## Project 1: the MATH of spirals

• Spirals are a wonderful topic. There are so many ways to create art work with and without a computer.

1. Spirals with equilateral triangles (IT)

• Tutorial

• Learning unit/students' result:(IT)
• Development/further experiments: GeoGebra-File (IT)

• Spirals with equilateral triangles mBlock Based on Scratch

Learning Unit (IT)/ Studens' results
Equilateraspiral Mblock based on Scratch.pdf

Click on the picture for the Equilater Spiral with Scratch h=[(sqr3)/2]*l (IT)

Learning Unit (IT) /Students' results

Click on the picture to view the Square Spiral d=l*(SQR2) IT

Triangles Spirals and Analytical Geometry (RO&IT) link

2. Spirals - easy created (GER)

• These spirals were easily created by using only 3 basic construction commands. They are dynamic. So students decided to show only a picture of such spirals and ask other students to find out how they are created and describe it.

3. Spirals of Theodorus (Square root spiral)

• Video (tutorial) with 3 steps (Maria - RO)

• Video (turorial) with 4 steps .... (Alexa RO)

• Geogebra Tool

• Learning unit  and results Italy GeoGebra Book (Thank You Maria and Alexa, we put your videos in the GeoGebra Book)

4. Spirals by "trace and animate" (GER)

• How to to create

5. Fibonacci's  Spiral (RO)

6. Padovan's Spiral (RO)

7. Spirals through dynamic ray (IT)

The video follows a tutorial:  "GeoGebra Tutorial 30 – Loci, Roses and Reflections" of Guillermo Battista Mathematics Teacher

This is my idea of a five petal rose using spirals and dynamic ray- by Norma Lisa Neiman (IT)

What happens when a circle constrains two  dinamic points inside the diameter and the  diameter depends on a bundle of  straight line?
After you discover it from the video, enjoy  customizing it. Turn your work into an art game- by Norma Lisa Neiman

8. Spiral by paperfolding (GER)

You can use coloured, transparent paper. Then it is a nice decoration for windows.

9. Right angle spiral (CRO)

9. Equilateral triangle spiral (RO)

Click to see explanations in ggb file

10. Spirals by polar coordinates (GER)

Click to try out in GeoGebra and animate the slider

11. Archimedean Spiral with Excel (IT)

• Tutorial

Archimedean Spiral with Excel

Learning Unit (IT) /Students' results

Archimedean Spiral.pdf

12. (Triangle) spirals with Scratch

a) I cannot embed it. It can be (remixed) modified and downloaded on the Scratch Website. Go there! (GER)

b) Students useed simple Scratch files and learned by remixing files more about Scratch commands. All files are in a so-called Scratch Studio.(GER).

c) More nice spirals with MblockScratch (IT)  see No. 1

13. 3d spiral (LV)

This spiral has been constructed according rules for a fibonnacci spiral with SketchUP, a 3d software and was then printed by with a 3d printer.

• #### Spirals

##### 1) Discussion before starting the project

I Have copied all comments to a PDF, links included

##### I like the work "circles and spirals from normalisa".

The colors of the points are nice and the point that "walks around" is funny. Can you tell us how it works?Or is it too difficult for us ????
Thanks,Torben, grade 5, PGU

##### Excellent help by a video from Italy

Florian, grade 5, has created without any help his own art work with equilateral triangles. He told me that it was very easy after having watched the video from Italy (spiral creation no.1).
M. Schwarze (teacher)

##### spiral no. 10

We don't teach polar coordinates in math lessons in the upper secondary Level. So ti was my first trial in GeoGebra.(Monika)

##### How to create a dynamic flower _Answer to Torben

It is about construction. If you build a dynamic ray, you can create flowers. I'll help you through this link. After, you have seen the construction, make it go dynamically. If you want point D to change colours, you must click on the right button of the mouse when you are on the point and go on ADVANCED. Select RGB: VALUE and SATURATION must be on 1, while HUE x(D). Only when you make it move dynamically it will change colour. You must remember to hide the construction to have the artistic effect.
Norma Lisa

##### Archimedean Spiral with SpreadSheet (IT)

Students are working on the Archimedean Spirals, I am waiting for their tutorials then I shall publish the outcomes

##### spiral with Scratch

My 5th grade students were very keen to modify the given script to create a spiral. (Renata)
Sorry, I haven't seen your comment. I will serach for it and send the link via email. (Monika, GER)

##### Mblock based on scratch

It is Mblock. Mblock based on scratch is easier than Arduino. Almost all the 9th grade classes of the Technological and Economical Pole of my school are working in a Robotics project. The IT teachers use the same installed program both for Mbot robots and for scratch. My students has started with me Robotics and with the IT teacher Scratch. Robotics covers three subjects: Physics, IT, Maths. Hopefully in a year or two I'll get better in programming. It is a challenge for me to learn by myself, through courses and with my students.
Norma Lisa