Questions tagged [geometry]

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

264 questions
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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; ...
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Find our neighbors

You live in a rectangular neighborhood which is completely partitioned into N rectangular plots, i.e. there are no gaps or overlaps. Plots do not necessarily have the same width/height as other plots. ...
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A Geometrical Challenge

Everybody loves geometry. So why don't we try and code golf it? This challenge involves taking in letters and numbers and making shapes depending on it. The Input The input will be in the form of <...
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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-...
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Find the line guaranteed by Sylvester-Gallai

The Sylvester-Gallai theorem says: Suppose you have a finite list of points in the plane. Suppose further that not all of those points are collinear (lie in a single line). Then there is some line ...
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Toilet Paper Mysteries

Today you need to solve a very practical problem: How many loops do you need to have a certain number of sheets on your toilet paper roll? Let's look at some facts: The diameter of a bare toilet ...
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Putting square pegs into square holes

I was intrigued by the design of this graphic from the New York Times, in which each US state is represented by a square in a grid. I wondered whether they placed the squares by hand or actually found ...
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Finding Exclusive Area in Circle Intersections

Here's a deceptively challenging geometry puzzle for you! Given a circle A, and n other circles ...
349 views

Lego Gear Train

Inspired by the Lego gear ratios challenge by Keith Randall. I, too, plan on building a giant lego robot that will eventually be able to destroy the other robots in the never-before-mentioned ...
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Draw a Christmas Star / Stellated Dodecahedron

Paper stars are a big thing in my family at christmas, so I thought a virtual one would be cool. Below is an image of a regular dodecahedron (from https://en.wikipedia.org/wiki/Dodecahedron, ...
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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, ...
546 views

Playing Billiards

In this code golf, you will have to determine the direction of the shortest shot that hits exactly n cushions before falling into a pocket. The billiard table is a 6 pocket pool table with the ...
166 views

Most logical rectangle formula from numbers [duplicate]

Introduction The task is simple. When given a number, output the most logical rectangle. To explain what a logical rectangle is, I provided some examples: Input: ...
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Rolling the Dice

Rolling the Dice So, I was rolling dice a while ago and thought of a challenge. Given the cube with a net taken from input and a list of moves, find the square on the bottom at the end. I will use ...
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Point in convex hull (2D)

Background The convex hull of a finite number of points is the smallest convex polygon that contains all of the points, either as vertices or on the interior. For more information, see this question ...
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Random Golf of the Day #6: Roll a d20

About the Series First off, you may treat this like any other code golf challenge, and answer it without worrying about the series at all. However, there is a leaderboard across all challenges. You ...
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Is it a Regular Polygon? [closed]

A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Your job is to find out if a given polygon is regular or not. ...
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Sprocket Science: Animating a Chain Drive System

The goal of this challenge is to produce an animation of a chain drive system, comprised of a set of sprocket gears connected together by a chain. General Requirements Your program will be given a ...
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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 ...
810 views

Spherical excess of a triangle

Spherical excess of a triangle As we all know, the sum of angles of any planar triangle is equal to 180 degrees. However, for a spherical triangle, the sum of angles is always greater than 180 ...
772 views

Square side pinpointing

Welcome to my first code-golf challenge! :) Let's hop right into it. Challenge: Given two floating point vectors, O (origin) and T (target), you have to create a program to print the values L and R ...
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Print a Pentomino Rectangle

Write a program or function that takes no input but prints or returns a constant textual depiction of a rectangle made of the 12 distinct pentominoes: The rectangle may have any dimensions and be in ...
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Area of Polygon [duplicate]

Given the number of vertices N of a convex polygon and each of their (x, y) calculate the polygon's area. vertexes are in ...
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Circular ​Blues

Write a program or function that takes in a positive integer N and recreates this pattern of circles scaled to fit an N×N pixel image: This image is a valid output example for N = 946. In case ...
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Print a cube's vertices and its covering triangles

Output coordinates of the vertices of a cube. Then, output a list of twelve triangles that will cover the cube, each triangle being a list of three vertex-indexes, consistently oriented. Output must ...
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Area of the triangle

Another easy challenge for you. Your task Write a program or function that takes the input, which contains 3 pairs of x- and y-coordinates and calculates the area of the triangle formed inside them. ...
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Can I Slide Apart The Puzzle?

Write a program or function that takes in a rectangular grid of text where every cell is either an A or a B. All the ...
511 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), ...
343 views

Is it L-convex?

Background A polyomino is called L-convex, if it's possible to travel from any tile to any other tile by an L-shaped path, that is, a path that goes in the cardinal directions and changes direction ...
359 views

Measuring Rectangles

Challenge Your goal is to write a program which will output the 8 measurements of a rectangle, with only some measurements in the input. Your program should throw an error if it cant be done. Here ...
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Beatles Songs and Hexagons

Write two triangle (i.e. pyramid) shaped programs. The first one should be an upwards pointing text triangle with a minimum base width of three characters. So it would have a structure like ...
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Pyramid Schemes

Mayan pyramids were (and are) an important part of ancient architecture, that were generally used for religious purposes. They were usually step pyramids, but the steps on each were too steep to ...
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Cut a pizza into identical slices

This is what I thought this question was going to be, before I fully read it. A group of code golfers walk into The Nineteenth Bite Pizzeria and order a pizza. It comes in an irregular shape, made of ...
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Visually Explain the Pythagorean Theorem

A common visual explanation of the Pythagorean theorem is as such: The squares are meant to represent the side length's squared, and the areas of a + b = c, just ...
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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 ...
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Can I make that shape with blocks, slabs, and stairs?

Consider a rectangular two-dimensional grid where each cell can either be empty (.) or full (0). e.g. ...
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Computing the geometric median

Given a list of integer points in an n-dimensional space, output the geometric median. Note that the output is not necessarily integer. Your answer must be precise to at least two digits after the ...
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Find the area of the largest convex polygon

Given a list of integer coordinates, find the area of the biggest convex polygon you can construct from the list such that - every vertex is in the list no element of the list is contained within ...
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Empty a Swimming Pool . . . With Only a Red Solo Cup

You have a swimming pool that is filled to the brim with water. You need to empty it, but you can't think of an efficient method. So you decide to use your red solo cup. You will repeatedly fill the ...
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Find the nearest clock hands

Challenge Given a number of seconds past midnight, output the smallest angle between any two hands on a clock face, using as few bytes as possible. You may assume that the number of seconds is ...
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Find the reference angle

This is a fairly simple question. According to this random website I found — Web Archive, a reference angle is ...
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Integral triangles and integral medians

Consider a triangle ABC where each side has integer length (an integral triangle). Define a median of ABC to be a line segment from a vertex to the midpoint of the opposing side. In the figure below, ...
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Go south, east and north, come to the same place

There is that famous riddle: A bear walks 1 km south, 1 km east and 1 km north, and comes to the place it started from. What color is the bear? This one is very old, so I'll generalize it: A ...
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Calculate the Orthocenter of a Triangle [duplicate]

Try to write the shortest program or function you can that prints or returns the calculated orthocenter of a triangle. The orthocenter of a triangle is the intersection point of the three altitudes ...
307 views

Cut a silicon wafer into dies

When manufacturing chips, circular silicon wafers are cut into dies of needed size: The goal of this challenge is maximizing the number of whole dies that can be cut from a wafer of a given diameter. ...
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Stacking Pythagorean Triangles

Background A Pythagorean triangle is a right triangle where each side length is an integer (that is, the side lengths form a Pythagorean triple): Using the sides of this triangle, we can attach two ...
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Worst Case Manhattan Exclusion

Imagine a W by H grid of squares that wraps toroidally. Items are placed onto the grid as follows. The first item can be placed on any square, but subsequent items must not be within a Manhattan ...
509 views

Chute-A-Pearing

Here are five images of pears and a steel chute: A: B: C: D: E: These are only thumbnails, click them for full size! (I made these with Algodoo.) This class of images always has the ...