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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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 ;)
value1's user avatar
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1 vote
1 answer
82 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 ...
azerbajdzan's user avatar
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1 vote
1 answer
57 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? ...
azerbajdzan's user avatar
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2 votes
1 answer
144 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 ...
Kamal Saleh's user avatar
3 votes
2 answers
202 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 ...
user64494's user avatar
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0 votes
0 answers
69 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 $l=1$): $\...
Math Attack's user avatar
3 votes
3 answers
124 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 ...
Zsombor's user avatar
  • 163
1 vote
1 answer
101 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 ...
A postdoc's user avatar
  • 159
9 votes
2 answers
267 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: ...
eldo's user avatar
  • 60.7k
2 votes
1 answer
112 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: ...
yode's user avatar
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6 votes
3 answers
125 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 ...
minhthien_2016's user avatar
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 ...
Syed's user avatar
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4 votes
1 answer
121 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 ...
Narasimham's user avatar
  • 3,138
9 votes
3 answers
530 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 ...
matrix42's user avatar
  • 6,946
5 votes
2 answers
522 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: <...
Nitra's user avatar
  • 347
3 votes
1 answer
132 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 ...
Peter Olson's user avatar
3 votes
3 answers
273 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 ...
Daniel Castro's user avatar
2 votes
2 answers
236 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)...
Mike Gotier's user avatar
0 votes
2 answers
98 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 ...
John Taylor's user avatar
  • 5,387
1 vote
1 answer
53 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 ...
Rubens Vilhena Fonseca's user avatar
3 votes
2 answers
188 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] ...
Syed's user avatar
  • 48.6k
1 vote
2 answers
124 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 ...
csn899's user avatar
  • 3,625
4 votes
3 answers
168 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 ...
lesobrod's user avatar
  • 1,501
3 votes
2 answers
366 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 ...
csn899's user avatar
  • 3,625
0 votes
0 answers
63 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 ...
Rubens Vilhena Fonseca's user avatar
4 votes
5 answers
334 views

Most concise code for tangent and normal line of implicit algebraic curve

Can you make the code for tangent line and normal line of implicit algebraic curve cu more concise than mine? The code for tangent line at ...
azerbajdzan's user avatar
  • 13.4k
1 vote
0 answers
54 views

SameTest for arrays of points

I need to gather arrays of points by some intuitive SameTest, so for some tolerance the next arrays will be treated as the same: Next code looks like suitable for ...
lesobrod's user avatar
  • 1,501
0 votes
1 answer
100 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 ...
Denis D. Bavrin's user avatar
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 ...
Denis D. Bavrin's user avatar
2 votes
0 answers
64 views

"RegularHyperbolicTilingGraph" Does Not Work Properly [closed]

I am trying to draw regular hyperbolic tesselations using the "RegularHyperbolicTilingGraph" function on Mathematica 13. Here is the introduction of this function on the repository: https://...
Tianyi Wang's user avatar
3 votes
4 answers
455 views

How can I deduce the distance formula from a point to a straight line?

Consider: Clear["Global`*"] reg = ImplicitRegion[a x + b y + c == 0, {x, y}] pt = {x0, y0} RegionDistance[reg, pt] The distance formula from a point to a ...
csn899's user avatar
  • 3,625
2 votes
2 answers
165 views

Graphing the locus of points a unit distance from a rectangular prism

I am a new Mathematica user. For one of my first projects, I am attempting to graph the locus of all points that are a unit distance from a rectangular prism with given dimensions. I have no idea how ...
Ahdhehshdjdj's user avatar
4 votes
4 answers
419 views

A simpler or more concise way to divide the boundary of a polygon into equal arc lengths?

I am really looking just for the least amount of code needed to do this but it is still readable. Here is the same polygon but the border is respectively split up into 10, 20, and 30 points along the ...
Teg Louis's user avatar
  • 625
2 votes
2 answers
237 views

How to approximate the distance from {x,y} to a hyperbola?

I can get a good approximation, but making this into a MMA algorithm is getting complicated. Consider this example: ...
Ted Ersek's user avatar
  • 909
0 votes
2 answers
85 views

How to make a function that outputs a mesh region object or some other geometric object that represents a cake number?

The lazy caterer's sequence, more formally known as the central polygonal numbers, describes the maximum number of pieces of a disk (a pancake or pizza is usually used to describe the situation) that ...
Peter Burbery's user avatar
-2 votes
1 answer
145 views

Can mathematica achieve symbolization of geometric drawing and operations? [closed]

For example, verifying the properties of a parabola: As shown in the following figure: For a parabola y ^ 2=2px (p>0), its focal point F and coordinates are (p/2,0). Point A (x0, y0) is on the ...
csn899's user avatar
  • 3,625
3 votes
3 answers
259 views

Drawing angle bisectors in a triangle

In triangle $\triangle ABC$, the angle $\angle BAC$ is equal to $60°$, $|AB|=2$, $|BC|=\sqrt 6$, and $AD$ bisects the angle $\angle BAC$ and $BC$ at point $D$. How can I find the length of the angle ...
csn899's user avatar
  • 3,625
0 votes
1 answer
163 views

Calculate the 1st Brillouin zone with given lattice basis vectors

Given two basis vectors in the 2-dimensional momentum space b1, b2, I want to write a function that returns the 1st Brillouin zone: ...
Zhengyuan Yue's user avatar
1 vote
3 answers
160 views

Fitting C-shaped points with right-pointing parabola, ellipse, circle or other

I was trying to fit the following points: ...
mgf's user avatar
  • 11
2 votes
0 answers
42 views

Inconsistence in calculating zero geometric area

First, let us see disk ...
matheorem's user avatar
  • 17.1k
3 votes
1 answer
102 views

minimal enclosing k-gon of binarized image

Similar to my previous post. I have a binarized image with 4 disk-like dots. I want to find a minimum quadrilateral enclosing 4 dots as below and extract the coordinates of 4 corners(yellow points) ...
matheorem's user avatar
  • 17.1k
2 votes
0 answers
96 views

How can I define a d-dimensional metric on mathematica with abstract components?

I want to define on Mathematica the (d+1)-dimensional metric: $ ds^2 =G_{\mu\nu}dx^{\mu}dx^{\nu}= 2tdt^2 + g_{ij}(t,x)dx^idx^j $ where latin indices go $i,j=1,...,d-1$ and $g_{ij}$ are unknown ...
Mike Ehrmantraut's user avatar
4 votes
4 answers
377 views

How can I calculate the volume of spatial geometry?

In the square prism ABCD A1B1C1D1, AB=2, A1B1=1, AA1=Sqrt [2], what is the volume of this prism? It is easy to calculate its volume using the volume formula: ...
csn899's user avatar
  • 3,625
5 votes
2 answers
181 views

RegionDifference imperfection

Consider the following two regions: ...
John Taylor's user avatar
  • 5,387
1 vote
1 answer
47 views

How to make the following region?

Consider the following region shown in green: It is a part of the annular cylinder with the inner radius $R$ and the outer radius $R+r$, which is cut off from the left and right. Is it possible to ...
John Taylor's user avatar
  • 5,387
1 vote
2 answers
159 views

Discontinuity in an embedded diagram

I am trying to plot the embedment diagram of a two-dimensional section along the equatorial plane $t =$ constant, $\theta = \pi / 2$ of a Morris-Thorne wormhole with the embed function: $$ z(r) = \pm ...
Soliton-104's user avatar
-1 votes
1 answer
75 views

Finding the dimensions of the cylinder that can cover $n$ given smaller cylinders (based on empty space, not least materials)

Let $r_k$ and $h_k$ be, respectively, the radius and the height of the $k^\text{th}$ cylinder. We have $n$ cylinders. Let $R$ and $H$ be, respectively, the radius and the height of the big that can ...
Hussain-Alqatari's user avatar
0 votes
1 answer
106 views

How can I draw a triangle and find the length of its height?

Given that the sum of three inner angles $a,b$ and $c$ in a triangle is $\pi$, and knowing that: $$2 \sin(a−c) = \sin b,$$ $$a+b=3c,$$ how can I draw this triangle and find the length of the height on ...
csn899's user avatar
  • 3,625
1 vote
0 answers
72 views

faster way to find intersections?

I'm writing a g-code generator for a CNC hot wire foam cutter. I have a block of foam (blue cuboid), and two airfoils that define the root and tip of a wing (shown as black curves on the ends of the ...
rhomboidRhipper's user avatar
2 votes
1 answer
74 views

Plane embedded in Non-Euclidean spacetime

The AdS-Schwarzschild black hole metric is given by, $$ds^2 = \frac{1}{z^2} \left( -f(z) dt^2 + \frac{dz^2}{f(z)} + dx^2 \right)$$ where $t$ is time, $z$ is the radial direction, $x$ is a transverse ...
mathemania's user avatar

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