Long ago back in the days when I used to teach maths to classes of unruly fifteen year olds, this time of year always brought cries of "Not more algebra miss, can't we do something fun instead of lessons?" And this was always one of my standbys... mathematical, seasonal and fun... well I thought so!
You will need twenty old Christmas cards, a compass and pencil, a biro, a ruler, scissors and glue. Before you express amazement that I was organised enough to keep my Christmas cards from last year in order to make this year's decorations, let me put you right. The bag of old cards was discovered hanging on the back of a cupboard door where I had put them ready to be recycled...and then forgotten all about them all year. Needless to say it's a while since I cleared out that cupboard.
Anyway... back to the task. I used a radius (here comes the maths) of about 4cm which gives a finished decoration about 15 cm across. On the back of one of the cards draw a circle using the compass. Then placing the point of the compass on the circumference, draw an arc on the circumference as in the photo.
Move your compass, so that the point is now at the point where the arc cuts the circumference and draw another arc. Repeat around the circle until you have divided the circumference into six equal parts. This will only work if you are accurate in placing your compass and you do not change the radius.
With a biro, and pressing hard, join alternate arcs on the circumference to give an equilateral triangle (I hope you are impressed by the amount of maths I'm throwing in here). Then cut out your circle.
By pressing hard with the biro you will have also scored along the lines so they can be folded giving a triangle with flaps.
Which should look like this! Hands up everyone whose circle looks like this....
Now repeat nineteen more times so that you end up with twenty identical folded triangles.
The next step is to take five of your triangles and begin by glueing two of them together by their flaps.
At this stage it should look like this.
Continue glueing the remaining three triangles to the first pair so that you end up with something that looks a bit like a hat. Much easier to demonstrate than to explain!
Set your "hat" aside and repeat with another five triangles, this time trapping a ribbon loop in the apex, from which to hang your decoration.
Then glue the remaining ten triangles into a strip as shown below.
Join the strip of ten triangles into a ring by glueing the first and last flaps together.
Almost there... Now take one of your "hats" and glue it to the top of your ring, matching the flaps.
Turn it upside down and glue the remaining "hat" to the bottom of your ring, again matching the flaps.
And hey presto... your decoration... which just in case you were wondering is actually an icosahedron.
Of course by now my class of fifteen years olds would be having lots of non-mathematical fun, playing darts with the compasses and football with their icosahedra... but you are far too sensible.
If you are not as
slovenlyorganised as me and don't have a handy stash of old Christmas cards... any card will do and you could always spray the finished item gold if it doesn't look festive enough!