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# Topological Puzzles

### Perplexing Pencil Problem

This week’s post introduces a wonderful topological puzzle. Topology is one of the newest fields in mathematics. To illustrate this, note that Henri Poincare’ (1854-1912), who is considered the founder of algebraic topology, published the first systematic treatment of topology in 1895. On the other hand, Euclid (330?-275? BCE), the father of geometry, wrote his… Continue Reading

### Tangled Hearts

This week’s activity is a disentanglement puzzle. These puzzles range from simple to difficult and most appear, at first glance, to be impossible. Once they are carefully studied, however, solutions usually present themselves. Since this puzzle is easily made from inexpensive materials, each student should have one. Make a sample copy of the puzzle beforehand… Continue Reading

### Leprechaun on the Loose

This week’s puzzle activity is another disentanglement puzzle. These puzzles range from simple to difficult and most appear, at first glance, to be impossible. Once they are carefully studied, however, solutions usually present themselves. Since this puzzle is easily made from inexpensive materials, each student should have one. Make a sample copy of the puzzle… Continue Reading

This week the Puzzle Corner activity utilizes concepts from one of the most recent fields in mathematics – topology. Topology is the study of geometric properties that are not affected by changes in size and shape. This includes the study of knots, inside and outside, networks, and the transformation of shapes and surfaces. Linking Loops is a classic… Continue Reading

### Snip and Clip

This week’s puzzle is an adaptation of a trick I found in Perplexing Puzzles and Tantalizing Teasers by Martin Gardner, perhaps the greatest living proponent of recreational mathematics. This wonderful book includes many tricks, puzzles, word problems, and brain teasers appropriate for upper elementary students. In the trick presented in this book, Gardner, who is also a… Continue Reading

### Möbius Mysteries

Puzzle Question How can you explain the apparent paradox of the double Möbius strips? Materials Scratch paper Scissors Tape Student sheets Puzzle Background The Möbius loop is a topological surface first discovered by August Ferdinand Möbius in 1858. Möbius was a mathematician and professor of astronomy whose work in topology revolutionized the field of non-Euclidean geometry. A… Continue Reading

### The Envelope Enigma

This weeks’s activity comes from the field of recreational mathematics. While the puzzle may not seem very mathematical (other than using mathematical language like points and line segments), it is actually related to the mathematical fields of network theory and topology. In this puzzle, students are asked to connect six points (labeled A-E) with line… Continue Reading

### Hand-To-Hand Switcheroo

The Puzzle Corner activity this week is a magic trick that requires no slight of hand, just a little dexterity of hand—and an application of topological principles. In the trick, two small cylindrical objects are switched back and forth between hands without dropping them. This is not as easy as it might seem since the… Continue Reading

### The Bridge Crossing Challenge

This week’s puzzle is a brief study of network theory whose roots began with a problem that was first approached in 1735 in Köningsberg, Prussia (now Kalinigrad, Russia), In this puzzle, students attempt to draw routes that cross every bridge in a bridge puzzle once and only once. Click here to download the directions for… Continue Reading