A Mathematical Concept Comes Easy With Visual Proofs.

with lots of interactive demos and pictures !

Basically this site deals with mechanical objects, such as the one below:

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Peaucellier Linkage

This machine is made of 2 Anchors, 4 Joints and 7 Rigid Bars.

 

In this site we study the configuration space of certain machines, all placed in the plane. Machine's configuration space is an abstract way to describe all the states the machine could take. After a short introductory to topology, we implicitly construct configuration spaces for a certain family of machines, which turn out to be, oriented surfaces of varying genus. In the third part we introduce the notion of functional linkages, which are  machines who can compute polynomial functions. It can be deduced from this that to each smooth manifold M, there exists a machine with configuration space homeomorphic to a finite number of copies of M. 

 

The site is organized into Lessons to allow people with various mathematical backgrounds to explore the subject.
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Starting from the top

Start here if you are new to topology or mathematics, here you will find and learn a few building blocks of topology which apart from enabling you to understand the next lesson can serve as an introduction to topology.

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Of Spiders and Toruses.

We study the configuration spaces of Spider like machines. The proofs are accompanied by interactive Java Applets. This lesson requires some knowledge in topology, that can be found in the in the introductory lesson: Starting from the top.

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Machines as Functions.

How diversified machines can be: an interactive outline of the fact that every polynomial function can be computed by the use of machines. And more...
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Want to see more machines at work ?

Various Java Applets of machines.

 

FHS World of Math WebringNext Site This FHS World of Math Ring site is owned by Dori Eldar.

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