Designing our own Escher tessellation

Now it's time to design our own Escher tessellations. Watch the videos carefully. You can either choose to make a tessellation using a equilateral triangle as a basic figure (1st video) or using a square (2nd video). Now, be imaginative and try to build your own tessellations using a piece of paper, colors, ruler, a protractor and a pair of scissors.

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Extra work: Studying Escher's Lizards transformations

Knowing MC Escher

M.C. Escher was a Dutch graphic artist. He was the first person to introduce a mathematical structure on tilings and tessellations. Today we'll explore some of its tessellations, paintings and woodcuts and we'll know a little better why his work represented a new insight on the way artists look at geometry.

Here below you have some links which will help you knowing the figure of M.C. Escher:

• Escher's tessellations
• Official MC Escher homepage

Activities

After reading those links and watching the videos, start designing a presentation. It should talk about the following points:

1. Who was M.C. Escher? Write a small biography in 4 or 5 lines.
2. After visiting a certain place, Escher became fascinated by the regular division of the plane (tessellations). Which was this place? How this affected his own work?
3. Why do you think that there are mathematics in tessellations?
4. Which things do fascinated MC Escher and why?
5. What are 'Escher's Illusions'? Are you able to talk about them?
6. List and comment some of the artist's most famous works.

Let's craft our own theoretical physicists Xmas decorations!

Hi There!

Today we'll change subject and we'll talk about Physics. Did you ever heard about Albert Einstein, Marie Curie or Erwin Schrödinger?

Today, meanwhile googleing for Xmas ideas, I found a fantastic site with physicists Xmas decorations: Let's try to build them, today!

• Einstein's template
• Marie Curie's template
• Schrödinger template

I want to tile a kitchen!

Have you ever wondered how to tile a floor? This may not be a trivial question. Today we'll practice a little bit. We'll use diferent tilings and we'll discuss which is the best option for us.
Click on the activities sheet to start.

Let's tessellate!

Did you ever heard about tessellations? Do you know how to tile a Kitchen? Had you heard about M.C.Escher? Today we'll start the tessellations' project. Are you ready?

Activity

Take a paper and try to answer the folllowing questions. You may need the resources listed below.

1. What does to tessellate mean? Explain it using your own words.
2. Are you able to list all the regular polygons?
3. Try to think about a method to discover if a regular polygon tessellates or not and explain it using your own words. Hint: use the number of sides and the interior angle measurements.
4. Build and fill in a table with the following columns: regular polygon; number of sides; interior angle between sides; does it tessellate?

Resources

• The regular polygons' names
• To tessellate with regular polygons
• Regular figure's interior angles
• Help: what is a tessellation

Fractal's presentation

Picture by Glòria Maspoch

Drawing by Gerard Hostench

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Build a slide presentation

Today we are going to summarize our fractal work. In order to do so, gather in groups of 4 people and build a slide presentation containing the following points:

1. What is a fractal?
2. Who first talked about fractals? When was it?
3. Can you list the different types of fractals?
4. Which are the most popular types of fractals?
5. Summary of the Sierpinsky triangle construction with pictures.
6. What is a Jurassic Park fractal? How is it built? Why do you think it has such a name?
7. Explain how to build a Koch snowflake fractal. Which relationship exists between Koch snowflake fractal and the coast of Australia?
8. Nature is full of fractals. Insert some picture examples and explain why they are said to be fractals.
9. Vocabulary of the project.
10. Your opinion about the project. 

Next day you'll present your slides to the class. To evaluate the oral presentation, we'll use the following rubrics. 

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Extra resources

Sometimes it's nice designing our own fractal using specific software. Here you have a couple of links about it:

• Fractal Grower
• Chaos Pro

Fractals in nature

Have you ever found a fractal in nature? The world is full of fractal structures. Do you want to explore few of them? Let's have a look!

Resources

• Earth's most stunning natural fractal patterns
• 17 amazing examples of fractals in nature
• Fractal tree 
• More examples
• More about fractals in nature

Activities

1. Write a 10 lines summary of which kind of fractals can we found in nature.
2. What does this sentence by Benoit Mandelbrot mean? "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line."
3. Finish the work with a photo of a fractal made by you.
4. Write a short vocabulary of related words.