Homework Discussion

• Read pages 372 – 382

• Page 394: 1 – 6, 11 – 12,

Translations (page 380)

Translations are proper rigid motions.

translation - A translation is a slide of an object in the plane. A vector showing the translation can be represented by an arrow giving its direction and length.

A

B

C

A

B

C

A’

B’

C’

Glide Reflections (page 381)

A glide reflection is an improper rigid motion.

glide reflection - A glide reflection is a rigid motion consisting of a translation followed by a reflection. The axis of reflection must be parallel to the direction of translation.

A

B

C

A

B

C

A*

B*

C*

A’

B’

C’

A

B

C

A

B

C

A*

B*

C*

A’

B’

C’

symmetry - A symmetry of an object or shape is a rigid motion that moves the object back onto itself.

identity - The identity motion is itself a symmetry, one possessed by every object and we will simply call it the identity.

Symmetry (page 383)

FIGURE 11-13

The Symmetries of a SquareEvery square has 8 symmetries - 4 reflection symmetries and 4 rotation symmetries.

FIGURE 11-14

Two objects or shapes are of the same symmetry type if they have exactly the same set of symmetries.

stands for the symmetry type with N reflections and N rotations .

ND

FIGURE 11-14

Symmetry type 4D

FIGURE 11-20

6D

FIGURE 11-21

6D 9D 21D

FIGURE 11-19

Symmetry type (only one reflection).1D

FIGURE 11-16

This propeller has no reflection symmetries at all! It still has 4 rotation symmetries (identity, and, 90, 180, and 270 degrees). It belongs to the symmetry family called (having 4 rotations only).

4Z

FIGURE 11-17

2Z

This propeller has no reflection symmetries. It has 2 rotation symmetries (identity and 180 degrees). It belongs to the symmetry family called (having 2 rotations only).

FIGURE 11-18

Symmetry type 2Z

S Z

FIGURE 11-20

Symmetry type (only identity symmetry).1Z

FIGURE 11-22

5Z 6Z 20Z

Homework

• Read pages 383 – 388

• Page 394: 7, 21 – 24, 27 – 29, 35-45, 47,