**Islamic Patterns**

**by Daniel Kage**

Sacred Geometry patterns

Geometric constructions

With only a compass and a ruler:

1st. Day:

-Line constructions:

-Perpendicular and Bisector

-Bissector of an angle

-Parallel

-Division of segment

-Circle and constructions of polygons inscribed in a circle.

-Symmetry of arcs and Spirals. (Vegetal patterns)

- Constructions of grids

2nd. Day:

- Construction of grids, motifs & rosettes (stars)

-Double line and enlace techniques

3rd.Day:

- Create your own pattern

Perpendicular line

Bisection of angle

Parallel line

Division of segment in equal parts

Construction of Polygons through the Vesica Piscis & circles

Triangle (3 sides)

Square (4 sides)

Pentagon (5 sides)

Hexagon (6 sides)

Heptagon (7 sides)

Octagon (8 sides)

Enneagon (9 sides)

Decagon (10 sides)

Dodecagon (12 sides)

Arabesques and vegetal patterns:

Symmetry of Arcs and Spiral constructions

Archimedean Spiral

Policentric Spiral

Spiral with three centers

Spiral with 4 centers

Spiral of 6 centers

Oval (Elipse)

Symmetry of arcs through points

Curved, vegetal and floral motifs

(16:00)

Square and Hexagon divisions

4 and 12

8 and 16

6 and 12

1. Draw a line and the point P

2. From point P trace A and B with same distance using the compass

3.Compass with distance bigger than half of AB, make an arc finding C.

4. Draw the perpendicular line.

1. Draw a line and a point P

2. From P make an arc intersecting the line.

3. From A and B draw two arcs intersecting each other (point C).

1. Draw an angle.

2. With compass, draw two arcs intersecting the angle.

3. From the arc, two more arcs intersecting each other.

4. Draw the line from the vertex passing through the intersection.

1.Draw a line

2. Draw two bisectors.

3. Compass with same distance, find point E

4. Draw the parallel line.

1. Draw a line

2. From A and B draw an arc

3. Compass with same distance, draw an angle

4. Divide the parallel lines in equal parts.

5. Connect the points of the parallel lines.

6. The intersections through AB show the division.

1. Draw an arc and a point

2. Bisector from T (end of arc) and P (point)

3. Draw a line from T passing through the center of the arc intersecting the bisector.

4. Draw the arc with center in the intersection.

1. Draw an arc and a point.

2. Bisector from T (end of arc) and P (point)

3. Draw a line from the center of the arc passing through T intersecting the bisector.

4. Draw the arc in a opposite direction.

Repeat the method from the previous examples.

Symmetry of two arcs with two other ones.

1. Draw two arcs with different sizes and a segment of line

2. Draw 2 other segment lines with the measure of each radius of the arc plus the segment of line

3. Draw the two prolongated segments so that they intersecting each other twice.

4. Draw two arcs from the intersecting points.

1. Draw a line AB

2. Divide in four equal segments

3. Draw the bisector between the first and second point and find O1.

4. Draw two circles with center in O1, distance O1A and the small one with diameter 1/4 of the segment.

5. Draw a second circle with center in O2 and distance O2B.

6. Draw two lines from C and D connecting O2

7. Bisector of these lines connecting the bisector of the first and second point

8. Draw the arc connecting the two intersected circles.

Elipses

1. Draw a line AB

2. Draw the Vesica Piscis (in blue)

3. Draw the lines from the intersection of circles passing through the intersection of the circle with the center line

4. With the center in the intersection of the Vesica Piscis, draw the arcs connecting the circles.

1. Draw a line AB

2. Divide the segment of line in 4

2. Draw the two circles with compass distances 1A and 3B .

3. With the compass distance 1-3, find points C1 and C2 using the bisection method.

4. Draw the arcs connecting the circles.

1. Draw a line

2. Divide the line in four equal parts using the method of bisector.

3. Bisector of A-2 to find point 1

4. Compass with distance 1A, center in 1, draw the first arc.

5. Compass with distance 2A, center in 2, draw the second arc.

6. Compass with distance 1C, center in 1, draw the third arc.

7. Compass with distance 2C, center in 2, draw the forth arc.

1. Draw the equilateral (equal sides) triangle

2. Extend the sides

3 Draw the arcs in each angle, starting from the triangle. The center f the arc is always in the vertex of the triangle

1. Draw the square

2. Extend the sides

3 Draw the arcs in each angle, starting from the square. The center f the arc is always in the vertex of the square

1. Draw the hexagon

2. Extend the sides

3 Draw the arcs in each angle, starting from the hexagon. The center f the arc is always in the vertex of the hexagon.

1. Draw a circle and divide in any equal parts.

2. Draw the same number of concentric circles

3. Mark one point of intersection of each circle with one radius.

4. Draw the spiral connecting them.

Division of circumference ( General process)

1. Draw the circle

2. Divide the circle in 4 extending the horizontal line

3. Draw the two outside arcs intersecting the horizontal line with the distance AB

4. Divide the vertical line in equal parts

5. Draw lines from the points CD crossing every two points in the vertical line to the circle

6. Draw the polygon.

Line

Definition: Union of countless points

Polygons: number of sides

11 sides: hendecagon

12 sides: dodecagon

13 sides: tridecagon

14 sides: tetradecagon

15 sides: pentadecagon

16 sides: hexadecagon

17 sides: heptadecagon

18 sides: octadecagon

19 sides: enneadecagon

20 sides: icosagon

30 sides: triacontagon

40 sides: tetracontagon

50 sides: pentacontagon

60 sides: hexacontagon

70 sides: heptacontagon

80 sides: octacontagon

90 sides: enneacontagon

100 sides: hectogon

1000 sides: chiliagon

10.000 sides: myriagon

1.000.000 sides: megagon

infinitely many sides (supposed): apeirogon

53 sides: tripentacontagon

Polygons: number of sides

The 5 Platonic Solids & the 5 elements: Greek Plato, 350 B.C.

Cube (6 square faces): Element Earth

Muladhara (Root Chakra)/ square: the four elements, four seasons, four directions, protection, stability

Octahedron (8 triangular faces): Element Air

Anahata (Heart Chakra)

Vishuddha (Throat Chakra)

Icosahedron (20 triangular faces): Element Water

Swadhistana (Sacral Chakra)

Tetrahedron (4 triangular faces): Element Fire

Manipura (Solar Plexus Chakra)/ triangle: trinity - Father, Son and Holy Ghost united; mind, body and soul.

Dodecahedron (12 pentagonal faces): Element Ether

Ajna (6th Third Eye), 7th Crown (Sahasrara), 8th Higher Crown and above

Universe,Heaven/ pentagon: Humanity, the 5 physical senses, the 5 Elements

Grids (lattices)

- The first underlying lattice

- Repetition of circles and geometric shapes (hexagons, squares, composition of pentagons with other polygons)

Square

Islamic patterns in Sacred Geometry (2nd part)

1) Grid

2) Motifs and stars

3) Ornaments (double line, interlacing)

Pentagon

Hexagon

1) Grid

2) Motif

3) Ornaments

Square grid

Hexagonal grid

Motifs and Stars

- Basing on the grids, these patterns can be combined, duplicated, curved, interlaced and arranged in intricate combinations.

- Stars: The most popular motif. As the rays of the star reach out in all directions, it symbolizes the equal radiation of God throughout the world.

Motifs constructions

The Great Mosque of Cordoba. Cordoba, Spain

Square grid divided in eight equal parts

The great Mosque of Kairouan. Kairouan, Tunisia

Mustansiriya Madrasa. Baghdad, Iraq

The Great Mosque of Herat. Herat, Afghanistan.

The Alhambra Monument. Granada, Spain

The Huand Hatun Complex. Kayseri, Turkey

The Mosque of al-Salih Tala'i. Cairo, Egypt.

Ben Yusuf Madrasa. Marrakesh, Morocco

The Mosque of al- Nasir Muhammad. Cairo, Egypt.

Mamluk Koran. Damascus, Syria.

Ornaments:

Double lines, interlace technique, coloring and vegetal patterns (arabesques)

- Bring harmony and balance

- Enrich the geometric pattern

- Transform a line drawing in a elaborated geometric composition.

Three kinds of double line

How to draw double lines with compass and ruler

- Construct small circles in each intersection in the motifs

- Connect the circles creating parallel lines.

Vegetal patterns (Arabesques) and ornaments

How to draw interlaced lines

- Draw the double lines

- Make them go over and under one another in a alternating sequence.

Square grid divided in eight equal parts

Hexagonal divided grid in twelve equal parts

Hexagonal grid divided in twelve equal parts

Hexagonal grid divided in twelve parts

Square grid divided in eight equal parts

Square grid divided in sixteen parts

Square grid divided in twelve parts

Hexagonal grid divided in twelve equal parts

Square grid divided in twelve equal parts

Square in 8 parts

1) Divide the A3 paper in four equal parts

2) Draw the circle with 90 mm

3) Draw the square

4) Divide in 8 equal parts

Hexagon in twelve parts

1) Draw the circle in the center.

2) Draw the second circle (Vesica Piscis)

3) Draw 5 more circles around the center one.

4) Connect the intersections.

Square in 8 parts

Square in 8 parts

Hexagon in 12 parts

Hexagon in twelve parts

Square in 16 parts

Square in 12 parts

Hexagon in twelve

Square in 12 parts

Double line with the original line in bold.

Double line without the original line

Two sets of double line interlaced

Books:

Islamic geometric patterns by Eric Broug

Geometric concepts in Islamic art by Issan El- Said & Ayse Parman

Islamic patterns by Keith Critchlow

Links:

http://patterninislamicart.com/

Circle: The Creator, the Infinite

Triangle:

The 3 aspects of human beings: Body, mind, spirit

Square:

The 4 Elements. Earth, water, wind and fire.

Hexagon:

Heaven

Star or Rosette:

The spread of the light throughtout all the world

Rumi and Tepelik

1. Draw the horizontal line

2. Draw the circle

3. Place the compass on the intersection of the circle and line and draw the bisection

4. Draw four secondary circles of equal size around the one in the center.

1. Draw the horizontal line

2. Draw the circle

3. Place the compass on the intersection of the circle with the VERTICAL line and draw another circle

4. Place the compass on the intersection of the circles and draw 5 more circles around the centered one.

Perpendicular of segment

AB

Perpendicular passing through

P

Interlace patterns

The Flower of Life

Metatron's Cube