Art in the Mathematics classroom: Charlotte Webb http://tiny.cc/IslamicGeometry Islamic Geometry
Art in the Mathematics classroom: Islamic Geometry
Mar 17, 2023
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Art in the Mathematics classroom: Islamic GeometryCharlotte Webb
1) hexagon
2) square
3) octagon*
4) pentagon
*You will need this later!
Activity: Constructing polygons
Islamic Geometry
Charlotte Webb
Four-fold patterns Based on squares, octagons and multiples of those.
Five-fold patterns Based on pentagons, decagons and multiples of those.
Pattern from Manifesting the Unseen project
Six-fold patterns
Activity: 7 overlapping circles grid
Starting with a horizontal line and a circle, radius 7cm, and using only a ruler and pair of compasses, construct the seven circles grid.
This grid is the basis for all 6-fold patterns.
A hexagon drawn using the intersection of circles
Activity: 7 overlapping circles grid
1) Add all the lines between “petals” onto your grid.
2) Place tracing paper over the central circle.
3) Using regular polygons, can you make a 12-pointed star? What other shapes can you make?
Student activity: exploring the 7 circles grid
Can you make a different 12-pointed star?
Student activity: exploring the 7 circles grid
Student activity: six-fold construction
Draw two overlapping equilateral triangles
Draw one hexagon Where the triangles meet, draw channels (continuing to meet the hexagon)
Colour in and outline the final pattern.
Using a hexagonal grid, this pattern can now be tiled.
Student activity: six-fold construction
Three overlapping squares found within this 6-fold pattern
Student activity: 5 overlapping circles grid
Lines between petals shown here.
8-pointed star from two squares
This grid is the basis for all 4-fold patterns.
Student activity: Four-fold construction
Using 5 circles grid
Student Activity: Exploring tessellations
Semi-regular tessellations
Each vertex has the same pattern of polygons around it
Hexagon, square, triangle, square (back to hexagon)
Hexagon, square, triangle, square (back to hexagon)
Semi-regular tessellations
Demi-regular tessellations
Student Activity: Exploring tessellations • Using the ATM tiles, explore regular and
semi-regular tessellations.
• Can you find all the regular tessellations? How can you be sure?
• Can you find all the semi-regular tessellations?
• Write down any conjectures you have.
• Can you explain why some regular polygons will tessellate and others will not?
Exploring tessellations
Basic design principles: Underlying grids and polygons
Most Islamic art geometric patterns are based on grids of repeated equilateral triangles/hexagons or squares.
Basic design principles: Underlying grids and polygons
Basic design principles: Underlying grids and polygons
Regular tessellations as an underlying grid
Semi-regular tessellations as an underlying grid
Student Activity: Collaborative Islamic art
We are going to create a collaborative art piece based on the tessellation of 8-pointed starts and crosses.
Student Activity: Collaborative Islamic art
Challenge:
1) Using the Octagon you made at the start, create this 8 pointed star.
2) By adding in additional “channels”, create the inner 8-pointed star.
3) Decorate and add to the tessellation wall! Template from Ayesha Gamiet’s website
(octagon and 8-pointed star templates available for use with students).
Collaborative Islamic art
Tutorial video by Samira Mian: https://www.youtube.com/watch?v=YyYPzoysJUg&feature=youtu.be
Student Activity: Collaborative Islamic art
We are going to create a collaborative art piece based on the tessellation of 6-pointed starts and hexagons.
Student Activity: Collaborative Islamic art
Challenge:
1) Starting with a circle of radius 7cm (drawing on the back of the patterned paper), cut out a 6-pointed star.
2) Add it to the tessellation wall!
Activity from Met Museum Islamic Art and Geometric design PDF
Student Activity: Patterns that can from equilateral triangle (isometric) grid.
7 circles grid This is the basis of the triangular underlying grid. Continue adding circles to expand the grid.
From this you can create a large number of patterns, e.g:
Challenge: Create one of these patterns using the isometric grid.
instagram.com/charlottexgeometry/
creating patterns) • Islamic Design Workbook (patterns and grids
– great for beginners) • Islamic Geometric Design (history and design
principals of many designs)
Cosmological Approach – (more about the meaning behind patterns)
Islamic Art and Geometric Design PDF (https://www.metmuseum.org/-/media/files/learn/for- educators/publications-for- educators/islamic_art_and_geometric_design.pdf) • Free activities/resources
Samira Mian (www.samiramian.uk) • YouTube videos/tutorials
Sources of inspiration: Websites
Art of Islamic Pattern (https://artofislamicpattern.com/#/0) • Resources, Courses • Study trips (e.g. to Morocco)
Ayesha Gamiet (http://ayeshagamiet.com/pattern-in-islamic-art/teaching-resources- islamic-art/) • Classroom resources • Blog posts, ideas.
• The Alhambra, Granada
• Seville
Art in the Mathematics classroom:
Starting with a horizontal line and a circle, radius 7cm, and using only a ruler and pair of compasses, construct a regular: 1) hexagon2) square3) octagon*4) pentagon(recommend starting with a new circle each time).*You will need this later!
Art in the Mathematics classroom:
From “Islamic Geometric Design” by Eric Broug
Based on squares, octagons and multiples of those.
Based on pentagons, decagons and multiples of those.
Based on triangles, hexagons, dodecagons and multiples of those.
Starting with a horizontal line and a circle, radius 7cm, and using only a ruler and pair of compasses, construct the seven circles grid.
This grid is the basis for all 6-fold patterns. A hexagon drawn using the intersection of circles
1) Add all the lines between “petals” onto your grid.2) Place tracing paper over the central circle. 3) Using regular polygons, can you make a 12-pointed star? What other shapes can you make?
Can you make a different 12-pointed star?
Draw two overlapping equilateral triangles
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 36
Slide Number 37
Slide Number 38
Slide Number 39
This is the basis of the triangular underlying grid. Continue adding circles to expand the grid.From this you can create a large number of patterns, e.g:
Slide Number 41
THANK YOU
1) hexagon
2) square
3) octagon*
4) pentagon
*You will need this later!
Activity: Constructing polygons
Islamic Geometry
Charlotte Webb
Four-fold patterns Based on squares, octagons and multiples of those.
Five-fold patterns Based on pentagons, decagons and multiples of those.
Pattern from Manifesting the Unseen project
Six-fold patterns
Activity: 7 overlapping circles grid
Starting with a horizontal line and a circle, radius 7cm, and using only a ruler and pair of compasses, construct the seven circles grid.
This grid is the basis for all 6-fold patterns.
A hexagon drawn using the intersection of circles
Activity: 7 overlapping circles grid
1) Add all the lines between “petals” onto your grid.
2) Place tracing paper over the central circle.
3) Using regular polygons, can you make a 12-pointed star? What other shapes can you make?
Student activity: exploring the 7 circles grid
Can you make a different 12-pointed star?
Student activity: exploring the 7 circles grid
Student activity: six-fold construction
Draw two overlapping equilateral triangles
Draw one hexagon Where the triangles meet, draw channels (continuing to meet the hexagon)
Colour in and outline the final pattern.
Using a hexagonal grid, this pattern can now be tiled.
Student activity: six-fold construction
Three overlapping squares found within this 6-fold pattern
Student activity: 5 overlapping circles grid
Lines between petals shown here.
8-pointed star from two squares
This grid is the basis for all 4-fold patterns.
Student activity: Four-fold construction
Using 5 circles grid
Student Activity: Exploring tessellations
Semi-regular tessellations
Each vertex has the same pattern of polygons around it
Hexagon, square, triangle, square (back to hexagon)
Hexagon, square, triangle, square (back to hexagon)
Semi-regular tessellations
Demi-regular tessellations
Student Activity: Exploring tessellations • Using the ATM tiles, explore regular and
semi-regular tessellations.
• Can you find all the regular tessellations? How can you be sure?
• Can you find all the semi-regular tessellations?
• Write down any conjectures you have.
• Can you explain why some regular polygons will tessellate and others will not?
Exploring tessellations
Basic design principles: Underlying grids and polygons
Most Islamic art geometric patterns are based on grids of repeated equilateral triangles/hexagons or squares.
Basic design principles: Underlying grids and polygons
Basic design principles: Underlying grids and polygons
Regular tessellations as an underlying grid
Semi-regular tessellations as an underlying grid
Student Activity: Collaborative Islamic art
We are going to create a collaborative art piece based on the tessellation of 8-pointed starts and crosses.
Student Activity: Collaborative Islamic art
Challenge:
1) Using the Octagon you made at the start, create this 8 pointed star.
2) By adding in additional “channels”, create the inner 8-pointed star.
3) Decorate and add to the tessellation wall! Template from Ayesha Gamiet’s website
(octagon and 8-pointed star templates available for use with students).
Collaborative Islamic art
Tutorial video by Samira Mian: https://www.youtube.com/watch?v=YyYPzoysJUg&feature=youtu.be
Student Activity: Collaborative Islamic art
We are going to create a collaborative art piece based on the tessellation of 6-pointed starts and hexagons.
Student Activity: Collaborative Islamic art
Challenge:
1) Starting with a circle of radius 7cm (drawing on the back of the patterned paper), cut out a 6-pointed star.
2) Add it to the tessellation wall!
Activity from Met Museum Islamic Art and Geometric design PDF
Student Activity: Patterns that can from equilateral triangle (isometric) grid.
7 circles grid This is the basis of the triangular underlying grid. Continue adding circles to expand the grid.
From this you can create a large number of patterns, e.g:
Challenge: Create one of these patterns using the isometric grid.
instagram.com/charlottexgeometry/
creating patterns) • Islamic Design Workbook (patterns and grids
– great for beginners) • Islamic Geometric Design (history and design
principals of many designs)
Cosmological Approach – (more about the meaning behind patterns)
Islamic Art and Geometric Design PDF (https://www.metmuseum.org/-/media/files/learn/for- educators/publications-for- educators/islamic_art_and_geometric_design.pdf) • Free activities/resources
Samira Mian (www.samiramian.uk) • YouTube videos/tutorials
Sources of inspiration: Websites
Art of Islamic Pattern (https://artofislamicpattern.com/#/0) • Resources, Courses • Study trips (e.g. to Morocco)
Ayesha Gamiet (http://ayeshagamiet.com/pattern-in-islamic-art/teaching-resources- islamic-art/) • Classroom resources • Blog posts, ideas.
• The Alhambra, Granada
• Seville
Art in the Mathematics classroom:
Starting with a horizontal line and a circle, radius 7cm, and using only a ruler and pair of compasses, construct a regular: 1) hexagon2) square3) octagon*4) pentagon(recommend starting with a new circle each time).*You will need this later!
Art in the Mathematics classroom:
From “Islamic Geometric Design” by Eric Broug
Based on squares, octagons and multiples of those.
Based on pentagons, decagons and multiples of those.
Based on triangles, hexagons, dodecagons and multiples of those.
Starting with a horizontal line and a circle, radius 7cm, and using only a ruler and pair of compasses, construct the seven circles grid.
This grid is the basis for all 6-fold patterns. A hexagon drawn using the intersection of circles
1) Add all the lines between “petals” onto your grid.2) Place tracing paper over the central circle. 3) Using regular polygons, can you make a 12-pointed star? What other shapes can you make?
Can you make a different 12-pointed star?
Draw two overlapping equilateral triangles
Slide Number 13
Slide Number 14
Slide Number 15
Slide Number 16
Slide Number 36
Slide Number 37
Slide Number 38
Slide Number 39
This is the basis of the triangular underlying grid. Continue adding circles to expand the grid.From this you can create a large number of patterns, e.g:
Slide Number 41
THANK YOU
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