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# 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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0 votes
3 answers
114 views

### All composite numbers are crossed by the lines

I'm trying a version of the code with the concavity of the parabola upwards (y=x^2), but I'm not succeeding. I appreciate any help. ...
0 votes
1 answer
59 views

### Verifying set emptiness with FindInstance versus Reduce [closed]

I have a semialgebraic set in $\mathbb{R}^4$ that I believe to be empty. FindInstance claims that it is empty in less than ten seconds. But Reduce has run for a week without visible progress --- and ...
• 549
4 votes
4 answers
219 views

### Lines of intersections in a parabola

To test the parabolic sieve, my intention was for the graph to show the coordinates of two points on the parabola and the value of the intersection on the y-axis. A table with this information would ...
0 votes
2 answers
57 views

### How to find the nearest point using RegionNearest for this case?

Consider the following region: ...
• 5,887
2 votes
1 answer
303 views

### Approximating country by rectangles

Say I have a list of coordinates (these form the border of a country) called testpolycoords that is about 400 points long. I want to use a quadtree to divide the ...
• 225
4 votes
2 answers
596 views

### Make two disks just touch

I have two disks, that I want to make touching each other. One disk is fixed, the other can shift along the x axis. The shift should be determined to make the disks intersecting in one point (or have ...
• 1,570
-3 votes
1 answer
101 views

### How to batch add vertex letters A, B, and C to each triangle？ [closed]

How to batch add vertex letters A, B, and C to each triangle？ I tried the following code myself, but was unable to successfully add it ...
• 4,523
-2 votes
1 answer
98 views

### How to determine the shape of each triangle? Are they an acute, right-angled, or obtuse triangles? [duplicate]

Given the coordinates of the three vertices of multiple triangles in a list, how can we determine at once whether each triangle is acute, obtuse, or right-angled? How can we determine the shape of ...
• 4,523
0 votes
2 answers
163 views

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• 4,523
5 votes
2 answers
180 views

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

I have a list of triangle coordinates in 2D-space: ...
• 1,131
8 votes
3 answers
557 views

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• 56k
2 votes
1 answer
91 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
314 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 ...
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
80 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
205 views

### Finite Differences:

I am having difficulty implementing finite differences in the correct columns of my code. ...
2 votes
0 answers
38 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"] ...
• 487
3 votes
2 answers
114 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 ...
-4 votes
2 answers
223 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 ...
• 27.3k
3 votes
2 answers
124 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: ...
• 25.6k
6 votes
1 answer
174 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 ...
• 26.9k
6 votes
1 answer
409 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 ...
• 1,134
1 vote
1 answer
96 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 ...
• 3,921
6 votes
2 answers
425 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. <...
• 3,921
5 votes
4 answers
233 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....
• 272
-2 votes
2 answers
56 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 ;)
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 ...
• 20.1k
1 vote
1 answer
59 views

• 101
3 votes
3 answers
135 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 ...
• 185
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 ...
• 159
9 votes
2 answers
288 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: ...
• 81.4k
2 votes
1 answer
125 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: ...
• 26.9k
8 votes
3 answers
143 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 ...
• 3,921
4 votes
1 answer
95 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 ...
• 56k
4 votes
1 answer
126 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 ...
• 3,198
9 votes
3 answers
545 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 ...
• 7,138
5 votes
2 answers
526 views

### Wrong solution in a geometry problem

I try to solve the simple problem of finding (integer numbers) for the sides of a triangle when its perimeter is 90 and its area is twice, three times or four times this number. My approach is this: <...
• 347
3 votes
1 answer
170 views

### How do I find all the nets of a polyhedron?

The following will show me a single example net of a polyhedron PolyhedronData["Dodecahedron", "Net"] And ...
• 133
3 votes
3 answers
366 views

### Gaussian curvature of a point cloud surface

Having a set of triplets like dsurf={{x1,y1,z1},{x2,y2,z2},...} whose interpolation defines an open surface (as shown by ...
2 votes
2 answers
247 views

### The center of mass of a semiellipsoid

I am trying to find the center of mass of a semiellipsoid using cylindrical coordinates. r^2/a^2+z^2/b^2 < 1, z < 0 the density = 1. I know that the center of mass is (1/M int,int,int rcos(theta)...
0 votes
2 answers
103 views

### How to build the following region?

Consider a 3D figure defined by the dependence $\Delta x(z),\Delta y(z)$. One example is a pyramidal frustum, for which $\Delta x, \Delta y$ are linear functions of $z$, and $z$ lies inside the ...
• 5,887
1 vote
1 answer
55 views

### Leading significant digits

Given that the initial area in a Sierpinski triangle is A_0 and the subsequent areas $$(A_n) =A_0 (3/4)^n$$ , what is the formula to calculate the leading ...
3 votes
2 answers
205 views

### How to get a RegionIntersection output as a primitive instead of a BooleanRegion?

line = ParametricRegion[{2 + 3 t, -1 + t, 3 - 2 t}, {t}]; plane = ImplicitRegion[2 x + 3 y - z == 9, {x, y, z}]; r3 = RegionIntersection[line, plane] ...
• 56k
1 vote
2 answers
136 views

### What are some quick methods for calculating hyperbolic equations?

Given that the hyperbola passes through three of the four points (m1, m2, m3, m4), find the equation for the hyperbola These four points are like this ...
• 4,523
4 votes
3 answers
172 views

### Problem with FindGeometricTransform and NMinimize

I'm interested in Centroidal Voronoi tessellation. Here are two examples of unit disk tessellations: They are the same with respect to rotation. Recently, I've found ...
• 1,849
3 votes
2 answers
401 views

### How to draw the trajectory of the circumscribed rectangle of an ellipse and determine the area range of the rectangle?

The equation for a known ellipse is: x^2/4 + y^2/3 == 1 The circumscribed rectangle of an ellipse, where the lines on all four sides of the rectangle are tangent ...
• 4,523
0 votes
0 answers
64 views

### A geometric application of Benford's law [duplicate]

I would like some help solving the following problem using Mathematica: Show that, no matter what the initial area of an equilateral triangle is, the sequence of areas (painted in black) of the ...