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

---

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. 

---

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.

Jurassic Park fractal (Dragon curve)

Have you ever read Michael Crichton's book, Jurassic Park? On such book it appears a very weird shape called dragon curve. And of course, it is a fractal. Today we'll discover more things about it.

 

After watching the videos you have to construct such a fractal using a strip of paper. You have to fold the strip very careful from left to right, several times. Do at least 4 iterations and see what happens.

Pythagorean tree

Another quite amazing fractal is the Pythagorean Tree. Do you know why it has such a name? Let's try to construct one!

Koch snowflake

Taken from https://smist08.wordpress.com/tag/koch-snowflake/

Today we are going to learn about one of the first fractals that where studied. Watch the following two videos and afterwards try to do the related activities.

---

Activities

1. Draw a Koch snowflake in a triangular grid. Do at least 3 iterations.
2. Why is the Koch snowflake considered a fractal?
3. Why the Koch snowflake is said to have an infinite perimeter? Explain it with your own words and equations.
4. What happens if you perform an infinite number of iterations?
5. How do you know that the area enclosed by the Koch Snowflake is finite?
6. What is the Australian coastline paradox?
7. Why the Australian and the English coastlines are said to be fractals?
8. What do the Australian coastline and Koch Snowflake have in common?

Fractals and infinite series

Doodling in math: Infinity elephants

---

Activities

After watching the video, try to solve the following qüestions:

1. What is an infinite series? Can you give an exemple?
2. What does it mean that an infinite sum approaches to 1? Explain it with your own words
3. Which relationship exist between fractals and infinite series?
4. What is an Apollonian gasket? How is it generated?
5. Try to drawn a fractal that yields into an infinite series. You can take the ones that appear in the video as an exemple. 

A Giant Sierpinski's Triangle

Taken from http://paulbourke.net/fractals/gasket/

Today we'll face a challenge: we'll design a giant Sierpinski's Triangle made of all your individual ones. In order to construct such a figure, we have to organize the work:

• Gather in groups of 4 or 5 people
• Within your group you should draw a scheme of a giant Sierpinski's triangle using the 26 small triangles we built in class:
• Take the measurements of one small triangle
• Make a sketch of the big composition with all the measurements
• How many small triangles will you use?
• How long is the side and the height of the big triangle?
• Will the big triangle fit in a wall of our school corredor?

The Sierpinski's triangle

Today we should sit in groups together. Group number 1 will start with the daily diary. Now that you know what a fractal is, let's start diving into it! One of the most popular Fractals is the Sierpinski's triangle. Are you ready to build a big one? Follow the instructions!

• The world largest fractal triangle
• How to build your own Sierpinski triangle
• Fractal triangles  
• Rubrics for the Sierpinski's triangle evaluation

Fractals

Do you know what a Fractal is? Have you ever heard this word before? Let's explore it!

---

---

• What are fractals?
• Why do people study fractals?

Welcome to the Maths and Beyond 4th ESO course!

This year you'll start a new experience: once a week, we'll explore nice and funny mathematical facts. And all these in English! Let's go! After presentation, you'll try to answer some early questions