The complex geometry of islamic design

Would you like to learn how to draw a tessellation like the ones that appear in arabic constructions, for example those found in the Alhambra? Some of the patterns shown there are easy to construct, some of them are not so trivial.
We are finishing the Maths and Beyond course. In the next 3 sessions we are going to visit some of the geometry constructions we find in Islamic Art.

Activities Day 1

1. Watch carefully the vídeo attached above
2. In groups of 4 people, try to answer the questions

Activities Days 2 and 3

1. Try to draw by hand you own geometric pattern. You can find more information here. In case you want to construct a six-fold geometry pattern, watch the video above.
2. Try now to draw the same figure using Geogebra. Is it easier or more difficult to construct?
3. Search on the internet pictures with nice arabic geometric patterns.
4. Create a presentation with all the things you learnt about the geometry of islamic design:
1. Answers to the questions of day 1
2. A picture of the handmade geometric pattern
3. An image of your Geogebra geometric construction
4. Pictures of geometric tessellations you can find in different monuments and ancient buildings. Write down also a little description about it.
   

Day 8: Reflection symmetry

Find a picture on the web that has some kind of reflection symmetry

Insert it in Geogebra

Draw the contour of an object.

Reflect this object

Does this picture has reflection symmetry? Why?

Send the results of your investigation on an email

Day 7: Constructing a square and understanding the Pythagoras theorem with geogebra

Today we'll continue with constructions using geogebra. Now it's time to build a square and a little proof of the Pythagoras theorem. You can download the instructions here:

• Exercise 1: How will you draw square without using the Polygon tool?
• Exercise 2: Proving the Pythagoras theorem

Help

• Pythagoras theorem demonstration

Day 6: How to construct an equilateral and isosceles triangle without using the polygon tool

Have you ever wondered how to draw an equilateral triangle with geogebra without using the polygon tool? Today we'll learn how to do it.

• How to draw an equilateral triangle
• How to draw an isosceles triangle

Extra work

For those that are finished with the triangle points, here you have some extra exercises:

1. Construct a triangle of sides 5, 7 and 3 cm with geogebra. Explain below how did you managed it.
2. Construct an acute triangle with two sides of 5 and 7 cm and an angle of 30º.
3. Construct a right triangle with sides 4 and 3 cm. What is the length of the hyphotenuse?
4. Construct an obtuse triangle with a side of 4 cm and an angle of 135º.

Day 5: Incenter and centroid with geogebra

After you finish your constructions, you should send the .ggb files altogether in a mail to the teacher.

Day 4: Circumcenter and Orthocenter with geogebra

Day 3: Triangle centers

Today we're going to study the different triangle centers: centroid, incenter, circumcenter and orthocenter. I'm sure you studied them before. Are you able to remember them?

Links

• Triangle centers  (maths is fun)
• Triangle centers (geogebra tube)

Activity

Now that you have read about triangle centers, try to do the following activities.

Day 2: Triangles with geogebra

You already know that we can classify the triangles acording to their angles and acording to their side lengths. Read this link if you want to know more.

Activity

1.  Open geogebra and draw in the same canvas the following triangles:
• Equilateral triangle
• Isosceles triangle
• Scalene triangle
• Save the .ggb file
2.  Open another geogebra file and try to draw the following triangles:
• Acute triangle
• Obtuse triangle
• Right triangle
• Save the .ggb file
3. Questions:
1. Draw here a short definition for each kind of triangle according to their side lengths.
2. In the second file, use then the angle utility of geogebra and measure each angle. How much is the sum of the 3 angles of a triangle?
4. Send an email to the teacher with the two .ggb files attached and the answer to the questions.

Day 1: Learning Geogebra!

Geogebra is an opensource multiplatform program that lets students experiment with geometry and maths in general. This trimestre we are going to learn the basic tips of this fantastic tool.

Activity 3.1

Sit in couples together. Try to make a drawing like the one in the picture. Save the .ggb file that you get. Send the file to the teacher.

Days 7 & 8: Let's summarize! Prepare your Tangram project presentation

Now it's time for summarizing. Take all what we have done and try to make a slide presentation using Impress or Prezi. You should gather in groups of 3 or 4 people. Next day you'll have to present it to all your class mates.

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Items to be considered in the presentation

1. The tangram
• Origin of the game
• Pieces of the tangram:
• Shapes and their names
• Sizes of the pieces
• Areas of the pieces
2. Nice tangram constructions with their names
3. The Tangram cousin: the Stomachion
   • Origin
   • Pieces
   • Constructions with this Tangram
4. What's your opinion about this project? Did you like it? Why?
5. Vocabulary and expressions of the project

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Your oral presentation will be evaluated according to the following rubrics.

Days 5 & 6: The Tangram Cousin. The Stomachion or The Archimedes puzzle

The Stomachion is a very ancient Tangram-like puzzle designed by Archimedes around the year 200 BC. Let's play a little bit in order to know something more about this puzzle. After that you'll have to fill in the following activities.

• More about the Archimedes puzzle

Day 4: Are you able to invent a story using 5 different tangram constructions?

Take your own tangram and try to build 5 different constructions. You don't need to use the ones of the picture, you can surf on the internet to find more. Draw the solution of the constructions on a piece of paper. Afterwards, try to invent a story in which all the created characters appear.

Day 3: The dimensions of the 7 Tangram pieces

Have you ever wondered how to compute the length of the sides of every tangram figure? To do so, first of all you should know what the Pythagoras theorem is. Watch the videos and do the following activity.

Day 2: The missing square mistery

Today we'll watch a video and we'll try to solve a mistery called 'the missing square'. After the mistery is solved, try to construct the 13 convex figures with the Tangram. Do you know what a convex figure is? If you choose any two points inside the figure, the whole line between the points must also be inside the figure.

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Activities

After the mistery is solved, try to construct the 13 convex figures with the Tangram. Do you know what a convex figure is? If you choose any two points inside the figure, the whole line between the points must also be inside the figure. Try to build each one of the following figures.

1. Take a white paper. Write down the solution to the missing square mistery. You can use a small drawing if you prefer.
2. Now, take your tangram pieces and try to build at least 2 of the convex figures below. Draw the solution on the paper. Remember that you must use all 7 tans in order to construct the shapes.

Day 1: Let's have fun with the Tangram!

Did you ever heard about tangram? Today we'll watch a little video explaining how to build one.

Later on, you should take the grid paper and try to build a tangram like the one you see in the image.

Taken from http://www.educacionplastica.net/Tangram1.htm

Day 6: Let's prepare slides for the oral project presentation

It's time for summarizing. Today you'll sit in groups together and you should start designing some slides for the oral presentation. Your presentation must contain:

• Length and distance issues
• Metric system length units. 
• Conversion within the metric system.
• Imperial system vs. metric system.
• Vocabulary
• 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.

Day 5: Imperial system vs metric system (II)

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Today we'll practice a little bit more the conversion between the two systems. Let's try to do the following activities:

1. Conversion exercises
2. Conversion factors between systems (web with online activities) 
3. Extra work 

Day 4: Imperial system vs metric system (I)

Do you know that in the UK and in the US sometimes people use another system for measuring? This system is called Imperial system.

Activities

1. Build a table with the correspondence between metric and imperial system for length, area, volume and mass measuring units
2. Information and online activities
3. Conversion charts

Day 3: Metric system unit conversion

Today we'll watch some vídeos from Khan Academy about mètric System unit conversion. You have to solve the problema before watching the video. Afterwards, you can check if you made the calculations right.

Unit conversion within the metric system

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Converting within the metric system

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Perimeter and unit conversion

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Applying the metric system

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Conversion between metric units