## Sunday, 19 October 2014

## Saturday, 18 October 2014

## Tuesday, 14 October 2014

### decomposition

work out each of the areas of the pieces and check that they total to 21 squares

find the area of each piece and check that they total 18 squares

find the area of each piece and check that they total 18 squares

## Sunday, 12 October 2014

## Saturday, 11 October 2014

### Lee Westwood and Sama Mara

maybe you should play these videos to your students

a collaboration between a composer (Lee) and an artist and geometer (Sama):

fascinating kaleidoscopic patterns, fully synchronised to an effective musical score

their work ('a hidden order') is to be found here

there is (static) art work as well as videos and other ways to explore generated patterns

several Vimeo videos explore their interpretation of the relationship between pattern and music including:

triangle ensemble

hexagon 1 ensemble

and, my favourite,

octagon 1 flute and marimba

thanks to J Mowl for bringing this to my attention

a collaboration between a composer (Lee) and an artist and geometer (Sama):

fascinating kaleidoscopic patterns, fully synchronised to an effective musical score

their work ('a hidden order') is to be found here

there is (static) art work as well as videos and other ways to explore generated patterns

several Vimeo videos explore their interpretation of the relationship between pattern and music including:

triangle ensemble

hexagon 1 ensemble

and, my favourite,

octagon 1 flute and marimba

thanks to J Mowl for bringing this to my attention

## Friday, 10 October 2014

### growing rectangles

width of 2

width of 3

squares

relating the perimeter to the numbers of inside dots

alternatively all three variables can be related to the (unknown) length (L) for the various (fixed) widths

you could also explore isometric shapes where the unit of area is the small equilateral triangle...

Labels:
generalising,
investigation,
nth term,
proof

## Sunday, 5 October 2014

### Euclid in pictures

Oliver Byrne produced a version of 'Elements of Euclid' in 1847 with colour used to emphasise relationships and very little text

this is proposition (theorem) 43 from Euclid Book 1

this theorem was intended to establish how to transform one parallelogram to another, of equal area and with the same angles

students could be asked to provide the words for this sequence of diagrams

a very helpful compendium of the works of 'Euclid' is provided by David E Joyce

at Clark University in Worcester, MA

this is proposition (theorem) 43 from Euclid Book 1

this theorem was intended to establish how to transform one parallelogram to another, of equal area and with the same angles

students could be asked to provide the words for this sequence of diagrams

a very helpful compendium of the works of 'Euclid' is provided by David E Joyce

at Clark University in Worcester, MA

## Saturday, 4 October 2014

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