Power Point for Contemporary Math ch 2

1. Chapter 1 follow-up Check digit division by 9: Usually the sum of the digits are divisible by 9 Mod 9 check digit scheme: Usually the last digit is congruent mod 9 to the sum of the previous digits.

2. Congruent mod 9 Some examples: 22 ≡ 4 mod 9 because 9|22-4 19 ≡ 1 mod 9 because 9|19-1 30 ≡ 3 mod 9 because 9|30-3

3. Congruent mod 9 Find the missing digit using mod 9 73?11 The sum of 7+3+d 3 +1 ≡1 mod 9 11+d 3 ≡1 mod 9

4. Congruent mod 9 Find the missing digit using mod 9 73?11 The sum of 7+3+d 3 +1 ≡ 1 mod 9 11+d 3 ≡ 1 mod 9 The missing digit must be 8 because 19 ≡ 1 mod 9

7. Tilings

8. Regular Tessellation

19. Regular Tessellations Look at the point where the triangle vertices meet. What is the sum of the angle measure?

20. Regular Tessellations What is the sum of the angles at the point where the hexagons meet?

27. Symmetry, Rigid Motion, and Escher Patterns Line of symmetry Rotational symmetry