Well, it s Gabriel, Gabriel playin !
Gabriel, Gabriel sayin
When I blow my horn?
- Cole Porter,
Anything Goes
The commenters in last week s Sunday Function proposed an excellent idea for this week. As we did then, we ll start simple and work up to it. Graph the curve f(x) = 1/x.
Now take the horizontal axis and think of it as an axle, one that can rotate smoothly. Hook a motor onto it and spin it up to a nice fast clip. The graph of the function will trace out a surface in three-dimensional space. In the business, we call it a
We've done a lot of discussion of the concept of integrals of a function here on this blog. Their definitions and applications are so broad as to defy any one-sentence description, but one of the most basic is the idea of the area under a curve. More precisely it's the signed area under the curve - that is, the area above the x-axis is counted as positive and the area under counts as negative. Stealing the image from Wikipedia, which communicates the concept well:
Saw "Up" yesterday. How Pixar manages to be so consistent in their astonishing quality is entirely beyond me. In a bit of a tribute, this Sunday Function is not about any dramatically important special function, but instead it's about filling a balloon. Air or water, as your preference.