# 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 the South Korean flag

When I stumbled upon this question I remembered that I had also once seen precise rules for the construction of the South Korean flag. And this is quite a different construction. Source: Wikipedia ...
3k views

### Block Building Bot Flocks!

The contest is over! Intro This is an interactive king-of-the-hill contest where the controller is fully contained in a Stack Snippet at the bottom of the question. The controller automatically ...
669 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 ...
24k views

### Draw the national flag of Iceland

This year's UEFA Euro 2016 is over and besides a couple of negative headlines there has been a very positive surprise as well – the Iceland national football team. Let's draw their national flag. ...
8k views

### Let's draw the flag of Nepal

Nepal’s flag (Wikipedia, Numberphile) looks very different from any other. It also has specific drawing instructions (included in the Wikipedia article). I want you guys to make a program which will ...
20k views

### Draw the national flag of France

There have been many other flag challenges posted but not one for the national flag of France. This week seems like an appropriate time. Produce this flag in the fewest bytes possible: The image must ...
10k views

### Draw the € sign

The goal is to output or display an image with an € (euro) sign according to the following specs (ignoring the border of the sign). Source: http://en.wikipedia.org/wiki/File:Euro_Construction.svg ...
8k views

### Check if point lies inside triangle

Your goal is to determine whether a given 2D point X lies within the area of the triangle with given vertices A,B,C. Write a function that takes in the coordinates of the test point X and the three ...
2k views

### Dennis, Doorknob, Martin Büttner, Chris Jester-Young - Pizzeria!

Programming Puzzles & Code Golf is about to get a new moderator, Dennis! This challenge is a tribute to him and our other active (or recently active) moderators: Doorknob, Martin Büttner, and ...
4k views

### Area of a Self-Intersecting Polygon

Consider a potentially self-intersecting polygon, defined by a list of vertices in 2D space. E.g. ...
6k views

### Draw an ASCII Rectangle

Given two integers as input in an array, draw a rectangle, using the first integer as width and second as height. Or, if your language supports it, the two integers can be given as separate inputs. ...
1k views

### 2D Collision Detection

This challenge is based on actual collision detection I had to write for a simple game recently. Write a program or function which, given two objects, returns a truthy or falsy value depending on ...
3k views

### What is the area of this polygon?

Calculate the area of a polygon. Inspired by this shoelace algorithm video. Task Your job is to create a program or function that calculates the area of a polygon. Program or function is defined ...
1k views

### The centers of a triangle

Circles and squares have a single, definite center point. However, the notion of the center of a triangle has long been discussed. Four different centers were known to the Ancient Greeks: Incenter: ...
647 views

### Simple Geometric problem

This problem (see below) has been given as a High School Programming League code golf challenge. The shortest codes submitted during the contest were: 177 bytes in Ruby, 212 bytes in Python 2.5, 265 ...
4k views

### Find the Convex Hull of a set of 2D points

When you hammer a set of nails into a wooden board and wrap a rubber band around them, you get a Convex Hull. Your mission, should you decide to accept it, is to find the Convex Hull of a given set ...
6k views

### Distance between two points in n-dimensional space

Here is another simple one: The Challenge Given two points in an n-dimensional space, output the distance between them, also called the Euclidean distance. The coordinates will be rational numbers; ...
914 views

### A cube of text ݀

Last time you made a square of text, but now, can you make a cube of text? The Challenge Given a string, output the string in the form of a cube. You can assume the string will always have 2 chars ...
3k views

### Chebyshev Rotation

Consider a regular grid, where each cell has integer coordinates. We can group the cells into (square-shaped) "rings" where the cells in each ring have the same Chebyshev distance (or ...
2k views

### I really wanted a rhombus, but all I got was this stupid rectangle

Given only a straightedge and compass, inscribe a rhombus inside the given rectangle, sharing two opposite points. Input Input is the dimensions of the rectangle. In the example shown, that would be <...
1k views

### Three-pointer! But what kind?

From http://en.wikipedia.org/wiki/Triangle: Write a program that takes three 2d coordinate tuples (Cartesian), and classifies what shape these three points describe. In almost all cases these points ...
4k views

### The happy Ender problem

The happy ending problem (actually a theorem) states that Any set of five points in the plane in general position has a subset of four points that form the vertices of a convex quadrilateral. The ...
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,...
2k views

### Generate a right triangle

In this challenge, you must take two numbers (separated by a space) as input and output an ASCII right triangle, made up of xs. The first number will be the width ...
2k views

### Hypercube elements

Write a function or program that outputs the number of each type of element (vertex, edge, face, etc.) of an N-dimensional hypercube. As an example, the 3 dimensional cube has 1 cell (i.e. 1 3-...
665 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 ...
542 views

### Regular Polygrams

Given the number of vertices n ≥ 3 and the "step size" 1 ≤ m < n/2 (indicating the distance between two connected vertices), ...
555 views

### Intersection of Two Lines

Given equation of two lines in the format Ax+By=C, determine their intersection point. If they are parallel print 'parallel' without quotes. For input/output format refer sample input/output. ...
797 views

### Hypercube sides

Your goal is to output all the "sides" (corners, edges, faces, etc.) of an N-dimensional unit hypercube, where N is non-negative. A "side" is defined as any (N-M)-dimension surface embedded in N-...
479 views

### How can I shorten this python code analyzing a 3d grid?

My Python 3 function golf(...) should take a list of lists of lists of strings representing a solid cube and return whether there are any places in which two equal ...
33k views

### Draw an Image as a Voronoi Map

Credits to Calvin's Hobbies for nudging my challenge idea in the right direction. Consider a set of points in the plane, which we will call sites, and associate a colour with each site. Now you can ...
10k views

### Little Chandler is sad. Draw him a cloud to cheer him up

Little Chandler is sad. Draw him a cloud to cheer him up. Note: Drawing a cloud won't actually cheer him up. A circle can be defined as a 3-tuple (x,y,r) where <...
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 ...
915 views

### Smallest region of the plane that contains all free n-ominoes

On Math Stack Exchange, I asked a question about the smallest region that can contain all free n-ominos. I'd like to add this sequence to the On-Line Encyclopedia of Integer Sequences once I have ...
3k views

### Fill the Screen with Wang Tiles

It has been proven that the following 13 square Wang tiles always tile the plane aperiodically. This means that when the squares are arranged in a grid with all neighboring sides the same color, a ...
7k views

### Angle between the hands on a clock [duplicate]

Given the time in 24 hour format (2359 = 11:59pm) return the angle between the minute and hour hands on a standard clock (on the ...
1k views

### Embedded Diamonds!

No, not this. And not this either. This question is nothing like those Write the shortest code to print/return the following output: ...
917 views

In mathematics, a cyclic quadrilateral is one whose vertices all lie on the same circle. In other words, every vertex is on the circumcircle of the other three. For more information, see the MathWorld ...
1k views

### Construct n-gons with a ruler and compass

The task is to draw a regular polygon of n sides using only a compass and an unmarked ruler. Input (n) is one of the following 10 numbers: 3, 4, 5, 6, 8, 10, 12, 15, 16, 17. Method: Because you only ...
2k views

### Triangular Lattice Points close to the Origin

Background A triangular grid is a grid formed by tiling the plane regularly with equilateral triangles of side length 1. The picture below is an example of a triangular grid. A triangular lattice ...
1k views

Disclaimer: This does not do any justice on the rich topic of elliptic curves. It is simplified a lot. As elliptic curves recently got a lot of media attention in the context of encryption, I wanted ...
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### Draw a regular polygon

The goal of this code golf is to draw a regular polygon (one with equal side lengths) given the number of sides and radius (distance from center to vertex). The number of sides and the radius can be ...
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.) ...
718 views

### Triangular battleships (A computational geometry problem)

You are the captain of a battleship. The engineering department's been cutting corners with designs this year, so the ship you're on takes the shape of a simple triangle. You walk out onto the deck ...
56k views

### Polygon prefixes

Polygons are named after the number of sides that they have. A pentagon has 5 sides, an octagon has 8 sides. But how are they named? What's the name for a 248-sided polygon? All polygons are suffixed ...
691 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, ...
3k views

### How much present did you get for Christmas?

Yes, how much, not how many... As we all know, a large present is far better than a small one. Therefore, the value of the presents should always be measured in total volume, not number of presents, ...
979 views

### Distances to coordinates

There are n people on a 2D plane. Using distances between them we're going to find their positions. To get a unique answer you must make four assumptions: There are at least 3 people. The first ...