Mathematical Illusions

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Mathematical Illusions

A Lesson in the “Math + Fun!” Series

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About This Presentation

This presentation is part of the “Math + Fun!” series devised by Behrooz Parhami, Professor of Computer Engineering at University of California, Santa Barbara. It was first prepared for special lessons in mathematics at Goleta Family School during four school years (2003-07). “Math + Fun!” material can be used freely in teaching and other educational settings. Unauthorized uses are strictly prohibited. © Behrooz Parhami

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Do you see circles or spirals?

Things May Not Be What They Seem

Are some of the squares bigger?

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1. Which of the two vertical lines is longer?

Activity 1: Appearances May Be Deceiving

3. Draw a 9”  11” rectangle and cut it along the dashed line, as shown. Slide the lower piece down and to the left. Cut out the small triangle that sticks out at the lower left and use it to fill the opening at the upper right. You get a 10”  10” square.

2. Which of the two white squares is larger?

Explain how the area of the figure increased from 99 to 100.

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Activity 2: Does 64 Equal 65?

Cut out an 8”  8” square as shown and rearrange the pieces to form a 5”  13” rectangle, thus proving 64 = 65. What is wrong with this?

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Hiding Pictures Within Pictures

Find the man’s face.

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Morphing and Mutation

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Morphing Images on a Computer

See “Tiger Face Morph” and other video clips at: http://creativesam.tfcentral.com/Animations.html

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Illusion of Motion

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Ambiguous Images

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What Do You See in These Pretty Patterns?

Fix your stare at a specific point and describe what you experience. Repeat the process, this time slowly moving your head back and forth.

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