Maths GIFs: parabolas
One of the fantastic features of dynamic graphing software is that you can animate how a graph changes as some aspect of it is varied. I'm particularly keen on making short GIFs of animated graphs that demonstrate interesting properties. One advantage of animated GIFs is that they are really easy to distribute via Twitter. There are loads of them if you have a look at the hashtag #mathgif . Parabolas I've been posting animated Maths GIFs to Twitter for quite a while now. Here are some of my favourites featuring parabolas: The midpoint of the points of intersection of y = x ² and y = mx + c lies on the line x = m /2. The tangent at point P to a parabola with vertex Q can be constructed by finding R, the point of intersection of the vertical through P and the horizontal through Q, finding the midpoint, M, of QR and then drawing the line through P and M. If the tangents at two points A and B on a parabola are perpendicular then the line AB goes through the focus and the tang