BRIAN SHELBURNE ASSOCIATE PROFESSOR OF MATHEMATICS AND COMPUTER SCIENCE DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE WITTENBERG UNIVERSITY Girl Scout.

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Presentation transcript:

BRIAN SHELBURNE ASSOCIATE PROFESSOR OF MATHEMATICS AND COMPUTER SCIENCE DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE WITTENBERG UNIVERSITY Girl Scout Science Night Wittenberg University April 26, 2013

What is Mathematics All About? It’s finding Patterns usually involving NUMB3RS! It’s creating/using Patterns to solve problems! It’s FUN! and It’s probing the Universe for its most mysterious secrets!

Patterns with Tilings A good place to start if you have the game

Polynominoes Start by Finding all the … Monominoes - 1 Dominoes - 1 Triominoes - ? Tetrominoes - ? Pentominoes - ? What about symmetry?

Polynominoes Reflections Translations Rotations Are Ok!

Polynominoes Hexominoes - 35 Heptominoes Octominoes – 369 …

Patterns with Tilings The 21 Blokus Tiles

Tetrominoes Questions! Can you arrange all 5 tetrominoes into a 4 by 5 rectangle? Can you create 4 by 4 squares with four of the same tetromino? Can you create a 5 by 4 rectangle with the Square, I, L and two T tetrominoes? (Note! No Z)

More Tetromino Questions Can you create a 5 by 4 rectangle with a Square, Z, I and two L tetrominoes (No T) What other combinations work to create rectangles? Coloring Problems! Can any pattern be created using just 4 colors where no two tetrominores of the same color touch except at a corner?

Pentominones! Can you arrange 4 pieces (including the F tile) into a big F Can you arrange 4 pieces (including the L tile into a big L? Can you arrange all 12 pieces in a 6 by 10 rectangle? Adding a 4 by 4 square can you fill a 8 by 8 chess board?

Patterns with Tilings Thank you