# Questions tagged [geometry]

Questions on the application of Mathematica to geometric problems. You might also consider adding the [graphics] tag, if appropriate.

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### Error in variable trying to perform SlicedVectorPlot

I have been trying to plot the normal vector over the Mobius Strip, which I know I cannot do asking it to be a well-defined continuous map, nevertheless you can do it in a small region, which I am ...
116 views

### Unable to compute the area of a polygon

I am having trouble computing the area of the following polygon. I have the following polygon: ...
423 views

### Computing the intersection area of two disks in 3D

Closely related to this question about highlighting intersection of two disks, I am trying to figure out if one can do so similarly for disks embedded in $3D$ (e.g. in a bounding box). The difference ...
2k views

### Is there a way to randomly distribute points within a circle on the surface of a sphere?

I'm attempting to set up a situation where on a 3D sphere, I choose a random point and construct a circle around this point with some radius. I then want to randomly distribute points within this ...
64 views

### Is it possible to plot a manifold from it's metric / line element in Mathematica?

i'm very new to using Mathematica and mostly just trying to work out what it can or can't do. I'm doing a course on differential geometry and was wondering if there might be a better way for me to ...
98 views

### How can I simplify my geometric calculation?

Here is a math problem I am dealing with right now: Given ellipse $C$: $x^2/a^2 + y^2/b^2=1$ ($a>b>0$). Ellipse $C$ passes through the point $P$: $(1,3/2)$, and has eccentricity $e=1/2$. ...
97 views

### Unable to find root for user-defined function

I created the function getSolution[xVal,yVal] for a geometry problem I'm working on and wish to solve it for getSolution[2,x]==0. I can plot it clearly showing the roots: However, when I attempt to ...
78 views

### RegionCentroid and center of mass

If we have three masses $m_1,m_2,m_3$ (assuming that are all equal to $1$) located at $r_1,r_2,r_3$ respectively, then the center of mass is at $(1.00,0.83)$. In the Wolfram Documentation page says ...
212 views

### Finding all the lines that can be defined a set of points

Input ten Points, calculate every possible straight line from each possible pair of points and check if any of the other points are on the lines. Is something like this possible in mathematica? and ...
56 views

### Legend for two parametric surfaces

I have the plot of two surfaces given by ...
34 views

### How can I always get one option of coordinates of the points A, B, C, D, and X of the Problem 6 in IMO 2018?

This is the Problem 6 of IMO 2018 https://www.imo-official.org/problems.aspx I use the code at Mapleprimes (with some prepairs) https://www.mapleprimes.com/questions/228162-How-Can-I-Get-One-Option-...
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### Determinant of Gauss (Area of a polygon of n vertices) how to implement

A very useful procedure to find the area of ​​any irregular polygon is through the Gauss determinant. It involves drawing the figure on a Cartesian plane, setting the coordinates of each of the ...
66 views

### HalfLine to draw lines “to infinity”

I'd like to draw a simple figure illustrating geometric perspective (so-called "central-point perspective") in which perspective lines on two cubes are extended "to infinity," where they meet. Here ...
59 views

### How would I plot the inequality lines together with the intersection plot of the inequalities?

For example, I've got the following code: Plot[{x >= 5, y >= 8, x + 2y <= 64, x + y <= 40}] This would plot: Now, this is fair enough. It shows me ...
67 views

### Using the Disk graphics primitive II

I ask again to clarify a couple more things How do I write the disk primitive to calculate these cases Cases follow this link 1 reply from @kglr thanks Using the Disk graphics primitive
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### How to obtain the positions of the points in a lattice

I want to know the positions of each point in a hexagon lattice, like I saw some posts where they obtain this lattice using a function ...
47 views

### How can I get coordinates and radius of Incirle of the triagle with the length three sides are a, b, c?

I used Insphere[SSSTriangle[5, 7, 9][]] and got Sphere[{11/2, Sqrt/2}, Sqrt/2] But, I cannot get the result when I used ...
268 views

### Using the Disk graphics primitive

Please be kind enough to give me some indication on how to use the Disk graphics primitive in any of these cases: I want to calculate the area and perimeter of the ...
438 views

### Rotating squares animation

Reference link: https://www.geogebra.org/m/RHYH3UQ8 , https://www.geogebra.org/m/xkzsqcyx , https://www.netpad.net.cn/svg.html#posts/55789 I want to generate an rotating squares animation like this, ...
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### How can reduce the code to get coordinates of vertices of tetrahedron so that O(0,0,0) is center of circumsphere?

Let be given tetrahedron $SABC$, $SA=14/3$, $SB=7*\sqrt{13}/3$, $SC=2*\sqrt{193}/3$, $AB=7$, $BC=3$, $AC=8$. I want to find the coordinates of $A, B, C, S$ so that $O(0,0,0)$ is center of circumsphere ...
51 views

### Apply non-linear transformation to graphics object

I would like to define some simple geometric primitives (e.g. points and lines) and see what happens when I transform them by a non-linear transformation (in my case $(x,y)\mapsto (\sqrt x,\sqrt y)$). ...
71 views

### Divide Graphics Line into i equal lengths

I have a line given by ...
45 views

### How to set up symplectic geometry without(!) metric (with xAct/xTensor)?

I want to define a symplectic manifold with symplectic form $\Omega_{[ab]}$ with $\Omega_{ab}\Omega^{ac} = \delta^c_b$, but without having a metric. I define a manifold and an antisymmetric (2,0) ...
What is the simplest method for coloring each polygon face of a polyhedron with a specified color? For instance suppose I have a list of $12$ colors (...