1. Warm-up Homework out on desk, ready to be checked
Get out a sheet of paper and answer the following question:
“What about a person’s face makes them attractive? Why do you think this is being asked in a MATH class?”

2. Symmetry

3. Symmetry
There are two types:

4. Symmetry There are two types:
Line symmetry – a figure that matches exactly when folded in half

5. Symmetry There are two types:
Line symmetry – a figure that matches exactly when folded in half
Rotational symmetry – a figure that can be turned less than 360o about the center and still look like the original

6. Line Symmetry

7. Line Symmetry
To determine if a figure has line symmetry, we look for a line OF symmetry.

8. Line Symmetry
To determine if a figure has line symmetry, we look for a line OF symmetry.
Line of symmetry – line that divides a figure into two halves that are reflections of each other

9. Livescience.com
Good symmetry shows that an individual has the genetic goods to survive development and is healthy.
"It makes sense to use symmetry variation in mate choice," said evolutionary biologist Randy Thornhill of the University of New Mexico. "If you choose a perfectly symmetrical partner … your offspring will have a better chance of being symmetric."
Thornhill has been studying symmetry for 15 years and scanned faces and bodies into computers to determine symmetry ratios. Both men and women rated symmetrical members of the opposite sex as more attractive and in better health than their less symmetrical counterparts. The differences can be just a few percent—perceivable though not necessarily noticeable.

10.
15 Fascinating Facts on Human Attraction
1. We love symmetry: Symmetrical features aren't just aesthetically pleasing, they symbolize good genes and healthy development. Those with better symmetry will most likely produce offspring who are also stronger and more immune to gene manipulations or alterations.

11. Rspb.royalsocietypublishing.org
Symmetrical human faces are attractive and it has been proposed that humans have a specialized mechanism for detecting symmetry in faces and that sensitivity to symmetry determines symmetry preferences … symmetry preferences are indeed driven by a mechanism that is independent of conscious detection … the result of specific pressures faced by human ancestors to select high-quality mates. Unconscious mechanisms determining face preferences may explain why the reasons behind attraction are often difficult to articulate.

12. The Science of Attraction: What makes a beautiful face?
It all started as a disagreement one evening. The men ended up vehemently defending their opinion that – yes, Keira Knightley did indeed have an attractive face. The women had a completely different point of view – I won’t repeat what they said, but it wasn’t pleasant (poor Keira).

13. Who is more attractive?

14. Surprise!
I’d bet that you think the faces on the right are the most attractive – and those faces aren’t even real!

15. Examples
P 287 Example 1
“Your Turn” (a-c)

16. Rotational Symmetry

17. Rotational Symmetry
To determine if a figure has rotational symmetry, we look for one or more angles of rotation.

18. Rotational Symmetry
To determine if a figure has rotational symmetry, we look for one or more angles of rotation.
Angle of rotation – the degree measure of the angle through which a figure is rotated

19. How to find angles of rotation

20. How to find angles of rotation
To determine angle(s) of rotation:

21. How to find angles of rotation
To determine angle(s) of rotation:
See how many times you can turn the figure and have it look the same

22. How to find angles of rotation
To determine angle(s) of rotation:
See how many times you can turn the figure and have it look the same
Divide 360 by that number

23. How to find angles of rotation
To determine angle(s) of rotation:
See how many times you can turn the figure and have it look the same
Divide 360 by that number
Your answer is the angle of rotation

24. Examples
P 287 (Examples 2 & 3)
P 288 (3-6)

25. Classwork
P 631
Lesson 6-6
(1-6)

26. Homework Pp 288-289 (7-18) Online Textbook Website: nc.msmath3.net
Click “Online Textbook”
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