This week I’ve been working through MS221 Chapter A2: Conics, and although I’m enjoying the chapter, I’m having a huge amount of trouble with sketching curves. I’m not sure whether my hands are particularly unsteady, or whether I’ve got terrible hand-eye coordination, but when I draw an ellipse it always ends up looking feathery and lumpy. A bit like a cross between one of these:

and one of these:

So I’m drawing a few practice curves every day at the moment, in the hopes that drawing eleventy billion hyperbolas, parabolas and lemons ellipses will train my hands to be steady enough to cope with drawing curves in the exam.

Apart from the sketching issue, I’m having lots of fun learning about conics. I didn’t really enjoy the corresponding chapter in MST121, the one about lines and circles, but for some reason I find the conic sections very appealing – I was cooing and pointing at the screen every five minutes during the “Visualising Conics” section of the MS221 DVD. There’s just something awesome about watching the transition of the curve from ellipse to parabola to hyperbola as the angle of the intersecting plane changes.

The section of Chapter A2 dealing with the focus-directrix property particularly wowed me too. I had a bit of trouble grasping the concept until I found this page which includes a nice applet that lets you change the eccentricity, focus and directrix of the curve, and thankfully after a few minutes of playing with the applet my understanding of the relationship went from “huh?” to “ooooh!”.

Similarly, the section about parametrised equations for curves took a little bit of repetition to really sink in, but I’m pretty happy with the subject now. And I’m especially happy about parametrisation exercises that involve sketching curves, since they allow me to plot several points of the curve rather than just the vertices, and the more points I plot the easier sketching the curve becomes. Unfortunately the TMA01 question involving curve sketching seems to only want us to plot the vertices and centre, but I might plot a few extra points as a guide anyway, otherwise my sketches will have a distinctly lemony appearance…