Questions tagged [geometry]

This challenge is intended to be solved by using, manipulating, or creating shapes or other geometric structures.

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15
votes
11answers
1k views

Rectangles in rectangles

This code-golf challenge will give you two positive integers n and k as inputs and have you count the number of rectangles with ...
17
votes
5answers
465 views

Triangles with rational side lengths

This challenge will have give you a positive integer \$n\$ and ask you to output \$t(n)\$, the number of triangles (up to congruence) satisfying the three conditions: The triangles have perimeter of ...
28
votes
22answers
3k views

Circumference of an ellipse

Challenge Unlike the circumference of a circle (which is as simple as \$2\pi r\$), the circumference of an ellipse is hard. Given the semi-major axis \$a\$ and semi-minor axis \$b\$ of an ellipse (see ...
19
votes
2answers
618 views

Cut a triangle into equal-sized parts!

Similar in spirit to Number of distinct tilings of an n X n square with free n-polyominoes and Partition a square grid into parts of equal area, this challenge will have you count ways of partitioning ...
15
votes
12answers
2k views

Is it in the polygon?

The challenge Given point and a path of points, say whether or not the point is in the polygon that is created by the path. Also return true if the point is on an ...
11
votes
4answers
204 views

Is it a uniform polyhedron?

Objective Given a vertex figure consisting of regular convex polygons, determine whether it represents a convex uniform polyhedron. What is a uniform polyhedron? A uniform polyhedron is a polyhedron ...
16
votes
7answers
1k views

Counting painted sides of cubic shapes

Sandbox Many of us have seen math problems where a shape made of unit cubes is dipped in paint, and the answer is the number of painted sides. We'll generalize that problem in this challenge. Input A ...
16
votes
19answers
2k views

Are they collinear?

Task Write a program/function that when given three 2d points in cartesian coordinates as input outputs a truthy value if they are collinear otherwise a falsey value Three points are said to be ...
4
votes
5answers
215 views

Divide into 2 isosceles triangles

Given the measures of two of the interior angles of a triangle (x and y; the other angle can be easily calculated with ...
2
votes
2answers
172 views

Create a text image by manual automation

Challenge Premise It's 2006, and Alice is trying to send Bob their her completed notes on their newly ended expeditions into the labyrinthine school library, which the two of them found suffers from a ...
12
votes
3answers
267 views

Friendly Incenters

The incenter of a triangle is the intersection of the triangle's angle bisectors. This is somewhat complicated, but the coordinate formula for incenter is pretty simple (reference). The specifics of ...
10
votes
2answers
375 views

Draw the “{🏅} CODE GOLF & coding challenges” logo!

Wow, time really flies! It's already been one year since the debut of the Code Golf Stack Exchange site design. Let's celebrate this milestone with a code golf challenge... to imitate the site logo! ...
11
votes
14answers
1k views

Calculate the vector component

Challenge Assume two vectors \$\mathbf{a} = (a_1,a_2,\cdots,a_n)\$ and \$\mathbf{b} = (b_1,b_2,\cdots,b_n)\$ are given in an \$n\$-dimensional space, where at least one of \$b_1,\cdots,b_n\$ is ...
13
votes
7answers
2k views

Who Took My Toilet Paper?

You step into the restroom, and notice that the toilet paper has missing! It occurs to you that someone had stolen it. Strangely enough, the first thing you would like to know is the amount of toilet ...
9
votes
0answers
239 views

Leon's shooting range problem

Leon's story Leon is a professional sling shooter and he comes to a shooting range everyday to practice. A casual target is not a challenge for him anymore so before shooting he first covers the ...
9
votes
5answers
445 views

Is this a cube?

This challenge is a riff on Dion's challenge "Is this a rectangle?". The goal of this challenge is to write a program to decide whether or not some collection of tuples of integers represents a ...
16
votes
1answer
199 views

Rubik's Snakes! (Part 1)

The Rubik's Snake (or Rubik's Twist) is a toy consisting of several triangular prisms strung together in a line in such a way that the pieces can be rotated about one another in 90 degree turns. Any ...
8
votes
3answers
378 views

Triangles in a tetrahedron

The goal of this challenge is to extend the OEIS sequence A334581. Number of ways to choose \$3\$ points that form an equilateral triangle from the \$\binom{n+2}{3}\$ points in a regular tetrahedral ...
9
votes
1answer
199 views

Counting hypercube Tetris pieces

Consider the Tetris pieces, but made out of some number of (hyper)cubes instead of four squares, where two blocks are considered the same if one is a rotation, reflection, or translation of another. ...
8
votes
1answer
349 views

Infinite Snake game

Infinite Snake is just like the video game Snake, except for that the snake is infinitely long, there are no items to eat, and the Snake needs to move in a repeating ...
21
votes
10answers
2k views

Perimeter of Conway hexagon

Background Given a triangle \$ABC\$, extend its three sides by the opposite side length, as shown in the figure below. Then the six points surprisingly lie on a circle called the Conway circle, whose ...
23
votes
7answers
2k views

Where to point a low-orbit ion cannon (asking for a friend)

Challenge Premise Bob lost1 Alice's precious grand piano. Big mistake. Alice has now stolen Bob's low-orbit ion cannon. Alice refuses to just make up with Bob, so let's help her give him a light ...
17
votes
8answers
2k views

Euler's Geometry Puzzle

Today (or tomorrow, depending on your timezone, by the time of posting) is the birthday of the great mathematician and physicist Leonhard Euler. To celebrate his birthday, this challenge is about one ...
16
votes
9answers
2k views

Is this a rectangle?

The challenge: Given four coordinates, each in x y form, your job is to find out whether or not the given coordinates form a rectangle, and output a truthy/falsey. Rules: For the sake of simplicity,...
14
votes
4answers
909 views

Reconstruct a 3d arrangement of cubes from two of its projections

Setup Take the following 4x4x4 cube along with a 2D view of 3 of its faces, with a common 1x1x1 cube highlighted: The arrows ...
10
votes
1answer
170 views

Counting polyominoes on (hyper-)cubes

This challenge like some of my previous challenges will have you counting free polyforms, which are generalizations of Tetris pieces. This code-golf challenge will have you count polyomino-like ...
17
votes
1answer
663 views

Impress Donald Knuth by counting polyominoes on the hyperbolic plane

This challenge is inspired by a talk about Schläfli symbols, etc that I gave in a Geometry seminar. While I was putting together this challenge, I saw that Donald Knuth himself was interested in (some ...
26
votes
4answers
766 views

Buildings made from cubes

In this fastest-code challenge, you are provided with a set of \$n\$ identical blocks and need to determine how many unique buildings can be constructed with them. Buildings must satisfy the following ...
4
votes
1answer
248 views

Cutting Sequence for N dimensions

Inputs: The program or function should take 2 vector-like (e.g. a list of numbers) O and V of the same number of dimensions, and a number T (all floating-point numbers or similar) Constraints: T >=...
16
votes
8answers
1k views

Is this quadrilateral tangential?

Related: Is this quadrilateral cyclic? Background A tangential quadrilateral is a quadrilateral which has an incircle: Examples include any square, rhombus, or a kite-like shape. Rectangles or ...
12
votes
1answer
265 views

Maximal 2-distance Sets

In the plane (\$\mathbb R^2\$) we can have at most five distinct points such that the distances from each point to every other point (except itself) can assume at most two distinct values. An example ...
14
votes
1answer
544 views

Circular robot instructions

This challenge is based on Project Euler problem 208. Also related to my Math Stack Exchange question, Non-self-intersecting "Robot Walks". You have a robot that moves in arcs which are \$1/...
39
votes
28answers
6k views

Draw the Ionising Radiation Hazard Symbol

Draw the ionising-radiation-hazard-symbol in an arbitrary colour on a distinctly coloured background. The specific proportions were published in the June 27th 1974 issue of the Federal Register of the ...
13
votes
10answers
1k views
+150

Area of diagonal-folded regular polygon

I have a piece of paper whose shape is a regular n-gon with side length 1. Then I fold it through some of its diagonals. What is ...
15
votes
13answers
1k views

Is it rectilinear?

Today's challenge: Given an ordered list of at least 3 unique integer 2D points forming a polygon, determine if the resulting polygon is Rectilinear. A polygon is rectilinear if every interior ...
16
votes
1answer
383 views

Counting symmetric grid chains

Notation and definitions Let \$[n] = \{1, 2, ..., n\}\$ denote the set of the first \$n\$ positive integers. A polygonal chain is a collection of connected line segments. The corner set of a ...
2
votes
0answers
147 views

Rotated analog clock [closed]

Given: a 12 hour time t in hours and minutes, a rotation r in degrees, return the time shown when an analog clock that is ...
19
votes
10answers
1k views

Write a function that returns an iterable object of all valid points 4-directionally adjacent to (x, y)

A very common need in algorithms classes and computer science in general is to iterate 4-directionally over a grid or matrix (such as in BFS or DFS). This seems to often result in a lot of clunky and ...
32
votes
21answers
7k views

Random point on a sphere

The Challenge Write a program or function that takes no input and outputs a vector of length \$1\$ in a theoretically uniform random direction. This is equivalent to a random point on the sphere ...
10
votes
2answers
413 views

​Plane​ ​Blow​up​

The Blow-up is a powerful tool in algebraic geometry. It allows the removal of singularities from algebraic sets while preserving the rest of their structure. If you're not familiar with any of that ...
25
votes
24answers
5k views

Count the number of triangles

Given a list of positive integers, find the number of triangles we can form such that their side lengths are represented by three distinct entries of the input list. (Inspiration comes from CR.) ...
27
votes
8answers
4k views

Billiard balls collision

Given the 2-dimensional positions and velocities of a pair of billiard balls right before impact, calculate their velocities after a perfectly elastic collision. The balls are assumed to be ideal ...
6
votes
6answers
582 views

The Knight's estate

And then the King said: You fought bravely, Knight, and your deed will not be forgotten for centuries. For your valor I grant you this castle and the lands around it. Things rush me, and I can not ...
43
votes
3answers
4k views

Construct a pentagon avoiding compass use

Rules You will start with only two elements: Points \$A\$ and \$B\$ such that \$A \neq B\$. These points occupy a plane that is infinite in all directions. At any step in the process you may do any ...
13
votes
2answers
668 views

Counting generalized polyominoes

This challenge will have you count pseudo-polyforms on the snub square tiling. I think that this sequence does not yet exist on the OEIS, so this challenge exists to compute as many terms as possible ...
30
votes
7answers
7k views

Golf the smallest circle!

The problem: Given a non-empty set of points in the Cartesian plane, find the smallest circle that encloses them all (Wikipedia link). This problem is trivial if the number of points is three or ...
9
votes
1answer
292 views

Partition and Restructure

Given two contiguous shapes of the same area, determine the optimal way to divide the first shape into a minimum number of contiguous segments such that they can be rearranged to form the second shape....
25
votes
7answers
860 views

Expand a hexagon

Given an ASCII art hexagon as input, output one whose sides are all one unit longer. ...
14
votes
16answers
690 views

Dihedral group D4 composition with custom labels

The dihedral group \$D_4\$ is the symmetry group of the square, that is the moves that transform a square to itself via rotations and reflections. It consists of 8 elements: rotations by 0, 90, 180, ...
11
votes
6answers
2k views

Area of a 2D convex hull

You are given an array/list/vector of pairs of integers representing cartesian coordinates \$(x, y)\$ of points on a 2D Euclidean plane; all coordinates are between \$−10^4\$ and \$10^4\$, duplicates ...

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