# Questions tagged [geometry]

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

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### 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 ...
214 views

### No Singles Allowed [closed]

This is a fairly simple challenge. Write a program that computes the distance between two points on a 2D plane. However, you can't use any functions or operators (referred to here as symbols) that ...
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### Schläfli Convex Regular Polytope Interpreter

Background The Schläfli Symbol is a notation of the form {p,q,r,...} that defines regular polytopes and tessellations. The Schläfli symbol is a recursive description, starting with a p-sided regular ...
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### Tiling the unit square

Background By expanding and cancelling terms, it is easy to show the following identity: However, it is an open problem whether all 1/n-by-1/(n+1) rectangles can tile the unit square. The Task ...
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### How Many Holes?

Challenge Given a graphical input of a shape, determine how many holes there are in it. Not Duplicate This question was marked as a possible duplicate of Count Islands. I believe this challenge is ...
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### Grids can be curvy. How long is yours?

Consider depicting a simple, open, two-dimensional curve on a W wide by H high grid of text where X represents part of the curve and ...
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### Two-Coloring Overlapping Circles

Write a program or function that takes in the following input in a reasonable format of your choice: Two positive integers W and H that define the width and height of the image you'll be generating. ...
538 views

### Average distance of two points in unit n-dimensional hypercube

An easy way to understand the unit n-dimensional hypercube is to consider the region of space in n dimensions that you can get if every coordinate component lies in [0, 1]. So for one dimension it's ...
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### Counting unit squares circle passes through

Write a program or function that given an integer radius r returns the number of unit squares the circle with radius r centered at the origin passes through. If the circle passes exactly through a ...
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### Contiguous Block Count

Count the number of contiguous blocks within a given 3D input. Input The input will consist of one or more rectangles of characters separated by blank lines. Each rectangle represents a cross ...
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### Print a cube net of the specified size

Challenge Given a size s, print a cube net of that size made of hash symbols (#) and spaces (). Examples: ...
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### 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 ...
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### ​P​i​ =​= ​3​.​2​

Inspired by this video of Infinite Series. Introduction Pi is defined as the ratio of the circumference to the diameter of a circle. But how is a circle defined? Usually a circle is defined as the ...
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### Let's Tessellate!

Introduction From Wikipedia: A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. A fairly well known ...
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### Volumes of ASCII boxes

Introduction In this challenge, you are given as input the ASCII representation of the net (unfolded surface) of a rectangular cuboid (3D box). The format is this: ...
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### 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 ...
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### Evaluate the B-spline basis

B-splines are defined using a set of "knots", "control points", and degree. For the purposes of this challenge, the control points are not needed. The knots are simply a list of strictly increasing ...
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### Help me I'm lost in the ocean!

Introduction Today I went fishing alone with my canoe, unfortunately I fell asleep and the stream brought me away, I lost my oars, now it's night and I am lost in the ocean! I can't see the coast so ...
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### Hexagonal coordinates: Polar to Cartesian

Wikipedia says about Polar Coordinates: In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a ...
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### Distance Between Two Points Travelling on a Polar Graph Chart

Brief Problem Explanation Write a program to find the minimum distance between two points traveling only on rays emanating from the origin and circles centered on the origin. Explanation of Premise ...
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### 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 ...
387 views

### Check if rectangles fill a rectangular space without gaps or overlaps

This challenge is based on another similar challenge. Because finding the most efficient packing of rectangles is NP-hard (that is, its solution is easy to check but hard to find), this challenge is a ...
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### 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 ...
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### 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: ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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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×...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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, ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 <...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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:...
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### 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 ...
339 views