# Questions tagged [geometry]

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

283 questions
Filter by
Sorted by
Tagged with
600 views

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 ...
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.) ...
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 ...
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 ...
244 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 >=...
902 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 ...
1k views

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 ...
251 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 ...
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 ...
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 ...
438 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 ...
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 ...
53k 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 ...
370 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 ...
985 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 ...
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 ...
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 ...
597 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 ...
870 views

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 ...
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 ...
140 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 ...
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 ...
6k 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 ...
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. ...
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 ...
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 ...
386 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 ...
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 ...
569 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 ...
2k views

### Circle intersection area

Description : Given x and y positions of two circles along with their radii, output the ...
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 ...
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 ...
850 views

### Expand a hexagon

Given an ASCII art hexagon as input, output one whose sides are all one unit longer. ...
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 ...
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 ...
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 ...
273 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....
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 ...
665 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, ...
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 ...
31k 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 ...
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 <...
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 ...
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 ...
286 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 ...
629 views

### How lit is this room? 🔥 pt. 1

Related to this question. A room is defined to be a (not necessarily convex) non-intersecting polygon, expressed as an ordered list of 2-dimensional coordinates. A sufficiently bright lightbulb is ...
352 views

### Can this container hold this much liquid?

Can this container hold this much liquid? Challenge Synopsis As you most likely know, liquids have an indefinite shape and a definite volume. As such, they always take the shape of their container. ...
8k views

### Check if point lies inside triangle

Your goal is to determine whether a given 2D point X lies within the area of the triangle with given vertices A,B,C. Write a function that takes in the coordinates of the test point X and the three ...