# Questions tagged [geometry]

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

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### Centerless Polygons

A centered polygonal number is a positive integer given by the number of vertices when a point is surrounded by (increasingly larger) polygons with the same number of sides, as shown below. For ...
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### Gluing tetrahedra together

(This challenge exists to extend sequence A276272 in the On-Line Encyclopedia of Integer Sequences, and perhaps create a new OEIS sequence1.) This is a code-challenge, which will have you write code ...
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### Polygons in a cube

Inspired in part by this Mathologer video on gorgeous visual "shrink" proofs, and my general interest in the topic, this challenge will have you count regular polygons with integer ...
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### Rectangles in rectangles

This code-golf challenge will give you two positive integers n and k as inputs and have you count the number of rectangles with ...
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### Triangles with rational side lengths

This challenge will have give you a positive integer $n$ and ask you to output $t(n)$, the number of triangles (up to congruence) satisfying the three conditions: The triangles have perimeter of ...
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### Circumference of an ellipse

Challenge Unlike the circumference of a circle (which is as simple as $2\pi r$), the circumference (arc length) of an ellipse is hard. Given the semi-major axis $a$ and semi-minor axis $b$ of an ...
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### Cut a triangle into equal-sized parts!

Similar in spirit to Number of distinct tilings of an n X n square with free n-polyominoes and Partition a square grid into parts of equal area, this challenge will have you count ways of partitioning ...
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### Is it in the polygon?

The challenge Given point and a path of points, say whether or not the point is in the polygon that is created by the path. Also return true if the point is on an ...
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### Is it a uniform polyhedron?

Objective Given a vertex figure consisting of regular convex polygons, determine whether it represents a convex uniform polyhedron. What is a uniform polyhedron? A uniform polyhedron is a polyhedron ...
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### Counting painted sides of cubic shapes

Sandbox Many of us have seen math problems where a shape made of unit cubes is dipped in paint, and the answer is the number of painted sides. We'll generalize that problem in this challenge. Input A ...
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### Are they collinear?

Task Write a program/function that when given three 2d points in cartesian coordinates as input outputs a truthy value if they are collinear otherwise a falsey value Three points are said to be ...
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### Divide into 2 isosceles triangles

Given the measures of two of the interior angles of a triangle (x and y; the other angle can be easily calculated with ...
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### Create a text image by manual automation

Challenge Premise It's 2006, and Alice is trying to send Bob their her completed notes on their newly ended expeditions into the labyrinthine school library, which the two of them found suffers from a ...
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### Friendly Incenters

The incenter of a triangle is the intersection of the triangle's angle bisectors. This is somewhat complicated, but the coordinate formula for incenter is pretty simple (reference). The specifics of ...
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### Draw the "{🏅} CODE GOLF & coding challenges" logo!

Wow, time really flies! It's already been one year since the debut of the Code Golf Stack Exchange site design. Let's celebrate this milestone with a code golf challenge... to imitate the site logo! ...
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### Calculate the vector component

Challenge Assume two vectors $\mathbf{a} = (a_1,a_2,\cdots,a_n)$ and $\mathbf{b} = (b_1,b_2,\cdots,b_n)$ are given in an $n$-dimensional space, where at least one of $b_1,\cdots,b_n$ is ...
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### Who Took My Toilet Paper?

You step into the restroom, and notice that the toilet paper has missing! It occurs to you that someone had stolen it. Strangely enough, the first thing you would like to know is the amount of toilet ...
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### Leon's shooting range problem

Leon's story Leon is a professional sling shooter and he comes to a shooting range everyday to practice. A casual target is not a challenge for him anymore so before shooting he first covers the ...
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### Is this a cube?

This challenge is a riff on Dion's challenge "Is this a rectangle?". The goal of this challenge is to write a program to decide whether or not some collection of tuples of integers represents a ...
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### Rubik's Snakes! (Part 1)

The Rubik's Snake (or Rubik's Twist) is a toy consisting of several triangular prisms strung together in a line in such a way that the pieces can be rotated about one another in 90 degree turns. Any ...
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### Triangles in a tetrahedron

The goal of this challenge is to extend the OEIS sequence A334581. Number of ways to choose $3$ points that form an equilateral triangle from the $\binom{n+2}{3}$ points in a regular tetrahedral ...
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### Counting hypercube Tetris pieces

Consider the Tetris pieces, but made out of some number of (hyper)cubes instead of four squares, where two blocks are considered the same if one is a rotation, reflection, or translation of another. ...
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### Infinite Snake game

Infinite Snake is just like the video game Snake, except for that the snake is infinitely long, there are no items to eat, and the Snake needs to move in a repeating ...
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### Perimeter of Conway hexagon

Background Given a triangle $ABC$, extend its three sides by the opposite side length, as shown in the figure below. Then the six points surprisingly lie on a circle called the Conway circle, whose ...
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### Where to point a low-orbit ion cannon (asking for a friend)

Challenge Premise Bob lost1 Alice's precious grand piano. Big mistake. Alice has now stolen Bob's low-orbit ion cannon. Alice refuses to just make up with Bob, so let's help her give him a light ...
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### Euler's Geometry Puzzle

Today (or tomorrow, depending on your timezone, by the time of posting) is the birthday of the great mathematician and physicist Leonhard Euler. To celebrate his birthday, this challenge is about one ...
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### Is this a rectangle?

The challenge: Given four coordinates, each in x y form, your job is to find out whether or not the given coordinates form a rectangle, and output a truthy/falsey. Rules: For the sake of simplicity,...
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### Reconstruct a 3d arrangement of cubes from two of its projections

Setup Take the following 4x4x4 cube along with a 2D view of 3 of its faces, with a common 1x1x1 cube highlighted: The arrows ...
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### Counting polyominoes on (hyper-)cubes

This challenge like some of my previous challenges will have you counting free polyforms, which are generalizations of Tetris pieces. This code-golf challenge will have you count polyomino-like ...
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### Impress Donald Knuth by counting polyominoes on the hyperbolic plane

This challenge is inspired by a talk about Schläfli symbols, etc that I gave in a Geometry seminar. While I was putting together this challenge, I saw that Donald Knuth himself was interested in (some ...
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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 ...
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### 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 >=...
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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 ...
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### 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 ...
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