August 31st, 2006
A plat diviseur is a plate designed to make portioning cakes easy. Click here to see one. It works by putting dots at appropriate angles around the rim of the plate, so that when someone wants to cut, for example, five portions they merely cut from the center of the plate to wherever there is a five. For neatness one cut is always common, and tends to have just the number 0!
Displayed on screen this image could be used to motivate an activity in which students practice finding angles by creating their own plat diviseurs. It can be quite a fun activity, especially if you buy paper plates for them to use (though I recommend that they practice on paper first!).
They could also be asked which numbers are absent; they hopefully notice that 2,4 and 8 are missing. Discussing why can get into thinking about halving and fractions.
The reciprocity of 3 and 1/3, 5 and 1/5 can also be brought up, by discussing how often the image of a divided circle is often produced as a visualisation of proper fractions.
Since 5 and 7 are not factors of 360 this is also an interesting discussion point. While discussing factors, they should note that points for 3,6 and 9 are coincident at two points, and that if 2,4 and 8 are added what other numbers would have coincident points. I remember asking whether 10 and 12 would have coincident points if we had them as divisions too, which caused some thought.
Note that there are very few good images of plat diviseurs on the internet. I originally got the idea from Problem Pictures.