The document describes a journey through the Alhambra Palace in Granada, Spain led by the renowned artist P. π-kasso. It discusses several architectural features of the palace like the Lions Court and Comares Tower. It also explains how Islamic art like the ceilings uses basic geometric patterns repeated through translations, reflections, and rotations along with different colors, producing multicolored geometric figures. The document aims to reveal the techniques of Islamic geometric art through this example.

1. Arabesque and linear
algebra
A journey to the magical world of artistic
mathematics and the riddle of P. π-KASSO
Created by:
Ali LABBENE ( )
Copyright © 2020 Ali LABBENE. P. π-KASSO and all related characters and elements © Ali LABBENE.
Version 1.0 (07/05/2020)

2. World-renowned artist P. π-kasso invites
us to a walk in the famous Alhambra
Palace in Granada, south of Spain.
Source: www.tripsmaps.com (visited 05/25/2020)
2

3. World-renowned artist P. π-kasso invites
us to a walk in the famous Alhambra
Palace in Granada, south of Spain.
Source: www.tripsmaps.com (visited 05/25/2020)
3
The works of P. π-kasso are considered
masterpieces by many art critics.

4. Source: www.travelingturks.com (visited 06/07/2020)
Welcome to the Alhambra, a jewel
of Islamic art in western Europe.
4

5. On these photos, you can admire the
Lions Court, in the Nasrid Palaces.
Source: www.travelingturks.com (visited 05/30/2020)
5

6. On these photos, you can admire the
Lions Court, in the Nasrid Palaces.
Source: www.travelingturks.com (visited 05/30/2020)
6

7. On these ones, the Comares tower.
In the Nasrid Palaces too.
Source: www.alhambra.org (visited 05/30/2020)
7

8. On these ones, the Comares tower.
In the Nasrid Palaces too.
Source: www.alhambra.org (visited 05/30/2020)
Source:www.losviajesdenena.com(visited07/06/2020)
8

9. Source:www.losviajesdenena.com(visited07/06/2020)
Source:www.wmuseum.ru(visited07/06/2020)
On these ones, the Comares tower.
In the Nasrid Palaces too.
Source: www.alhambra.org (visited 05/30/2020)
9

10. Still in the Nasrid Palaces, This is a
detail from the ceiling of the
Ambassadors hall.
Source: www.evainmadrid.wordpress.com.com (visited 05/30/2020)
10

11. (*) Pure invention of the author for the sake of this riddle.
11
This old parchment - one of a few found - *
provides precious indications about One of the
most typical techniques of this Islamic art.

12. (basic pattern)
12
As you may have noticed, a basic pattern is repeated
using geometric operations of translation,
reflection, and rotation.

13. (basic pattern)
13
As you may have noticed, a basic pattern is repeated
using geometric operations of translation,
reflection, and rotation.

14. (basic pattern)
14
As you may have noticed, a basic pattern is repeated
using geometric operations of translation,
reflection, and rotation.

15. (basic pattern)
15
As you may have noticed, a basic pattern is repeated
using geometric operations of translation,
reflection, and rotation.

16. (basic pattern)
16
As you may have noticed, a basic pattern is repeated
using geometric operations of translation,
reflection, and rotation.

17. (basic pattern)
17
(Geometric figure obtained)
As you may have noticed, a basic pattern is repeated
using geometric operations of translation,
reflection, and rotation.

18. (*) Pure invention of the author for the sake of this riddle.
(basic pattern)
1,0 0,0
0,0 1,0
-1,0 0,0
0,0 -1,0
‫ا‬‫بيض‬
(Geometric operations and
colours used)
0,0 -1,0
1,0 0,0
18
0,707 -0,707
0,707 0,707
White ‫اصفر‬Yellow
‫ا‬‫حم‬‫ر‬Red‫ا‬‫ز‬‫ر‬‫ق‬Blue
a different colour is used to repeat the basic
pattern Each time*. The geometric figure
obtained is a multicoloured one.
(Geometric figure obtained)

19. (basic pattern)
1,0 0,0
0,0 1,0
-1,0 0,0
0,0 -1,0
(Geometric figure obtained)
‫ا‬‫بيض‬
(Geometric operations and
colours used)
0,0 -1,0
1,0 0,0
19
0,707 -0,707
0,707 0,707
White ‫اصفر‬Yellow
‫ا‬‫حم‬‫ر‬Red‫ا‬‫ز‬‫ر‬‫ق‬Blue
Now, if you have followed my explanations, you
should be able to reproduce that geometric
figure using the right colours. Shouldn’t you?