An Introduction to Organics
This page provides an overview of the Proceedings, a quick
reference guide to the various mechanisms involved and a list of
some of the highlights of the mathactivated articles.
The Proceedings of the Organic Mathematics Workshop is the
offspring of a workshop in Experimental Mathematics (held Dec. 12-14
'95) and of an experiment in activated mathematics publishing. In
order to explore the issues attached to on-line information, especially
documents that are critical to the life and health of academic
mathematics, a non-trivial
collection of articles have been coupled with a variety of
interfaces designed for use within the Web.
In particular, the possibility of connecting powerful mathematical software
with on-line text is at the forefront. Mathactivation involves
identifying the mathematics within formatted text (in this case LaTeX),
separating it out for parsing into an appropriate intermediate format,
and then feeding it to an interactive mathematical platform (like Maple).
The results are then displayed, allowing the user to manipulate the parameters
within the mathematics to explore the content of the text.
Below are a number of examples of how the interfaces appear and function.
In addition, several exemplary pages from within the proceedings are
highlighted for immediate examination.
-
Document Map
- a graphic map to the various major features of the Proceedings
-
Document Vault
- The Vault provides access to the variety of document formats that are
available.
-
An example of the Annotation Form Interface
- Local Extrema of Functions
-
Interface Tutorial
- A simple tutorial demonstrating the integration
of the Maple Form Interface and the Annotation Form Interface
used throughout the Proceedings
-
Generic Maple Form Interface
- A Web-based cgi-bin script interface to a standard Maple engine
-
Math on Wheels
- An example of the Maple Form Interface
-
Maple Assisted Animation
example 1 and
example 2
- Two examples of push-pull animation from Maple generated images
(requires Netscape)
~ Some Illustrations from the Proceedings ~
-
Pascal's Triangle:
Fast C version
or
Maple version
- from
Andrew Granville's article on
The Arithmetic Properties of Binomial Coefficients
-
Roots of Polynomials:
Fast C version or
Maple version (click on Maple icon)
- from
Andrew Odlyzko's article on
Zeros of polynomials with 0,1 coefficients
-
Cascade juggling demonstration (996K)
- a QuickTime movie for
Joe Buhler's article on
Juggling Drops and Descents
-
A discussion of a formula of Newton's for pi
- from
Bailey, Borwein and Borwein's article on
Ramanujan, Modular Equations, and
Approximations to Pi or
How to compute One Billion Digits of Pi
-
A demo of the Maple Form interface generating projective planes
- from
C. W. H. Lam's article on
The Search for a Finite Projective Plane of Order 10
- (Follow the link and click on the first Maple Leaf icon)
-
A Card Trick
- from
W. Haga and S. Robins' associated article
On Kruskal's Principle
Hilbert's 1896 proof of the transcendence of pi (in the original)
from
Bailey, Borwein and Borwein's article on
Ramanujan, Modular Equations, and
Approximations to Pi or How to compute One Billion Digits
of Pi
(Scanned originals of Hilbert's paper)
Interactive plots on a torus
from
R. Corless's article on
Continued Fractions and Chaos
(Follow the link and look for "Maple program for graphing arbitrary...")
A variety of examples of mathactivated text using
Mathematica
from New Visualization Ideas
for Differential Equations
by Stan Wagon
- Activated Mathematica Example 1
- Activated Mathematica Example 2
- Activated Mathematica Example 3
- Activated Mathematica Example 4