median
don steward
mathematics teaching 10 ~ 16

## Saturday, 29 November 2014

### triangle and quadrilateral tessellations

a tessellation of a triangle:
label each of the angles on the grid with the appropriate letter:
(a , b or c)

what are the angles in a complete turn? (2a + 2b + 2c)

in half a turn?
what happens on parallel lines?

find various quadrilaterals on the grid

decide which the inside corner angles are

write down what they are in terms of a , b  and c

look at various pentagons or hexagons drawn on the grid

decide which the corner angles are

write down what they are in terms of a , b and c

to complete the tessellations encourage students to draw the three sets of parallel lines - so that their tessellations go to the edges of the dotty grids
the triangles are chosen so that they can be rotated (180 degrees) about the mid-points of the sides

every tessellation of a quadrilateral is a disguised tessellation of parallelograms

which is a tessellation of the triangle that is half of the parallelogram
there are various 'skeleton' (as David Wells calls them) tessellations of parallelograms that can be discerned

the easiest to 'see' is the one that joins corresponding corners - based on the vectors that they translate through to generate the tessellation

hinged tessellation by Al Grant
(there are interactive versions)