Posts Tagged ‘puzzle’
Hinged square dissection
In several recent posts I have referred to ‘linkages’ (which should more properly be called ‘hinged dissections‘. One good recent book on these is Hinged Dissections: Swinging and Twisting, by Greg Frederickson, but there are several classics out there that discuss hinged dissections, including Amusements in Mathematics by H. E. Dudeney.
Dudeney was responsible for one of the most well known hinged dissections, of which this is a simplified example. It converts a square into, well, something else.
The white circles are the hinges — move the coloured circles to move the corresponding parts of the square.
Can you predict what the end result of the transformation is? Can you prove it?
(Source: dudeney-dissection.ggb.)
The Haberdasher’s Puzzle
Dudeney’s classic dissection, published in his ‘Canterbury Puzzles‘ in 1907, is a slightly altered version of this, which allows you to transform a square into an equilateral triangle. You can download a program which will allow you print out a template for this here.
Constructing Dudeney’s dissection takes a touch more effort than the dissection illustrated above, but the process is described incredibly well in this lesson plan, which demonstrates how to make a model of the dissection using foam rubber. I haven’t tried it yet, but it may make a tempting break from lesson planning next week!
Tags: dissection, Dudeney, geogebra, linkage, puzzle
A quickie on quadratics
Fix two points in the plane, and consider all the quadratics which go through those two points.
Find the locus of the stationary points of these quadratics.
The following Geogebra worksheet might help. If you select “Show stationary point” and move the blue point, it will trace out the locus.
(Source: quadratic_stationary_points.ggb.)
Thinking about this question kept me from going to bed until far too late on Thursday. My answer, and other thoughts, will appear tomorrow.