fold & unfold puzzles · problem 1. pinwheel puzzle fold the first square as shown below. color...

“Creativity in the Mathematic Education”

Fold & Unfold Puzzles

Geometry of Origami !

Fold & Unfold Puzzles

Krystyna [email protected]

www.origami.edu.pl

Līvāni, Latvia2010-09-25, Saturday, 9:00-10:30

Fold with Us!

1(c) Krystyna Burczyk, 2010

Problem 1.Pinwheel Puzzle


Problem 1. Pinwheel Puzzle

Take 2 squares. Fold them in the same way as below.



Fold the first square as shown below. Color the visible part of the first square.Open the second one. Try to color this square in the same way like the first one (without opening the first square).Compare efects.


Problem 2.How Many Possibilities are There?


Problem 2. How Many

Possibilities are There?

There is a square. Find the center points of all sides of this square. Fold one crease line as show in the picture: first end of line is a vertex of the square, the second one is in the middle of a side of the square.

Note. We wouldn’t like to use sides of a square as crease lines.

Fold another crease line in the same way.

How many different pairs of lines you may find?

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How many different pairs of lines you may find?Note. You should decide which pairs of lines are different.

For axample

(c) Krystyna Burczyk, 2010

Problem 2. cont.


Problem 2. cont.

Additional questions1. How may you describe a position of a point which belongs to both lines (from a pair)? If, of course, such point does exist.2. Is it possible to calculate an area of all

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2. Is it possible to calculate an area of all polygons you find during dividing a square with two lines described above.


Problem 3. (Sundara Row)What a Polygon is There?


Problem 3. (Sundara Row)

What a Polygon is There?

There is a square ABCD. Find the center points of all sides of this square. Call them K, L, M, N (a point K is a center point of the side AB, a point L is a center point of the side BC, etc.).Jointhe point A with the point M, the point B with the point N,the point C with the point K,the point D with the point Lby folding four crease lines.

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by folding four crease lines.These lines divide a square in 9 parts.In the middle of the square ABCD there is a quadrangle EFGH.Do you know what polygons there are?

This polygon EFGH is smaller than the square ABCD. How many times?

Do you know how to calculate a distance between the point E and the point B, the point C, etc?


Problem 3. Problem 3. (Sundara Row)


Solution?


Problem 3. (Sundara Row)


Additional QuestionsIs it possible to fold four lines in the other way and obtain

another quadrangle?What kind of quadrangles we can obtain?How many times are these quadrangles smaller/bigger

than the square?

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than the square?


Problem 4. (KB)Let’s Fold a Star in a Square


Problem 4. (KB) Let’s Fold a Star in a Square


Problem 4. cont.

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How many times is a star smaller than a square?How many times is a small square smaller than a big square?


Problem 4. cont.

Additional Questions.We may change flaps positions. We may hide a flap or change a direction of folds (mountain to valley).So, we can obtain many other multi-angular patterns in the square.

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angular patterns in the square.Try to find as many polygons as you can.


Problem 4. cont.


Thank you!

Geometry of Origami !

Krystyna [email protected]

www.origami.edu.pl

Līvāni, Latvia2010-09-25, Saturday, 9:00-10:30

Fold with Us!


fold & unfold puzzles · problem 1. pinwheel puzzle fold the first square as shown below. color...

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