Designs and patterns, music and fractions…and mathematics

Ray Sutton with thanks to Jacky HoareJune 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 artIdentify the symmetries of translation, rotation,

reflection, glide reflectionLook for symmetries in an Escher patternTry to match to one of the 17 plane symmetry

patternsCreate your own Escher pattern

www.tessellations.org

http://incompetech.com/graphpaperhttp://www.mcescher.com/, http://mathforum.org/geometry

The works of MC Escher

www.tessellations.org

Explore the artIdentify the symmetries of translation, rotation,

reflection, glide reflectionLook for symmetries in an Escher patternTry to match to one of the 17 plane symmetry

patternsCreate your own Escher pattern

Maths everywhere – from the graph paper websiteCalculating 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) = 1x^2 = 1/10.4x^2 = .096x = .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