parabola

Building on my last post, here is another way to construct a parabola using a collection of straight lines. First, the description, taken from Lockwood’s A Book of Curves (page 7): Draw any two lines and mark on each a series of points at equal intervals. (The intervals on the second line need not be equal to those on the first.) Call the points on the first line $A_1, A_2, A_3$, etc.

There are several ways to draw a parabola using straight lines. If you get a chance, you should try one sometime - it is always satisfying to see the outline of a curve slowly emerging from a collection of straight lines. One method uses a set-square. As described in A Book of Curves by E.H. Lockwood (page 3): Draw a fixed line $AY$ and mark a fixed point $S$. Place a set square $UQV$ (right-angled at $Q$) with the vertex $Q$ on $AY$ and the side $QU$ passing through $S$ (Fig.