BRIAN SHELBURNEASSOCIATE PROFESSOR OF

MATHEMATICS AND COMPUTER SCIENCE

DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE

WITTENBERG UNIVERSITY

Girl Scout Science NightWittenberg 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!

andIt’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 - 1Triominoes - ?Tetrominoes - ?Pentominoes - ?

What about symmetry?

Polynominoes

ReflectionsTranslations

Rotations

Are Ok!

Polynominoes

Hexominoes - 35Heptominoes - 108Octominoes – 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