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Nossi ch 2

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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.
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
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
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
Chapter 2 Shapes in Our Lives ,[object Object],[object Object],[object Object]
Tilings ,[object Object]
Tilings
Regular Tessellation
Regular Tessellations ,[object Object],[object Object],[object Object],[object Object]
Regular Tessellations ,[object Object],Sum of the measures of a triangle = 180 degrees
Regular Polygons ,[object Object],Sum of the measures of a triangle = 180 degrees What is the sum of the measures of the interior angles of a square, hexagon?
Regular Polygons ,[object Object],[object Object],[object Object]
Regular Polygons ,[object Object],[object Object],[object Object]
Regular Polygons ,[object Object],[object Object],[object Object],[object Object],[object Object]
Regular Polygons ,[object Object],[object Object],[object Object],[object Object],[object Object]
Regular Polygons ,[object Object],[object Object],[object Object]
Regular Polygons ,[object Object],[object Object],[object Object],[object Object]
Regular Polygons ,[object Object]
Regular Tessellations Look at the point where the triangle vertices meet. What is the sum of the angle measure?
Regular Tessellations What is the sum of the angles at the point where the hexagons meet?
Semiregular Tessellations ,[object Object],[object Object]
Escher Tessellations ,[object Object],[object Object]
Pythagorean Theorem ,[object Object]
Pythagorean Theorem ,[object Object],5 12 hypotenuse
Section 2.1 assignment ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Symmetry, Rigid Motion, and Escher Patterns ,[object Object],[object Object]
Symmetry, Rigid Motion, and Escher Patterns Line of symmetry Rotational symmetry
Symmetry, Rigid Motion, and Escher Patterns ,[object Object],[object Object],[object Object],[object Object]
Symmetry, Rigid Motion, and Escher Patterns ,[object Object],[object Object]
Symmetry, Rigid Motion, and Escher Patterns ,[object Object]
Symmetry, Rigid Motion, and Escher Patterns ,[object Object],[object Object]
Symmetry, Rigid Motion, and Escher Patterns ,[object Object],[object Object],[object Object]
Fibonacci Numbers and the Golden Mean ,[object Object],[object Object]
Fibonacci Sequence ,[object Object],[object Object],[object Object]
Fibonacci Sequence ,[object Object],[object Object],[object Object]
Geometric Recursion ,[object Object],[object Object]
Geometric Recursion ,[object Object]
The Golden Ratio ,[object Object]
The Golden Ratio ,[object Object]
The Golden Ratio ,[object Object],[object Object],[object Object]
Section 2.3 assignment ,[object Object],[object Object]
 
 

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Nossi 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
  • 5.
  • 6.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17.
  • 18.
  • 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?
  • 21.
  • 22.
  • 23.
  • 24.
  • 25.
  • 26.
  • 27. Symmetry, Rigid Motion, and Escher Patterns Line of symmetry Rotational symmetry
  • 28.
  • 29.
  • 30.
  • 31.
  • 32.
  • 33.
  • 34.
  • 35.
  • 36.
  • 37.
  • 38.
  • 39.
  • 40.
  • 41.
  • 42.  
  • 43.