median
don steward
maths teaching 10 ~ 16

Sunday, 19 October 2014

equations and equivalent fractions


problem number 8 of book 1 of Diophantus' Arithmetica (~ 200 CE) asks which number must be added to 100 and to 20 (the same number) so that the sums are in the ratio 3 : 1    these questions are in the same vein



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

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

Friday, 10 October 2014

rooftops





















then there are always 3D rooftops to explore...

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...







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