TITLE: Applications of visual calculus
QUESTION [16 upvotes]: Mamikon's visual calculus (see Mamikon, Tom Apostol, Wikipedia) is a very beautiful and surprisingly efficient tool.
The basis is

Mamikon's theorem. The area of a tangent sweep is equal to the area of its tangent cluster, regardless of the shape of the original curve.

For a nice picture, see this, and the following picture from Apostol's introduction:
    
 (source: Wayback Machine)
The above links provide interesting applications, like very easy ways to find the area of a cycloid and tractrix.

Question.

What are other new applications?
Are there new developments of visual calculus?
What are some similar visual results, which can simplify calculations, and can be included in visual calculus?

REPLY [3 votes]: Perhaps this previous MO question may help:
Taking “Zooming in on a point of a graph” seriously,
e.g., this answer link.