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

I have a list of triangle coordinates in 2D-space: ...
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### 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 ...
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1 vote
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### 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. ...
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### 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 ...
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 ...
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### 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).
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### 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
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### 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 $\lim_{r \rightarrow 2M}r_*(r) \rightarrow - \infty$ ...
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### Finite Differences:

I am having difficulty implementing finite differences in the correct columns of my code. ...
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### 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"] ...
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### 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 ...
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### 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 ...
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### 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: ...
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### 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 ...
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### 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 ...
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### How to find the farthest distance from the point to the region?

Consider the following 2D regions: ...
1 vote
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### 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 ...
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### 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. <...
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### 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....
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### 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 ...
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: ...
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### 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
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### 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 ...
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 ...
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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 ;)
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### Divide a Graphics Line into $i$ equal lengths

I have a line given by ...
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### 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 ...
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### Inverted version of Sierpinski triangle

In Michael Trott's The Mathematic Guidebook for Graphics, Section 1.5.1, he first does this: ...
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### 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 ...
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### 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: ...
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
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### 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
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### 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: ...
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### 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
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...