Polyominoes. Presented by Geometers Mick Raney & Sunny Mall. Our Task. How does the particular mathematics discussed fit into the tapestry of geometry as a whole? What are some aspects of its historical development?
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Presented by Geometers
Mick Raney & Sunny Mall
Solomon Golomb, mathematician and inventor of pentominoes. If two squares side by side is a "domino", then n squares joined side by side to make a shape is a "polyomino", an idea invented by mathematician Solomon Golomb of USC. There are two distinct "triominoes" (three squares): a straight line and an L. There are five distinct "tetrominoes" (four squares), popularized in the computer game Tetris, which was inspired by Golomb's polyominoes.
P = 26
P = 34
A five square polyomino is a pentomino. There are a multitude of applications for pentominoes from games to tilings to packing problems.
Sort the shapes below. Explain how you sorted them.
Match each pentomino with the letter that it most closely resembles:
F I L N P T U V W X Y Z
Which pentominoes do you think will make a box (open cube)? Make a prediction. Then cut out the shapes and try to form a box.
Using all 12 3-D pentominoes, make the following:
Which hexominoes do you think will make a cube? Make a prediction. Then cut out the shapes and try to form a cube.
Determine the surface area and volume of each cube that you form.
Given the original hexomino below, classify each transformation as either a flip, slide, turn, or scaling.
“Chasing Vermeer is a novel about a group of middle school students who tackle the mystery behind the disappearance of A Lady Writing, a famous painting by Joahnnes Vermeer. Students employ pentominoes to create secret messages to communicate as they use their problem-solving skills and powers of intuition to solve the mystery. They explore art, history, science, and mathematics throughout their adventure.”
Mathematics Teaching in the Middle School
Draw a pentomino by connecting, in order, the coordinates below.
(0, 0), (0, 1), (2, 1), (2, 0), (1, 0), (1, -1), (-2, -1), (-2, 0), (0, 0)
Find the new set of coordinates to connect after applying the following transformations: