Visual Calculus Article Index for
Visual
Website Links For
Visual
 

Information About

Visual Calculus




The method was devised by Mamikon in 1959 whilst a young undergraduate. It is based on the old puzzle about what is the area of a ring if the tangent to the inner circle is 6" long? With Mamikon's insight the solution becomes obvious - the area is the same as that swept by a tangent from the inner circle to the outer circle, and the tangents can all be translated parallel to themselves to make a smaller circle the points of tangency at the centre and with same radius as the tangent length. Thus it doesn't really matter that the inner and outer curves are circles, just that the tangent to one side of the inner curve should have a constant length.

Mamikon generalised the insight to Mamikons Theorem:

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


and Tractrix can be solved by very young students. To quote him "Moreover, the new method also solves some problems ''insoluable by calculus, and allows many incredible generalizations yet unknown in mathematics''." Solutions to many other problems appear on Mamikon's Visual Calculus site.


SEE ALSO


  • Hodograph This is a related construct which maps the velocity of a point using a polar diagram.



REFERENCES



EXTERNAL