Questions on the application of Mathematica to geometric problems. You might also consider adding the [graphics] tag, if appropriate.
Questions tagged [geometry]
852 questions
26
votes
4 answers
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
- 485
- 4
- 9
12
votes
2 answers
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
- 4,503
- 3
- 31
- 46
11
votes
2 answers
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
- 14,883
- 4
- 44
- 117
11
votes
5 answers
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
- 4,503
- 3
- 31
- 46
10
votes
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
- 19,917
- 1
- 31
- 78
9
votes
1 answer
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
- 6,677
- 3
- 28
- 64
7
votes
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?
Stefan Rheeders
- 71
- 1
6
votes
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
- 4,321
- 1
- 19
- 46
6
votes
1 answer
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
- 3,347
- 14
- 22
6
votes
2 answers
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
- 4,503
- 3
- 31
- 46
6
votes
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
- 9,233
- 4
- 40
- 96
5
votes
2 answers
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
- 53
- 3
5
votes
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
- 53
- 3
5
votes
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
- 2,091
- 5
- 10
5
votes
2 answers
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…
Johan Grankvist
- 121
- 3