Chapter Four -- Polygons

Lesson 1:

Equilateral Triangles

• Triangles

  • Three sides and three angles

• Equilateral triangles

  • Triangles with the three sides of the same length and the three same angles

  • Each angle is of 120 degrees

• Command:

  • REPEAT 3 [FD 30 RT 120] -- clock
  • REPEAT 3 [FD 50 LT 120] -- counterclock

Activities: A)  B)  C)  D)  E)  F)

 

Lesson 2:

Regular Polygons

• Polygon
  • a closed shape that has non-crossing straight sides and three or more angles
  • Special polygons
    • squares
    • rectangles
    • triangles
• Regular polygon
  • a polygon with all sides of the same length and all angles being equal
  • Examples: square, equilateral triangle
  • Angle computation
    • Assume the number of sides n
    • The turn angle will be 360/n
    • Examples:
      • Triangle:        REPEAT 3 [FD 30 RT 120]
      • Square:         REPEAT 4 [FD 30 RT 90]
      • Pentagon:      REPEAT 5 [FD 30 RT 72]
      • Hexagon:       REPEAT 6 [FD 30 RT 60]
      • Octagon:       REPEAT 8 [FD 30 RT 45]
      • Nonagon:      REPEAT 9 [FD 30 RT 40]
      • Decagon:      REPEAT 10 [FD 30 RT 36]

Activities: A), B), C), D), E)

Exploration: Paper work, program, and compare

Lesson 3:

The Total Turtle Trip Theorem --- TTTT

• The total turn degree is 360.
• Framework:       
  • REPEAT n [FD <length> RT <360/6>]
  • REPEAT n [BK <length> RT <360/6>]
  • REPEAT n [FD <length> LT <360/6>]
  • REPEAT n [BK <length> LT <360/6>]

Activities:    A)  B)  C)  D)

 

Lesson 4:

Other Polygons

• The total turtle trip theorem still applies.
• Left turn and right turn cancel each other.
• Examples:
  • RT 50 LT 50 ==> trun nothing
  • RT 90 LT 50 ==> turn right 40
• Procedures:
  • Block
    • TO BLOCK
    •         FD 80 RT 90
    •         FD 40 RT 90
    •         FD 40 LT 90
    •         FD 40 RT 90
    •         FD 40 RT 90
    •         FD 80 RT 90
    • END
  • Arrow
    • TO ARROW
    •         FD 20 RT 90
    •         FD 80 LT 90
    •         FD 20 RT 120
    •         FD 60 RT 120
    •         FD 60 RT 120
    •         FD 20 LT 90
    •         FD 80 RT 90
    • END
• Others: Page 92

Activities:    A)  B)  C)  D)  E)

Exploration: Paper work, program, and compare

 

Lesson 5:

        More Total Turtle Trips

• TTTT applies to any design the turtle makes by turning
• Example: Draw a stick and turn to make different designs
• Procedure STICK
  • TO STICK
  •         FD 40 BK 40
  • END
• Procedure TRIPOD
  • TO TRIPOD
  •         REPEAT 3 [STICK RT 120]
  • END
• Procedure CROSS
  • TO CROSS
  •         REPEAT 4 [STICK RT 90]
  • END
• Procedure ASTERISK
  • TO ASTERISK
  •         REPEAT 6 [STICK RT 60]
  • END

Activities:    A)  B)  C)

Exploration: Paper work, program, and compare

Lesson 6:

        Designs With Polygons

• Partition the design into small patterns
• Examples: refer to Pages 101-103

Activities:    A)  B)

Lesson 7:

Finding the Perimeter

• Perimeter: the distance around the outside of a polygon
• determined by the distance the turtle moves forward before each turn
• Forward and backward may cancel each other
• Perimeter can be found by adding all forward steps and subtracting all backward steps

Activities:    A)  B)  C)  D)  E)  F)

Lesson 8:

Putting it all Together

• Polygon and regular polygon
• Non-regular polygon
• TTTT -- The Total Turtle Trip Theorem
• Any designs by turning the turtle and repeating a shape
• Design partitions and patterns

Activities: A) B) C) D) E)