Questions tagged [geometry]

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

30
votes
1answer
551 views

Fishing for Cube Nets

Cubes can be made of six squares as sides. But you could also fold three 2x1 rectangles in half and glue them together to form a cube. Now in this challenge you get a set of pieces which are each made ...
3
votes
0answers
101 views

Draw an oblique line [duplicate]

Given the width and height of a line in characters, draw it using ascii characters. Input Two integers separated by a space, the first one being the width, the second one being the height. Example: ...
8
votes
15answers
851 views

Maximal number of regions obtained by joining n points around a circle by straight lines

Let's define f(n) as the aximal number of regions obtained by joining n points around a circle by straight lines. For example, two points would split the circle into two pieces, three into four, like ...
16
votes
13answers
2k views

Find the Centroid of a Polygon

From Wikipedia: The centroid of a non-self-intersecting closed polygon defined by n vertices (x0,y0), (x1,y1), ..., (xn−1,yn−1) is the point (Cx, Cy), where and ...
15
votes
2answers
302 views

Real Chebyshev Rotation

This is a challenge inspired by Chebyshev Rotation. I suggest looking at answers there to get inspiration for this challenge. Given a point on the plane there is a unique square (a rectangle with ...
37
votes
19answers
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 chessboard ...
134
votes
27answers
19k views

Appease Your Google Overlords: Draw the “G” Logo

Write a program or function that takes in a positive integer N, and outputs an N×N pixel image of Google's "G" logo according to this* construction: For example, if N is 400, a 400×...
20
votes
41answers
5k 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. ...
9
votes
1answer
265 views

Flexagonal flexagation

Being programmers, watching us flex aren't very interesting. Today we change that! In this challenge you will lex and flex hexaflexagons. About For a video introduction, watch viharts video(s) on ...
22
votes
1answer
1k views

Solve Grid-Tangram

The Tangram is a dissection puzzle made from seven shapes: Five differently sized triangles, a parallelogram and a square. Given a shape, the goal is recreating the shape using all the pieces and ...
17
votes
6answers
839 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 ...
20
votes
14answers
2k views

My triangle needs more nodes

Consider the standard equilateral triangle, with nodes labeled using barycentric coordinates: We can turn this 3 node triangle into a 6 node triangle by adding a new line of 3 vertices (one more than ...
13
votes
4answers
264 views

Staggered Starts

In races in which racers go around at least one turn of a curved track, the starting positions for each racer are staggered, so that each racer travels the same distance around the track (otherwise, ...
22
votes
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 ...
21
votes
5answers
886 views

Count the rectangles in a diagonal grid

As a follow-up to this challenge, we now want to count the number of rectangles in grid with r rows and c columns where there is a line crossing through every diagonal of a square in the grid. Now, we ...
105
votes
79answers
22k 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. ...
21
votes
2answers
648 views

Borders of overlapping circles

Given the coordinates of several points on a plane, and the radius of a circle surrounding each point, draw polygons representing the circles and the edges where the circles meet. Straight edges will ...
4
votes
0answers
183 views

Decompose the domain

In scientific computing, it is often desirable to decompose some large domain into smaller "subdomains", then parallelize the computation by performing the work on each subdomain in parallel and the ...
18
votes
15answers
1k views

g​o​l​f​ ​a​t​a​n​2

Sometimes it really is a struggle to convert Cartesian coordinates (x,y) to Polar coordinates (r,phi). While you can calculate <...
27
votes
5answers
2k views

Rotate a hypercube

Introduction A hypercube/tesseract is the 4 dimensional equivalent of a normal cube. It's made by taking a cube net, extending it to the 3rd dimension, then – using the 4th dimension – folding it ...
2
votes
0answers
74 views

Does the triangle contain the origin? [duplicate]

Challenge description On a Cartesian plane, a triangle can be described as a set of three points, each point being one of the triangle's vertices. For instance, coordinates ...
32
votes
4answers
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 ...
9
votes
9answers
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 ...
11
votes
4answers
2k views

Calculate the Fermat Point of a Triangle

This is somewhat similar to The centers of a triangle, but with a different point. The Fermat Point is the point P in triangle ABC such that the value of AP + BP + CP is minimized. There are two cases:...
33
votes
1answer
832 views

Gasket Weaving - draw a Sierpiński knot

Given an integer N >= 2, produce an image showing a Sierpiński knot of degree N. For example, here are knots of degree 2, 3, 4 and 5: Click on the images to view full size (the higher the degree the ...
-7
votes
18answers
336 views

Find the remaining side of the tangential quadrilateral

(Taken from https://en.wikipedia.org/wiki/File:Tangential_quadrilateral.svg) A tangential quadrilateral (see example above) is a quadrilateral in which a circle can be inscribed. Your task is to ...
5
votes
1answer
281 views

Tiling by substitution

EDIT: The incorrect A rhomb substitution has been fixed. Apologies to anoyone who had started working on a solution. Consider the following substitutions, where the substituted rhomb(us) is scaled up ...
4
votes
15answers
357 views

Counting triangles with integer perimeter

Mary has given John two sticks of lengths a and b respectively, where a and ...
10
votes
3answers
1k views

Draw a simple cube

We don't have a single challenge about drawing a real 3 dimensional cube, so here it goes: Challenge Your task is to draw a rotated, cube with perspective. It can be in a separate window or as an ...
17
votes
1answer
276 views

Symme-Try This Triangle Trial

A string whose length is a positive triangular number (1, 3, 6, 10, 15...) can be arranged into an "equilateral text triangle" by adding some spaces and newlines (and keeping it in the same reading ...
8
votes
21answers
1k views

Form tiles in a rectangular ring

Given the input tilesX and tilesY create a method that would make a rectangular ring from the tiles. The function must order ...
9
votes
2answers
404 views

Find the area of a polygon

Given consecutive side lengths s1, s2, s3... s_n of an n-gon inscribed in a circle, find its area. You may assume that the polygon exists. In addition, the polygon ...
7
votes
3answers
457 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 ...
44
votes
9answers
5k views

Build a triangle without any triangles

As a little kid, I liked to play with these toys a lot: They probably intended for these to be used for art, but I always used them for math! Fractals, patterns, etc. One time, I was given this ...
4
votes
1answer
735 views

Need help golfing Python 3 code to calculate volume & surface of spheroids in <150 bytes

I want to write a function golf(C, A) that takes the height (C = 2*c) and the width (A = 2*a)...
21
votes
9answers
2k views

Rectangle Detection

Write a program or function that takes in a multiline string of 0's and 1's. No other characters will be in the string and the ...
23
votes
3answers
887 views

Draw a random hexa-glyph

The above image is called a hexa-glyph. Hexa-glyphs are some cool patterns I made up while doodling during my DiffEq class. Here's how you make one: Consider the following set of points, shaped ...
14
votes
5answers
229 views

Identify arborally satisfied point sets

An arborally satisfied point set is a 2D set of points such that, for any axis-aligned rectangle that can be formed using two points in the set as opposite corners, that rectangle contains or touches ...
8
votes
2answers
252 views

Count rectangle intersections

The Challenge Given an arbitrary amount of rectangles, output the total count of intersections of those when drawn in a 2D plane. An intersection here is defined as a point ...
15
votes
5answers
360 views

How far from the exterior?

Take a 2D region of space divided into axis aligned unit square elements with their centers aligned at integer intervals. An edge is said to be internal if it is shared by two elements, otherwise it ...
11
votes
3answers
353 views

Trilaterate your position

Introduction Imagine you are on a two dimensional cartesian plane and want to determine your position on it. You know 3 points on that plane and your distance to each of them. While it is always ...
29
votes
2answers
829 views

Addition on Elliptic Curves

Addition on Elliptic Curves 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 ...
8
votes
7answers
363 views

Hexagon-In or Hexagon-Out?

There is a great story to tell about regular hexagons found for example in honeycombs. But this busy bee needs your help in telling him which point is inside or outside his honeypot. So, given a ...
18
votes
12answers
2k views

Calculate the volume of an object

You can determine the volume of objects based on a given set of dimensions: The volume of a sphere can be determined using a single number, the radius (r) The ...
18
votes
2answers
587 views

Cities: Sightlines

I'm at position (0, 0) of an infinite two-dimensional city, which is perfectly divided into blocks centered at each lattice point, some of which contain buildings. A building at a certain point (x, y) ...
18
votes
3answers
567 views

Text on a circle

Write a program or function that prints an input string around the discrete circle that has the minimum possible radius. For example, for input This is an example, ...
8
votes
1answer
204 views

Extend the line

Task Given an image with a line on it, produce or display an image with the line extended the the line to the edge of image. The line is black and the background is white. The image size is ...
15
votes
3answers
459 views

Where does the spaceship go?

Based on an idea suggested by Zgarb. A spaceship is moving around a regular 3D grid. The cells of the grid are indexed with integers in a right-handed coordinate system, xyz. The spaceship starts at ...
6
votes
1answer
162 views

Test if a point is in an Icosahedron

Take as input 3 floating point numbers, which represent the x, y, z coordinates of a point. Return a truthy or falsey value indicating whether the point is inside the regular icosahedron centred at ...
15
votes
4answers
693 views

Compute the winding number

The winding number is the integer number of net counterclockwise revolutions an observer must have made to follow a given closed path. Note that any clockwise revolutions count negative towards the ...