a shape is shown

enlarge it by a scale factor that is the square root of 2

one of the shorter lengths or the shortest length is shown

then enlarge by this scale factor again

again a/the shorter/shortest length is shown

the shapes should not overlap with the original or each other

this can be done or confirmed by dissecting the shapes into simpler shapes (e.g. right angled triangles)

or you can use Pythagoras and multiply surds

students can compare the areas of the original and enlarged shapes

a previous version of this task seemed difficult:

## Wednesday, 16 July 2014

## Tuesday, 15 July 2014

## Sunday, 13 July 2014

### river crossing

some puzzles with a long history, variations appearing in many cultures

there are phone aps for several of these

a flash version of this at onlybestflash

see wikipedia article

NRICH 5916 goes full screen

there are phone aps for several of these

a flash version of this at onlybestflash

see wikipedia article

NRICH 5916 goes full screen

## Friday, 27 June 2014

## Thursday, 26 June 2014

### angle proofs

thanks to gogeometry

and the UKMT junior challenge

and Doug French, when he was at Hull University

for several of these ideas

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