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# Islamic Patterns

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## Daniel Kage

on 29 January 2016

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#### Transcript of Islamic Patterns

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:
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
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
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
The Great Mosque of Herat. Herat, Afghanistan.
The Huand Hatun Complex. Kayseri, Turkey
The Mosque of al-Salih Tala'i. Cairo, Egypt.
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
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
Full transcript