[This seems to be an example of how, in practice, it is now possible
to patent mathematical discoveries--something which traditionally was
not supposed to be allowed, and which Congress never voted to permit.
People on the Internet who have seen this desciption say that the idea
sounds like something obvious. I've heard from some who say they came
up with the same technique independently many years ago--sometimes
decades.]
date: 07-26-91 1640EDT
category: Financial
subject: BC PATENTS
author: EDMUND L. ANDREWS
text:
WASHINGTON -- Some of the patents recently granted:
Two mathematicians in Michigan have patented a faster way for
computers to calculate the volume or weight of objects with
complicated dimensions.
The method could make it easier to make a variety of difficult
measurements: the total interior space of an automobile, the amount
of oil in a dome-shaped reservoir or the volume of toxic waste in
soil on a piece of property.
Calculating the volume of a cube requires multiplying length by
height and width. But the process becomes far more complicated and
cumbersome when measuring more irregular shapes that cannot be
reduced to a simple formula.
The new technique is a modification to one of the longstanding
approaches to such challenges, a method sometimes called the Monte
Carlo approach.
The new method was invented by Wilfred Kaplan, a professor
emeritus at the University of Michigan in Ann Arbor, and Frederick
B. Sleator, a mathematician with Ford Motor Co.
As its name implies, Kaplan said, the basic Monte Carlo approach
resembles a game of chance. Conceptually, it works like this. An
irregular object, like a rock, is depicted inside a cube or other
object with straightforward dimensions.
The cube is then pelted with a random blitz of imaginary pellets
that either stick to it or to the rock inside. If done properly,
the percentage of pellets hitting the rock should be equal to the
ratio of the rock's volume to that of the cube. Thus, to calculate
the rock's volume, a person simply multiplies that percentage
against the volume of the cube.
Kaplan said the new method, which is employed in a computer
system, simplifies this process for objects that have somewhat
regular shapes, such as domes, ovals and rough rectangles.
Instead of a purely random volley of pellets, the pellets are
distributed evenly over a given area. The advantage, the
mathematician said, is that far fewer pellets need to be used to
get an accurate indication of proportional volumes. The method
becomes less accurate when dealing with extremely complex shapes,
he said.
Kaplan and Sleator received patent 5,031,134.