Questions tagged [geometry]

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

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16
votes
3answers
539 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), ...
14
votes
5answers
368 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 ...
3
votes
2answers
373 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 ...
30
votes
8answers
3k views

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 ...
13
votes
5answers
1k views

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 ...
16
votes
1answer
537 views

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 ...
36
votes
18answers
4k views

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 ...
42
votes
8answers
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 ...
13
votes
1answer
641 views

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. ...
7
votes
1answer
459 views

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 ...
29
votes
1answer
1k views

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 ...
14
votes
11answers
2k views

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 ...
15
votes
5answers
1k views

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 ...
17
votes
14answers
1k views

Find the reference angle

This is a fairly simple question. According to this random website I found — Web Archive, a reference angle is ...
15
votes
8answers
833 views

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, ...
7
votes
1answer
494 views

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 ...
9
votes
4answers
852 views

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 ...
4
votes
2answers
328 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. ...
23
votes
3answers
2k views

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 ...
20
votes
2answers
974 views

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 ...
16
votes
1answer
535 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 ...
14
votes
5answers
813 views

Determine the Dimensions of a Rotated Rectangle

This Stack Snippet draws an aliased white rectangle on a black background given parameters for its dimensions, position, angle, and the grid dimensions: ...
42
votes
5answers
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 ...
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 ...
22
votes
10answers
2k views

Tile the plane with this modified circle

Take a unit circle centered on the origin. In any two neighboring quadrants, mirror the curve of the circle across the lines connecting the circle's x and y intercepts. With the resulting shape, you ...
24
votes
3answers
895 views

Can you fold a hexomino into a cube?

One of my kid's favorite toys is a set like this. Actually its one of my favorite toys - I've been playing with it and its been giving me some PPCG challenge ideas. Here's one: Write a program or ...
19
votes
15answers
3k views

Random Golf of the Day #4: The Bertrand Paradox

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 ...
31
votes
8answers
2k views

Area of an ASCII polygon

You should write a program or function which receives a string representing an ascii-art polygon as input and outputs ot returns the area of the polygon. The input is a string consisting of the ...
19
votes
2answers
1k views

Determining the rotation of square given a list of points

In this challenge, you will be given a list of points. These points lie on the perimeter of an imaginary square. Your goal is to: If possible, print out the rotation of the square, which will be a ...
14
votes
7answers
1k views

Tiling a 2^N by 2^N Grid with L-Shaped Trominoes

When students are first taught about the proof technique of mathematical induction, a common example is the problem of tiling a 2N×2N grid with L-shaped trominoes, leaving one predetermined grid ...
7
votes
1answer
304 views

Help My Brother Work on his Tan(gent)!

This challenge is entirely fictional. There is no time limit for this challenge. My little brother is terrible with computers! He saved up all of his money to buy a new one, and within half an hour ...
19
votes
11answers
2k views

Output a Face on a Numbered Cube

Assign the numbers 0 through 7 to the 8 vertices of a cube in any way you want. Exactly one number must be assigned to each vertex. For example, your vertices might be assigned like this: ...
16
votes
6answers
901 views

Overlapping circle

You should write a program or function that given an N by N equally spaced square grid and a solid inscribed circle outputs or ...
20
votes
3answers
975 views

Remove an unobstructed rectangle

This image was made by overlaying 7 differently colored rectangles on top of each other: The black and maroon rectangles are unobstructed, that is, no other rectangles are above them. Write a ...
14
votes
1answer
299 views

Finding Symmetries in Squares

Write a program or function that takes in a list of positive integers. Each of these integers represents the side length of a square on a 2D plane. Each square can be moved to any integer coordinates ...
32
votes
3answers
3k views

Area of a Self-Intersecting Polygon

Consider a potentially self-intersecting polygon, defined by a list of vertices in 2D space. E.g. ...
11
votes
4answers
594 views

Identifying the triangles

Counting the amount of triangles in a picture is a task commonly used in brain tests. You are given a picture that contains shapes consisting of triangles. You then must find all possible triangles in ...
22
votes
7answers
2k views

Cover a Region with Rectangles

Input Your input in this challenge is a list of integer pairs. They represent the southwest corners of unit squares on the plane, and the list represents their union as a subset of the plane. For ...
13
votes
1answer
690 views

Sharing pizza fairly

The difficulty with sharing pizza with friends is that it is hard to make sure that everyone gets the same amount of pepperoni on their slice. So, your task is to decide how to fairly slice a pizza so ...
18
votes
4answers
4k views

Draw A Snowflake

Joe lives at the Bahamas. It is winter. His children are disappointed that there is no snow. Joe needs to make snow for his children. Fortunately, he has a 3-d printer. He plans to make snowflakes ...
27
votes
3answers
748 views

Squarefinder – Locating regular tetragons

Imagine a bunch of rectangles drawn in the plane, each rectangle with its vertices at integer coordinates and its sides parallel to the axes: The rectangles partition the plane into a number of ...
7
votes
1answer
676 views

Digesting Polygons

Digesting a polygon is a process in which you take an input polygon, and create another polygon that can contain the entirety of the input polygon, while having one side less than it. The goal of ...
11
votes
4answers
1k views

Tiling, given vertex configuration

Task The task is to tile polygons, given a vertex configuration. Scoring Your score is equal to the "complexity level" your submission reaches. Complexity levels are cumulative, meaning that to ...
16
votes
5answers
1k views

Mondrian painting description language

This challenge consists in coding an interpreter for a Mondrian painting description language (MPDL). Language definition The language operates on a stack of rectangles. A rectangle is defined by ...
23
votes
1answer
884 views

Can you hear me now?

Background You are a rich executive of a software empire. Your time is worth a lot of money. As such, you must always travel in the most efficient route possible. However, as an executive, you spend ...
7
votes
1answer
396 views

Crafting Canonically Cöcher Crosswords

The Setup Most of us are familiar with crossword numbering, which follows three basic rules: in a character grid consisting of blacks and whites (see below), any maximal contiguous horizontal or ...
18
votes
4answers
715 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 ...
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 ...
1
vote
1answer
304 views

Find a representative submatrix

You have a matrix of size m x n. Each cell in the matrix has a uniformly random integer value v, where 0 ≤ v < i, and i ≤ (m x n). (Meaning, the matrix contains a maximum of m x n distinct values, ...
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 ...