A straight line can be drawn with a straightedge.
A circle can be drawn with a compass.
An ellipse can be drawn with string and pins.
How can we draw a parabola, using basic equipment?
Remarks
The parabola should be "perfect" (like a circle drawn with a compass), not just a rough sketch. As far as how much of the parabola should be shown: enough so that it looks like a "U".
We can use basic equipment such as string, pins, etc. The simpler the equipment, the better (so for example, a method using an unmarked straightedge is better than a method using a marked straightedge). High tech tools like computers are not allowed. You are given paper, pen and a flat table.
We can define a parabola as the set of points in a plane equidistant to a fixed line (directrix) and a fixed point (focus), or use any equivalent definition.
I tried to find how the ancient Greeks physically drew parabolas, but found nothing.
Students at my school made an almost-perfect parabola using strings and pins, by setting strings such that for each string the sum of its $x$– and $y$– intercepts is $30$, so the strings are tangent to an envelope curve $\sqrt x + \sqrt y = \sqrt{30}$, which is a rotated parabola.
But this is not quite what I'm looking for, because it's not quite perfect, as the number of strings is finite.
In this video a carpenter shows how to make a beautiful almost-perfect parabola, similar to the string art above, but again it's not quite perfect because the number of lines is finite.
If it's not possible to draw a perfect parabola using basic equipment, then is there an explanation?
Best Answer
Here is video of a brilliant "conic section compass".
Here is a closer look at how it works. It is very simple: the axis of the compass is the axis of a cone. The pencil is a slanting "edge" of the cone. The axis of the cone, and the axis of the pencil, intersect at the vertex of the cone. The paper is a plane intersecting the cone. The pencil traces the intersection of the plane and the cone - literally, a conic section.