LIVE Mathematics on the web
JAVA and Geometry
If you have a JAVA-enabled browser (Netscape 3 or Internet Explorer 3) then you should see what this new computer language can mean for live mathematics on the web.These pages are the work of David Joyce: he is putting all of Euclid's elements on the web in dynamic geometry form. The Geometry Applet he has created allows you to create your own dynamic geometry pages to be viewed either online or offline using a web browser.
If you like the taste of dynamic geometry that you experience here, then contact AAMT about purchasing Cabri-Geometry II.
David is still working on his applet. Some of these pages are incomplete, but serve to give a taste of the possibilities!
- Fancy a taste of Live Geometry? All you need is a Java-enabled browser (Netscape 3+, IE 3+)
- The Geometry Applet
An introduction and breakdown of the Geometry Applet version 1.3.1.- About the Geometry Applet
Learn how to create your own dynamic geometry pages.- Create your own Geometry Pages
Try out this new JavaScript front-end which allows you to create your own dynamic geometry pages using the Geometry Applet.
Given lines AB and CD, what is the locus of points P such that the angle APB equals the angle CPD?
My first attempt: the angle at the centre of the circle is twice that at the circumference. Students quickly learn to recognise the familiar arrow, but what about the other configurations?
Start with a triangle ABC: constructing the centre of gravity of a triangle.
Constructing the circumcentre of a triangle ABC and, from this, the circumcircle.
The cyclic quadrilateral has many interesting properties. Explore them here.
It's amazing how much geometry there is in the lowly triangle!
Consider any triangle ABC. Can you fit a circle inside it that is tangent to all three sides? How can you construct such a circle?
Constructing the regular pentagon inside any circle - which also gives the Golden Section!
Start with two fixed circles, one inside the other, but not necessarily right in the center of the other. Place a circle between and touching the two circles. Place another between and touching the two circles but also touching the circle you just placed. Repeat. Eventually, your circles will go all the way around the ring. In some instances, the last circle you placed will just touch the first circle. Steiner's Porism says that if that occurs, then it doesn't matter where you put the first circle; the last will always touch the first.
The source files for version 1.3.1, the associated class files, and a couple of html files have been zipped into the file Geometry.zip.
David E. Joyce
Department of Mathematics and Computer Science
Clark University
Worcester, MA 01610
Email: djoyce@clarku.edu
My nonJava Homepage
and my
Java homepage