Parity and Pigeons

Legend

Interactive | |

Notice | |

Slideshow | |

Video |

Konigsberg Interactive: Help a monster cross the bridges of Konigsberg |

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Handshaking Monsters Interactive: None |

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Konigsberg Tweak Interactive: Help a monster cross the bridges of Konigsberg, but now add and remove bridges! |

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Chessboard Interactive: Lay dominoes on a chessboard with the corners removed |

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Chessboard Interactive Tweaked: Lay dominoes on a chessboard and pick which squares to remove |

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Monsters with Umbrellas Interactive: Find a loop in a tangle of ropes |

Under construction....

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Loopy Monsters Interactive: Keep track of ropes under umbrellas while finding loops |

Under construction....

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Monsters with Sox Interactive: How many sox do you need for a pair? |

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Pigeonhole Interactive: Help the pigeons find a pigeonhole |

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A shortcut for those who need it: Take the sidetrack to avoid the most intricate part of this Exploration. If you're feeling lost, by all means use this, but you will miss a truly beautiful piece of mathematics |

**A shortcut for those who need it:**Take the sidetrack to avoid the most intricate part of this Exploration. If you're feeling lost, by all means use this, but you will miss a truly beautiful piece of mathematics

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Messy Monsters: Some Monsters offer insight |

Konigsberg Intro: Introduces the Bridges of Konigsberg problem. |

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Pigeons Explained: Describes what's going on when too many pigeons try to fit into a small pigeon roost. Otherwise known in mathematics as the Pigeonhole Principle. |

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Handshaking Monsters Explained: Explains what's happening when a bunch of monsters start shaking hands and what that has to do with pigeons. |

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Konigsberg Tweak: Exploring changes to the Bridges of Konigsberg problem. |

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Try Some Monsters: Where to find insight into the Bridges of Konigsberg problem? |

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Monsters In Konigsberg & Domino Intro: Monsters take to the streets of Konigsberg to help solve the famous problem. Then, a new problem is introduced, involving a chessboard and dominoes. |

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Domino Tweak: How we might tweak our Chessboard Interactive. |

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Dominoes Explained: Explains the insights you might have observed in the last Interactive. |

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Konigsberg Graph: Describes how the Bridges of Konigsberg and Messy Monsters with Umbrellas are really both different views of the same mathematical object called a graph. |

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Loops: Examines loops in problems related to the Bridges of Konigsberg and Messy Monsters with Umbrellas. Specifically mathematical loops in their corresponding graphs. |

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Konigsberg Induction: The beautiful induction argument that shows when problems like the Bridges of Konigsberg and Messy Monsters with Umbrellas can be solved. A pictorial argument involving graphs. |

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Sox Explained: A beautifully simple way of guaranteeing you can pick a pair of sox from your drawer, even if you happen to be a three-footed monster (in which case, obviously, you'll want a triple). |

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**Dominoes and Chessboard:**

Problems with cover partial chessboards with dominoes.

**Age Range:**

7+, younger audiences will need more guidance interpreting problems, but all will have fun playing with it. Great for everyone!

**Mathematics:**

Parity. Matching. Geometric intuition. Exploring with Trial and Error.

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**Konigsberg:**

Explore the famous Bridges of Konigsberg problem. Simplify and alter the problem to shed light on what is happening. Finally, clever counting reveals the solution.

**Age Range:**

5+, younger audiences will move slower, but everyone will get something from these activities

**Mathematics:**

Parity. Exploring with Trial and Error. Simplifying and altering questions as a mode of inquiry.

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**Messy Monsters:**

Using Messy Monsters to see reverse of Bridges of Konigsberg problem

**Age Range:**

10+, younger audiences will move slower, but the arguments are beautiful and well worth showing everyone.

**Mathematics:**

Induction. Exploring with Trial and Error. Elementary Graph Theory

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**Monster Handshake:**

If a group of students shake hands, must two of them have shaken the same number of hands?

**Age Range:**

5+, younger audiences will move slower, but everyone, including adults, will be delighted and surprised by these activities.

**Mathematics:**

Pigeonhole Principle. Exploring with Trial and Error. Simplifying as a mode of inquiry.

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**Pigeonhole:**

How easy is it to find a pair of sox, or fill pigeonholes with pigeons?

**Age Range:**

5+, younger audiences will move slower, but everyone will get something from this task.

**Mathematics:**

Pigeonhole Principle. Exploring with Trial and Error. Simplifying and altering questions as a mode of inquiry.

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