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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5 votes
4 answers
290 views

Draw regular polygon (maximum n = 12) with semicircles on each side,painted black

I need to draw a regular polygon on n sides, n <13 for side L, L <11 in cm. with semicircles on its sides, completely black in such a way that I save it as a xxx.png image to print and cut out ...
0 votes
1 answer
97 views

Is there a better method and more efficient way to determine the type of triangle based on the coordinates of its three vertices?

...
5 votes
2 answers
124 views

How to select right triangles and non right triangles given their coordinates

I have a list of triangle coordinates in 2D-space: ...
0 votes
0 answers
29 views

Covariant derivative of a Riemann tensor

I'm trying to calculate the covariant derivative of a Riemann tensor, and I'm using the following way, but there is some problem in my calculations because my calculations do not match with the ...
7 votes
3 answers
500 views

Fitting a disk in a non-polygonal region

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1 vote
2 answers
91 views

Calculating area for triangular geometries

Is there a function suitable for calculating areas for geometries involving triangles? I have used the formula for the area of the triangle. ...
2 votes
1 answer
77 views

The intersection of the same overlapping rectangles

A math challenge had the following statement: [[OVERLAP -Three identical rectangular frames are placed one on top of the other, as Shown (A frame on the left tilted over the center frame and ...
3 votes
3 answers
289 views

Parabola from a focus and a directrix

The code below is an attempt to obtain the graph of a parabola from two pieces of information: a focus and a directrix. I am not able to get the correct graphical shape of the parabola. I appreciate ...
0 votes
0 answers
32 views

How to merge multiple ellipse of radii R [closed]

Let us say that I have a point at (0,0) and I have 4 radii values for ellipses. How can I merge them together to form a single ellipse from the centre (0,0).
9 votes
3 answers
1k views

Taxicab Geometry

According to taxicab geometry, there are 1226 possible paths from A(2,5) to B(7,9), all with a distance of 9 units, |2-7|+|9-5|=9. I wanted to write a code where I could be obtaining the plots of some ...
1 vote
0 answers
74 views

Solving the expression of tortoise coordinate differential equation in Mathematica

I want to solve the differential equation of the form $\dfrac{dr_*}{dr} = \dfrac{1}{\left(1-\dfrac{2M}{r}\right)}$ under the boundary conditions $\lim_{r \rightarrow 2M}r_*(r) \rightarrow - \infty$ ...
3 votes
3 answers
198 views

Finite Differences:

I am having difficulty implementing finite differences in the correct columns of my code. ...
2 votes
0 answers
36 views

GeoProjection used in area computation of relatively small regions

Let's define a relatively small region via GeoPosition as follows. pos = GeoPosition[{{48, 9}, {48.0001, 9}, {48.0001, 9.0001}, {48, 9.0001}}, "WGS84"] ...
-1 votes
2 answers
200 views

How to solve this geometric problem with Mathematica?

I try to solve the following problem, making use of 14.0 on Windows 10 Let a triangle $\Delta$ (a contour with its interior) be chosen in the unit square $S$. To prove that the closure of the ...
3 votes
2 answers
107 views

Calculating vertical displacement to intercept the perimeter of the circle after a horizontal shift

I can't come upon a solution for the question below. The background of the actual work is not interesting for the question, so l won't explain why I need the solution. I would be very thankful if ...
2 votes
2 answers
113 views

How to get angles along a line?

What is the best way to get the angles along a line? I have tried this for example: ...
6 votes
1 answer
170 views

How to get properties from a Polygon object?

We can get polygons by this code: polys = (SeedRandom[#]; Polygon[RandomInteger[20, {4, 2}]]) & /@ Range[6] How to get those properties? When I dig ...
6 votes
1 answer
403 views

Finding an ellipse of minimum area that encloses a set of points

Is there a built-in function or set of functions in Mathematica that can take a set of points in the x-y plane and determine the ellipse of minimum area that contains all of the points? I am sure ...
3 votes
1 answer
115 views

How to find the farthest distance from the point to the region?

Consider the following 2D regions: ...
1 vote
1 answer
93 views

How can I find distance from a point to a straight line by using projection of the point to the line?

I have a point A(1,2,3) and a line having parametric equation x = 1 + 2t, y = 3t, z = -4+6t. I want to find distance from ...
6 votes
2 answers
390 views

What is simpler way to find projection of a point on a plane?

This is my code to find the coordinate of projection of the point pA = {2, 3, 5} on the plane -284 + 14 x + 2 y + 5 z == 0. <...
4 votes
3 answers
196 views

Solving where an Interpolating Function crosses a Region Boundary

I have a function which takes in a parameter t and outputs a point {x, y}, which together describe a continuous and smooth curve....
8 votes
5 answers
721 views

How can I shorten this code to rotate a line segment around its center?

I have a list of line segments stored in the form: { {{x11,y11},{x12,y12}} , {{x21,y21},{x22,y22}} , ... , {{xn1,yn1},{xn2,yn2}} } Now I want to rotate all of ...
16 votes
5 answers
2k views

How can I plot a loxodrome?

Can someone show me how to plot a rhumb line (loxodrome) in Mathematica via the ParametricPlot3D function? Here is what I got so far: ...
15 votes
6 answers
909 views

How to separate the regions enclosed by curves

There are three arbitrary curves that defined by three implicit functions. How to separate the 12 regions(one of them is the outside infinite region) Although we can use image methods to distinguish ...
1 vote
1 answer
150 views

Plotting Two ListDensityPlot3D Plots Together

I would like to plot two ListDensityPlot3D plots in the same plot. My two data sets are intersecting, and I would like to see that the two shapes intersect. However, when I plot them only one is ...
20 votes
5 answers
1k views

Divide a geometric region by (many) lines

Given a shape (e.g., a rectangle, a circle, etc.), how to divide it by $n$ randomly chosen lines. It is trivial to plot those lines (see figure below), using code like ...
-2 votes
2 answers
54 views

Coordinates of two points near a circle [closed]

Could someone help me find the locations of the points A and B? Let me know if you need more information. Thanks ;)
5 votes
3 answers
221 views

Divide a Graphics Line into $i$ equal lengths

I have a line given by ...
0 votes
1 answer
101 views

How to force Wolfram solve the ODE with respect to h[s]?

I have a problem with the DSolve operator. It just gives me the initial ODE as an answer, however, obviously, I need to find the answer h[s] as a function of f[s] and its powers (or whatever else). It ...
14 votes
5 answers
3k views

Inverted version of Sierpinski triangle

In Michael Trott's The Mathematic Guidebook for Graphics, Section 1.5.1, he first does this: ...
0 votes
1 answer
83 views

How to reduct the terms of differential equation?

How can one bring the terms of a differential equation below to a standard form with coefficients before h[s], h'[s], h''[s] and their powers? Or, better, can someone help me with solving it with ...
2 votes
1 answer
117 views

How can I compute the maximum value of a ConditionalExpression?

If we use GeometricSolveValues in version 14.0, we can use this code to get a ConditionalExpression expr: ...
6 votes
1 answer
895 views

How to Export to/Import from GeoGebra?

I'd like to convert geometric figures between Mathematica and GeoGebra. Does anyone know how to do that?
1 vote
1 answer
84 views

Is this a bug in RegionEqual or something else?

Is this a bug or I am missing something again? I ran the following code on a fresh kernel and each time it outputs randomly different result consisting of all combination ...
1 vote
1 answer
59 views

Is this a bug in RegionEqual?

$Version "13.0.1 for Microsoft Windows (64-bit) (January 28, 2022)" Is this a bug or I am missing something? ...
2 votes
1 answer
153 views

Speeding up minimization problem related to a minimal surface

I am trying to find the minimum of the function $$f(x)=\int_0^1(1+t^x)\sqrt{1+x^2 t^{2(x-1)}}dt$$ which arises from trying to minimize the surface area of a function rotated around the $x$ axis. Here ...
3 votes
2 answers
206 views

How to solve a geometric problem about a triangle using GeometricSolveValues?

I try to solve not so difficult geometric problem from an exercise book on elementary math with 14.0 on Windows 10: Let a triangle $\triangle ABC$ be given and the area of $\triangle ABC$ be equal to ...
19 votes
2 answers
975 views

Project map to a particular shape

I want to project a map to a particular shape, like a circle or ellipse. For example, let's imagine we want to project a map of the continental United states so that its outline is that of a circle. ...
0 votes
0 answers
72 views

Volume of self-intersecting polyhedra

Is there a method to calculate the volume of self-intersecting polyhedra with Wolfram? I did the calculations by hand taking the coordinates from this site for some of them (considering $l=1$): $\...
9 votes
2 answers
275 views

Envelopment of space curves

In their answers to Creating sculptural forms The respondents showed how to envelop space curves with a net-like structure. I used kglr's answer to create the following function: ...
3 votes
3 answers
127 views

Integrating a function over a region defined as the epsilon-neighborhood of a triangle

I would like to integrate the function f(x,y) = x^2 + y^2 over the epsilon-neighborhood of the triangle {{-1, 0}, {0, 1}, {1, 0}}. By epsilon-neighborhood, I mean the set of points which are closer to ...
1 vote
1 answer
103 views

Fit a point that defines a 90° angle

I'm trying to come up with a fit that will give me x,y coordinates of a point, that best fit in 2 slopes, the 2 slopes intercepting at 90°. At the moment I fit individually 2 lines to a 2 sets of ...
8 votes
3 answers
138 views

What is another way to write the equation in the form $A x + B y + C z + D = 0$ where A > 0 and GCD[A,B,C,D]=1?

I am trying write the equation of the plane passing through a point $A(x0, y0, z0)$ and take vector $w(A,B,C)$ as a normal vector. The equation has the form $$A(x-x0) + B(y-y0) + C(z-z0)=0.$$ I would ...
4 votes
3 answers
251 views

Computing and dynamically displaying the intersections of three circles

I don't understand why I get the following output: when in fact I was expecting to get $Failed, 1 or ...
4 votes
1 answer
123 views

Fourier Coefficients of Polygon Functions [closed]

Polygon function for a regular pentagon sketched and defined below: Fourier Coefficients are required for polygon functions with sharp discontinuous vertices; $n$ can be either integer or real. In ...
4 votes
1 answer
90 views

Residual triangles after incircle placement

After calculating the incircle for a triangle, I would like to get the vertex coordinates of the three left-over triangular regions. The additional constraint is that the angle bisectors are at right ...
9 votes
3 answers
537 views

Painted faces of n×n×n cube

Given a 3×3×3 cube made of 27 unit blocks. If the cube is painted, then each of the blocks has 3 of its faces painted, a given block may have 0, 1, 2 , or 3 of its faces painted. I want to mark ...
38 votes
1 answer
654 views

Bug in RegionMember?

Bug introduced in 10.0 and have been fixed before 13.3.1 RegionMember is new in 10.0 A commenter notes that the issue is with ...
4 votes
7 answers
420 views

Determination of radius based on data points

I have some data points: ...

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