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