Pointer talks about Squares
The idea for Squares in Magpie 257 came from a little problem I created for my pupils some time ago:
Fit together the three identical L-shapes to make a square.
After practical investigation, the pupils would be encouraged to relate the area of a square to the sum of the three areas. However, the trick in the solution is to form the representation of a square number from the three pieces. And we can refer to a square number as simply a square. This may be compared to what we say in describing Pythagoras’ Theorem, viz. “the square on the hypotenuse …”. We may picture the geometry of a square constructed on the longest side…, or we may think of (length of side)2. As another example, I recall from my own schooldays in lessons on Euclidean geometry, we were to interpret rectangle as product. For instance, we encountered “where two chords of a circle intersect, the rectangle contained within the segments of one chord equals the rectangle contained within the other chord. I’m sure the language used in geometry textbooks has moved on a lot since then. By the way, does anyone remember using the term “Rectangle Theorem” to describe what is now known as “the Intersecting Chords Theorem”?