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Education Through Origami,
My New Origami Book
Krystyna Burczyk, Wojciech Burczyk
[email protected]
www.origami.edu.pl
Didaktik des Falten,
Freiburg im Breisgau, 2013
Origin of the book
• A publisher approach to write a book on
origami for teachers
• The publisher specializes in collection of
math problems for secondary and high school
(K7-12) students
© Krystyna Burczyk, 2013
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Target group for my book
• Gifted students
• Math teachers (no origami experience
expected)
• Origami community (interested in math
related models)
• Simple or medium advanced mathematics
(below university level)
© Krystyna Burczyk, 2013
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General idea
• Set of problems to be investigated
• Each problem suitable for different levels of
education
• Problems may be studied in the classroom, as
long term school projects or individually
• Detailed description of the basic problem +
open questions suggesting further directions
of investigation / possible problem extension
© Krystyna Burczyk, 2013
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Paper mosaics
• Mosaics are both the title and leading motif
• 20 Problems
1.
2.
3.
4.
5.
6.
7.
8.
9.
Two crossed squares (math without borders)
Flapping mosaic
3-4-6-8
Poly-tiles
Rhombic tiles
Kite mosaic
Quadrilateral tiles
Hearth tangram
Arrow mosaic
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Paper mosaics
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Square in square
Two lines in a square
Three scales tile
A new position of the point A
Trapezium tiles
Quadrilateral tiles
How many possibilities
Parallelogram
Section of a square into 9 pieces
A star in a square
“Wojtek” mosaic
© Krystyna Burczyk, 2013
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1. Two crossed squares (math without borders)
© Krystyna Burczyk, 2013
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2. Flapping mosaic
© Krystyna Burczyk, 2013
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3. Mosaic 3-4-6-8
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4. Poly-tiles
© Krystyna Burczyk, 2013
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5. Rhombic and kite tiles
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6. Kite mosaic
© Krystyna Burczyk, 2013
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7. Quadrilateral tiles
© Krystyna Burczyk, 2013
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8. Hearth tangram
Tiles designed by Francis Ow
© Krystyna Burczyk, 2013
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9. Arrow mosaic
Module designed by Nick Robinson
© Krystyna Burczyk, 2013
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10. Square in square
© Krystyna Burczyk, 2013
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11. Two lines in a square
© Krystyna Burczyk, 2013
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12. Three scales tile
© Krystyna Burczyk, 2013
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13. A new position of the point A
© Krystyna Burczyk, 2013
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14. Trapezium tiles
© Krystyna Burczyk, 2013
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15. Quadrilateral tiles
© Krystyna Burczyk, 2013
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16. How many possibilities
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17. Parallelogram
© Krystyna Burczyk, 2013
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18. Section of a square into 9 pieces
© Krystyna Burczyk, 2013
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19. A star in a square
© Krystyna Burczyk, 2013
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20. “Wojtek” mosaic
Designed by Bennett Arnstein,
Krystyna Burczyk
© Krystyna Burczyk, 2013
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Example
Problem 3: Mosaics 3-4-6-8
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Example problem 3: 3-4-6-8
•
•
•
•
Simple origami construction
Detailed description of the basic problem
Open questions
Intentionally, there is no answer for open
questions. Exploration may result (depending of
the students’ abilities) in
–
–
–
–
Hypothesis formulated by a student
Examples confirming hypothesis
Analytical solution of the problem
Mathematical proof of the hypothesis
© Krystyna Burczyk, 2013
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3-4-6-8 - problem
• Fold tiles: equilateral triangles, squares,
hexagons, octagons
• Detailed instruction of pre-folding of A4 paper
to cut starting sheets of paper
• Detailed instruction (including description
using math terms) of folding
• Problem: arrange folded tiles into a
tessellation (= packing a plane)
• Patterns of Archimedean tiling provided
© Krystyna Burczyk, 2013
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3-4-6-8 – open questions
What is side length of the square, triangle and
hexagon (A4 is the sheet size)?
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3-4-6-8 – open questions
Is this dodecagon regular?
What is size of triangle, square, hexagon and
dodecagon tiles?
Is it possible to fold a dodecagon tile out of a single
sheet of paper?
© Krystyna Burczyk, 2013
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3-4-6-8 – open questions
How many tiles for these mosaics?
© Krystyna Burczyk, 2013
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Thank you!
www.origami.edu.pl
© Krystyna Burczyk, 2013
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