Questions tagged [geometry]
This challenge is intended to be solved by using, manipulating, or creating shapes or other geometric structures.
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Draw a Regular Reuleaux Polygon
Related: Draw A Reuleaux Triangle!, Draw a regular polygon
A Reuleaux polygon is a curve of constant width made up of circular arcs of constant radius. The most well-known Reuleaux polygon is the ...
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Plot the ground path of a satellite
If you model a satellite as a free point orbiting a body, you can pretty easily see it has 6 degrees of freedom: three for the X, Y, and Z position, and three for the X, Y, and Z velocity. However, ...
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Find the most isolated point
Given two non-empty sets of points \$P,T = \{(x,y)\ |\ x,y \in \mathbb{Z} \}\$, find the point \$p \in P\$ such that it is the "most isolated" from all points in \$T\$. The "most ...
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How far are you?
Write a program that gets coordinates of two objects on Earth, and calculates how far they are from each other directly in space (a straight line through Earth) and on the surface (through the ...
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Construct the point with two segments
Given a rational point P, return four integral points A, B, C, and D, such that the line segments AB and CD intersect only at P. To make it a bit more interesting, segment AB doesn't include A and B.
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The primitive circle problem
Challenge
The primitive circle problem is the problem of determining how many coprime integer lattice points \$x,y\$ there are in a circle centered at the origin and with radius \$r \in \mathbb{Z}^+
\...
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Ellipse Lattice Point Counter
Challenge
Determine how many integer lattice points there are in an ellipse
$$\frac{x^2}{a^2} + \frac{y^2}{b^2} \leq 1$$
centered at the origin with width \$2a\$ and height \$2b\$ where integers \$a, ...
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Where to stand to throw circles over sticks
Consider a horizontal line with vertical lines centered on the x-axis and placed at gaps of \$\sqrt{2}/2\$. For a positive integer \$n \geq 3\$, the first half of the lines have lengths \$0, \sqrt{2},...
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Counting Collinear Points
Given two points \$(x_1, y_1)\$ and \$(x_2, y_2)\$ with integer coordinates, calculate the number of integer points (excluding the given points) that lie on the straight line segment joining these two ...
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vote
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Where to put a circle?
Consider an \$n \times n\$ grid of integers which is part of an infinite grid. The top left coordinate of the \$n \times n\$ grid of integers is \$(0, 0)\$.
The task is to find a circle which when ...
- 3,098
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Construct this point
Given a constructible point \$(x, y) \in \mathbb R^2\$, output the steps required to construct \$(x, y)\$
Constructing a point
Consider the following "construction" of a point \$(\alpha, \...
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Construct the Constructability sequence
Consider compass-and-straightedge construction, where you can construct new points from existing ones by examining intersections of straight lines and circles constructed with one of the following two ...
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Calculate the Distance to a Line Segment
The Challenge
Given two vertexes and a point calculate the distance to the line segment defined by those points.
This can be calculated with the following psudocode
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Cutting a Circular Pizza Vertically
Most people would cut circular pizzas into circular sectors to divide them up evenly, but it's also possible to divide them evenly by cutting them vertically like so, where each piece has the same ...
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Generate the vertices of a geodesic sphere
As in this challenge, the task is to generate the vertices of a polyhedron. The polyhedron here is the one obtained by dividing a regular icosahedron's triangular faces into smaller triangles so that ...
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