You've probably seen this shape before. It is several straight lines whose outline seems to be curved. Connect the following pairs of points with segments:

(1,0) and (0,8)
(2,0) and (0,7)
(3,0) and (0,6)
...
(8,0) and (0,1)

The 8 segments seem to form the outline a curve, but what curve? Is it a circle or maybe one branch of a hyperbola? Some other conic? Does it's equation have some other nice form?

In fact all agree its a section of a parabola, as broll originally pointed out, and Steve Herman's portion of a superellipse is, as he states, part of a parabola, as the special case of a superellipse, and my computer finding that it's a portion of a parabola. So there actually seems to be no disagreement that this is a section of a parabola, that is also a section of a particular type of superellipse.

Posted by Charlie on 2017-04-19 20:36:36