Mathematical Illusions

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Impossible Designs

Slide 13

Impossible Objects

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Illusion of Distortion

Horizontal lines appear slanted in the middle portion of the diagram

Vertical lines appear crooked, but they are perfectly straight

Which line on the left is a continuation of the one on the right?

Slide 15

3D Illusions

Slide 16

Illusion of Distortion or Deformation

The figure on the right spins when you view

this page in a slide show.

Notice how the shape is deformed as it spins.

Slide 17

Activity 3: Experiencing Distortion

In each of the following diagrams, use a ruler and pencil to connect the black dots on either side using two horizontal lines. Explain what you see.

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Activity 4: Where Does the Sixth Box Go?

Cut along the dashed line . . .

and shift the bottom half to left, as shown below.

What happened to one of the boxes?

Slide 19

Activity 5: Making People Appear and Disappear

1. Count the people in the picture to the right and write the number down.

2. The upper half of the picture is redrawn below. Cut out the rectangular pieces 1 and 2 by cutting along the dashed lines.

3. Now, put the two cut-out pieces in reverse order on the picture above, covering the original pieces (piece 1 on the right and piece 2 on the left).

4. Recount the number of people and explain what happened.

Slide 20

Next Lesson

Late May or early June 2007

Area and Tilings