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## 'Clock Hands' printed from http://nrich.maths.org/

I've been wandering around the shops where I live in Cambridge -
there are a lot of shops that seem to be selling interesting
looking watches and clocks. Some challenges on NRICH are about
digital numbers but lots of people like to use an analogue clock or
watch instead. ('Analogue' for our use, means that it is not
digital and has a round face with two hands and twelve
numbers!)

Well, there are some fascinating ideas. I have a clock in which
the hands go around anticlockwise and so do the numbers! There are
so many designs, perhaps you've seen some and have been fascinated
by them.

I was wondering about different shaped hands. How about a pair
of square hands, but we will tilt each hand 45 degrees so that the
corner points and the opposite corner is in the centre. I've tried
drawing some of these ideas. (However I have not allowed the hour
hand to move and the hour is 12, it's only the minute hand that's
moving at the moment!). To help to understand the pictures I placed
a little dot where the hands are pointing.

So at 12 o'clock it would look like this:-

Every ten minutes later (Remember that I'm not allowing the hour
hand to move) we'll have:-

I like the overlap shapes that have been formed.

You could try this with paper squares and a pin stuck very, very
close to the corner that's pretending to be the middle of the clock
face. I do not have any coloured see-through sheets but I guess
that would be great, and even better if you can borrow the OHP in
the classroom.

Have a go and see what things occur as the minute hand moves and
you hold the hour hand still, look at shapes of overlap and a sort
of "Jaw" shape that opens and closes.

We should be used to asking "I wonder what would happen if
...?''

As you can guess I do this frequently and so I used my computer
to help me with an equilateral triangular one. Here they are:-

Of course why should we stop there? Circles!:-

You can try and explore all different designs. You don't have to
just look at the position every ten minutes like I have done; you
could try any minutes past/to that you liked.

If you are the sort of person who prefers to work with a clock
that the hour hand moves properly with the minutes hand then you
might like to look at these:-

Good luck.