Designs and patterns, music and
fractions…and mathematics
Ray Sutton with thanks to Jacky Hoare
June 26th 2008
Quilt pattern
Have a look at the quilt and try to identify
the details of the pattern.
Given that this kind of quilt does not have
to be stitched one square at a time, think
of an efficient way of making it.
Objectives
To appreciate the richness of the links
between mathematics and arts
To experience relevant activities and reflect
on how they might be adapted and
extended for use in the classroom
To explore relevant websites
www.problempictures.co.uk/examples
Websites
www.earlywomenmasters.net/quilts/
www.philtulga.com (Time for music!)
Patterns we see as we go
The works of MC Escher
www.tessellations.org
Explore the art
Identify the symmetries of translation, rotation,
reflection, glide reflection
Look for symmetries in an Escher pattern
Try to match to one of the 17 plane symmetry
patterns
Create your own Escher pattern
www.tessellations.org
http://incompetech.com/graphpaper
http://www.mcescher.com/,
http://mathforum.org/geometry
The works of MC Escher
www.tessellations.org
Explore the art
Identify the symmetries of translation, rotation,
reflection, glide reflection
Look for symmetries in an Escher pattern
Try to match to one of the 17 plane symmetry
patterns
Create your own Escher pattern
Maths everywhere
– from the graph paper website
Calculating various bits about regular hexagons
Given length of a side x...
Tip to tip across the hex is 2x.
Height of the hex flat side to flat side is 2x(sqrt(3/4)) or about 1.732x.
Area of the hex is 1.5(x^2 (sqrt(3)) or about 2.56x^2.
Example: Making graph paper with 4 hexes per square inch
Hexagon with a side length of x... The area of that hex would be about...
2.6 (x^2)
So for 4 hexes per square inch...
4 * 2.6 (x^2) = 1
x^2 = 1/10.4
x^2 = .096
x = .31 inches per side.
Extra: 1 sq. in. per hex ~= 0.6204
www.pims.math.ca/pi/cartoons.html - copyright W.Krawcewicz, University of
Alberta
ray.sutton@ncetm.org.uk