Geometry and Spatial Reasoning

Geometry, Spatial Reasoning, and Visualization

• Around the World

  

  The circumference of the Earth is 40,076 km (24,902 mi). Let’s say we had a rope that long and used it to circle the Earth, like the red line in the picture. read more  

• Boxes, Cubes, and Nets

  

  We have puzzles on polyominoes, but here's one on how to make pentominoes and hexominoes with an extra dimension.  read more  

• Build a Cube

  

  How many ways six squares be arranged to form a cube? Come give it a try, then see what we came up with! read more  

• Can You Build A Wall around France?

  

  The Great Pyramids at Giza in Egypt were built nearly 5,000 years ago as tombs for the Pharaohs. read more  

• Connected Loops

  

  This puzzle challenges you to find a way to tie the three loops of string together so that untying any one of them causes the other two to be disconnected. read more  

• Four Square Matchsticks

  

  Using four matchsticks of equal length, we can enclose an area of one square matchstick. read more  

• How Can This Be True?

  

  This month’s math puzzle was submitted by Dougal McVicar. read more  

• How Can This Field Be Evenly Divided?

  

  An old farmer in Seedonia was getting ready to retire.  He wanted to pass his farm on to his children with half going to his son and the other half to his daughter.  read more  

• How Fast Are You Moving?

  

  Right this minute. Sitting or standing in front of your computer monitor—or reading this on a printed sheet of paper—how fast are you moving? read more  

• How Long Is the Coast of England?

  

  …asked mathematician Benoit Mandelbrot. This math puzzle explores questions related to fractal geometry. read more  

• How Many Regular Mosaics Can You Make?

  

  This regular mosaic is a pattern made up of equilateral triangles. read more  

• Is It Straight?

  

  Mitchell hung a mirror on the wall in his house. To make sure it was perfectly straight he measured exactly 40 cm (16 in) from . . . read more  

• Land and Water

  

  An elderly farmer in Seedonia decided to pass his farm on to his four children by dividing the land up equally among them.  read more  

• Trees in a Row

  

  You have seven trees to plant. They need to be arranged in six rows with three trees in each row. How do you do it? read more  

• More Trees in a Row

  

  You have ten trees. Can you arrange them in four rows of five? read more  

• Nets for Polyhedra

  

  In the Boxes, Cubes, and Nets puzzle we found nets—two-dimensional shapes that can be folded up to form a three-dimensional shape—to fit cubes. This puzzle we try to find nets to fit polyhedra. read more  

• Painted Cube Face Patterns

  

  Start with a set of wooden building blocks in the shape of cubes.  read more  

• Rearrange the Coins

  

  Rearrange six coins from a triangle to a circle in the fewest possible moves. read more  

• Tennis Ball Container

  

  You have a cylindrical container just big enough to hold three tennis balls. read more  

• Toothpick Puzzles

  

  Toothpick puzzles (more commonly called “matchstick puzzles”—but it’s safer to use toothpicks than matchsticks) are an old form of geometric puzzle. read more  

• Toothpick Triangles

  

  Toothpick puzzles can be done with many different geometric shapes. Here, we use triangles for our puzzles. read more  

• Where Are You?

  

  If you are standing somewhere on the Earth, can you to figure out where in the world you must be based on the information we give you? read more  

• Which Letter Is This?

  

  This puzzle is attributed to Scott Kim.  He cut out an uppercase letter from a piece of paper and then made one fold.   read more