion. They have the following attributes to them: position known (in three axes) a direction vector (in three axes) a scalar speed ...
83 views

### 3D donuts and the centre of a black hole [closed]

I have been trying to imagine ways to visualise the gravitational field of the earth... It's near zero at the outer edges of the atmosphere, strong at sea level, strongest at the quarter point, then ...
16k views

### Seeing something from only one angle means you have only seen (what?)% of its surface area at most?

Is there a logical/mathematical way to derive what the very maximum percentage of surface area you can see from one angle of any physical object? For instance, if I look at the broad side of a piece ...
3k views

### Should linear algebra and vector calculus from traditional courses be replaced with geometric algebra? [closed]

geometric algebra gives geometric meaning to linear algebra and much more. it can provide a coordinate free geometric interpretation of spaces. those who learn of ...
2k views

### The Reeh-Schlieder theorem and quantum geometry

There have been some very nice discussions recently centered around the question of whether gravity and the geometry and topology of the classical world we see about us, could be phenomena which ...
9k views

### Why can the cross product of two vectors be calculated as the determinant of a matrix?

The cross product $\vec{a} \times \vec{b}$ can be written as the determinant of the matrix: \left| \begin{matrix} \vec{i} & \vec{j} & \vec{k} \\ a_i & a_j & a_k \\ b_i & b_j &...
987 views

### Generalized Complex Geometry and Theoretical Physics

I have been wondering about some of the different uses of Generalized Complex Geometry (GCG) in Physics. Without going into mathematical detail (see Gualtieri's thesis for reference), a Generalized ...
### Why does the $L_2$ norm give the shortest path between 2 points?
Why not the $L_1$ or $L_3$ distances? Is there some deep reason why the universe (at least at human scales) looks pretty much Euclidean? Could we imagine a different universe where a different \$...