Questions tagged [geometry]

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

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4
votes
4answers
245 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
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4answers
845 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 ...
-4
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0answers
83 views

wasting n-dimensional peanut butter

I was scraping the last peanut butter out of the jar during the Covid19 pandemic, and wondering how much of the good stuff was left down inside the jar, inaccessible but for the most desperate ...
42
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 ...
10
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1answer
143 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 ...
25
votes
4answers
719 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 ...
15
votes
13answers
2k views

Circle intersection area

Description : Given x and y positions of two circles along with their radii, output the ...
16
votes
1answer
569 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 ...
24
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.) ...
35
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25answers
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 ...
23
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10answers
3k views

Is this square symmetrical?

Write a program or function that takes in a 4×4 text grid consisting of exactly 4 A's, 4 B's, 4 ...
4
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1answer
245 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 >=...
17
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6answers
904 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 ...
15
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 ...
11
votes
1answer
255 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 ...
8
votes
1answer
2k views

Circle packing in a rectangle

Your task is to write a program that finds the largest radius that N circles can have and still fit inside of a rectangle that is X by Y pixels large. (similar to this wikipedia article) Your program ...
63
votes
16answers
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 ...
14
votes
1answer
498 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/n\$ of a ...
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 ...
17
votes
3answers
54k 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 ...
16
votes
1answer
373 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 ...
12
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9answers
991 views

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 ...
19
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9answers
2k views

Does this line pass through that square?

Divide the first quadrant (including the positive x-axis, the positive y-axis, and the origin) into 1x1 grids, with each grid labelled by the coordinates of its bottom-left corner, as demonstrated ...
26
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 ...
13
votes
2answers
636 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 ...
19
votes
8answers
879 views

Is this quadrilateral cyclic?

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 ...
26
votes
11answers
1k views

Triangular Manhattan Distance

The Manhattan distance on a regular grid is the number of orthogonal steps one needs to take to reach one cell from another. Orthogonal steps are those that go through the edges of the grid cells (as ...
2
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0answers
141 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 ...
18
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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
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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 ...
107
votes
79answers
23k 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. ...
11
votes
11answers
2k views

Do these squares overlap?

Given the coordinates of the upper left corners of two squares and their side lengths, determine whether the squares overlap. A square includes the top and left lines, but not the bottom and right ...
36
votes
21answers
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 ...
10
votes
2answers
388 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 ...
34
votes
15answers
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 ...
6
votes
6answers
571 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 ...
18
votes
7answers
1k views

Count the squares

Challenge Origami (folding paper) is a creative form of art. As far as I know, master of Origami prefers square paper. Let's start from beginning - convert a rectangular paper to a square one. So ...
24
votes
7answers
850 views

Expand a hexagon

Given an ASCII art hexagon as input, output one whose sides are all one unit longer. ...
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 ...
35
votes
41answers
4k views

Evaluate the aspect ratio of a triangle

Given three sidelengths of a triangle, evaluate its aspect ratio AR given the following formula: where The closer to equilaterality a triangle is, the closer to 1 ...
11
votes
6answers
1k 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 ...
9
votes
1answer
278 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....
58
votes
10answers
12k views

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 ...
14
votes
16answers
669 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, ...
19
votes
12answers
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 ...
169
votes
8answers
32k 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 ...
56
votes
10answers
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 <...
20
votes
4answers
393 views

Rectangular difference

In this challenge, you are given two overlapping rectangles, and you need to calculate the rectangles created by removing one from the other. For example, if you remove the red rectangle from the ...
27
votes
43answers
4k views

Diamond creator +

Challenge : Given an integer n as input. Create a diamond that is 2x the given number n. Input : Input is integer ...
6
votes
1answer
289 views

Stereographic projection of polyhedra

You will create a program that generates the stereographic projection of polyhedra. In particular, to keep things simple, we'll only focus on n-chamfered dodecahedron. Given a natural number ...

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