I’ve posted before about how even though in the US we define squares to be equilateral rectangles, there are many forces (often in the form of picture books on shapes) that treat squares and rectangles as distinct beings, and so it is really no surprise that many students reach college a little uncertain. The mathematical definition doesn’t match the cultural one.
Anyway, this week in Geometry I was going over Euclid’s definitions, and I pointed out that he wrote explicitly that rectangles (oblongs) weren’t allowed to have four equal sides, which is different than the definitions we use today.
Then one of my students spoke up. Katie is a senior math major getting certified to teach elementary & middle school, and this past fall she did part of her student teaching in Wales (courtesy of a study abroad program here at the college). She was in a 5th grade class, and according to their formal curriculum squares are not rectangles. Indeed, Katie said that the definitions they used were pretty much the same as what appears in the translation of Euclid (rectangles have four right angles but can’t be equilateral; rhombi have four equal sides but can’t have right angles; parallelograms have parallel sides, but can’t be equilateral or have right angles).
Similarly, when she taught about diamonds, she couldn’t call them squares even if they had four equal sides and four right angles. She had to prove the same rules twice (say, that the diagonals of a square are equal, and that the diagonals of a equiangular diamond are equal) and when she drew them, she had to add a line to show whether the figure she was referring to was a square or a diamond.
That explains this Failblog post from last October:
(I’m not sure if this picture was from Wales, but she did see Shreddies in the store there. She really liked the frosted kind.)
So now I’m wondering: how are geometric figures (squares versus rectangles and the like) defined in other countries?
The image above is from Oliver Byrne’s way-cool color edition of Euclid’s Elements.