Quote of the Day
I think the surest sign that there is intelligent life out there in the universe is that none of it has tried to contact us.
— Calvin and Hobbes
Figure 1: Ellipses are Common in Carpentry (Source).
Today, I received an issue of Fine Homebuilding Magazine (Dec/Jan 2011) that contained a bit of math that caught my eye. In this issue's "Tips & Techniques" section, there is a short piece called "A No-Math Method to Draw An Ellipse." Of course, this method does use mathematics, just no equations. It is a nice little geometric construction.
The basic construction approach shown here requires only a compass and square – tools in every carpenter's kit. Figure 2 illustrates the basic approach. First, draw two circles, one having a diameter equal to the ellipse's major axis and the other having a diameter equal to the ellipse's minor axis. You can locate points on the ellipse by drawing a number of lines through the axes' origin and both circles. For each line, draw perpendiculars from the line's intersection points on the outer and inner circles to the x and y-axes, respectively (see Figure 2). The intersection of the perpendiculars determines the points on the ellipse. Once we have a sufficiently dense set of points on the curve, we can accurately draw an ellipse by interpolating between the points. Carpenters usually interpolate between the points using a thin strip of wood called a spline.
Figure 1: Ellipse Construction Using Compass and Square.
If you want a proof that this construction produces an ellipse, all you need is a bit of algebra.
