Questions tagged [geometry]

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

852 questions
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How do I calculate the area of a polygon given its coordinates?

I have a polygon: Polygon[{{0, 200 }, {200, 100}, {500, 300}, {100, 700}}] How can I figure out its area? The docs page does not have any example. So far I've reached this point with no success: Needs["Polytopes`"] Area[Polygon[{{0, 200 }, {200,…
d.k
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Is there a triangle like this?

I want to find the numbers $a$, $b$, $c$, $d$ of the function $y = \dfrac{a x + b}{c x + d}$ so that the triangle $ABC$ with three points $A$, $B$, $C$ have integer coordinates and lies on the graph of the given function, then the centroid of the…
minthao_2011
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11
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Determine height of box packed with spheres

I got such a wonderful answer regarding The Diagonals of a Regular Octagon, so I thought I'd try asking another question we had on our Pizza and Problem quiz activity at College of the Redwoods. The question was: A 4 × 4 × h rectangular box contains…
David
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How to choose three points on the circle so that the triangle is not a right triangle?

I want to choose three points $A$, $B$, $C$ has integer coordinates on the circle $$(x+2)^2 + (y+1)^2 = 25$$ so that the triangle is not a right triangle. But I can not. I tried ClearAll[a, b, r]; a = -2; b = -1; r = 5; Solve[{(x - a)^2 + (y - b)^2…
minthao_2011
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10
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4 answers

How to find all data points within closed curve

I want to find all data points inside curve as given below: data = RandomReal[{-1, 1}, {200, 2}]; ParametricPlot[{Sin[u], Sin[2 u]}, {u, 0, 2 Pi}, Epilog -> {Red, Point[data]}] Short solution is preferable Thanks.
Basheer Algohi
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9
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Distance of a point from the closest surface

Consider the situation in which I have a cuboid: Cuboid[{0,0,0},{1,1,1}] and a point in the cubiod {0.9,0.4,0.6} How do I find the distance from the closest surface of the cuboid?
mattiav27
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7
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3 answers

How to display the smallest-circle enclosing random points

Still a complete noob to Mathematica. How can I create random points on a x,y graph and then enclose all the points with the smallest possible circle?
6
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3 answers

Reflect point over a line in 3D

I'd like to sample points on a triangle randomly. The following code yields points that are uniformly distributed on a quadrilateral: point = RandomReal[]*(v2-v1) + RandomReal[]*(v3-v1); I'd like to take advantage of the symmetry and transform…
dionys
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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-Coordinates a = {0, 0}; b = {5, 0}; c = {3, 4}; d…
minhthien_2016
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How to determine the remaining sides given the three angles and one side of a triangle?

The measure of the interior angles of a triangle are $15^\circ$, $30^\circ$, $135^\circ$ and the length of one edge is 3. In order to determine the length of the remaining two edges, I've tried a := 3; eq1 := (a^2 + b^2 - c^2)/(2*a*b); eq2 :=…
minthao_2011
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6
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4 answers

How to get the height of a triangle from three points

Having three distinct points as it is possible to obtain the height of the triangle ABC? What is the distance between the point A to segment BC? a = {4, 2, 1}; b = {1, 0, 1}; c = {1, 2, 0};
LCarvalho
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5
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Calculate area under a polyline

Consider the following code: tmp = {{0, 0}, {1, 1}, {2, 1}, {3, 2}, {1, 0.5}}; ListLinePlot[tmp, Filling -> Axis] Is there any easy way to compute filled area? Edit: Actual data consists of thousands of points, so some analytical solution would be…
user25235
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5
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2 answers

Plane Geometry Diagrams With Labels

I can make some basic diagrams in Mathematica (stolen from their pages, for example see the below: LaminaData["FilledIsoscelesTriangle", "Diagram"] However, I'm trying to make a simple, set of labelled diagrams, similar to this one, with certain…
Randy
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5
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2 answers

How can I get the volume enclosed by two orthogonal cylindrical surfaces (Radius is a variable, not a specific value)?

I can get the volume enclosed by two orthogonal cylindrical surfaces when the radius of the bottom circle of the cylinder is a specific value (for example, r1=r2=2): Clear["Global`*"]; v1 = ImplicitRegion[x^2 + y^2 <= 2^2, {x, y, z}]; v2…
lotus2019
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Calculate unknowns in a set of triangles

I got a problem of which I can't get mathematica to calculate. The known inputs are a=17 degree, b=12 degree and side d is 300. The whole thing is actually 4 right-angled triangles (left side as A, right side as B, the red at bottom as C and the…
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