- EulerAPE. Ellipses are far more accurate than circles, and still look good. The software has an SVG output option.
- Euler 3 Applet. Allows zero size regions and always gives accurate region areas. Has an SVG option.

**Downloading** If you can't get this applet to work in a browser, you can try downloading the jar using this: a link to the applet.
Left click this and choose 'Save Target As...' or similar,
depending on browser. Once saved to your hard disk, double click the Euler3Applet.jar file and (assuming your java installation is set up suitably)
a version of the applet will run.

The applet draws Venn Diagrams with 3 circles. It attempts to make each of
the *zones* (the set intersections) proportional to the *population*
(value) assigned to the zone. Note that, in general, the areas will be
approximate, as an ideal solution is generally not possible using circles.

To draw a diagram with your own data, simply type in the data for the zones in the 'population' column, and click the 'Draw Diagram' button, you should map the 3 set names of your data to A, B and C. The population values can be any you like, the program will scale them.

By default the label in each zone is the zone name, followed by the population. You can change this to any label you like by choosing the 'Define Labels' option and typing in the label for each zone in the 'label' column. The 'monochrome' option changes the display to black and white. After any change you should click the 'Draw Diagram' button.

At the moment the only way to use this diagram is to take a screen shot ('Print Screen' key in Windows) and paste the bitmap into a document.

A version of the applet is also hosted at the University of Victoria.

The use of the results of this applet is free for research and non profit use. Contact us for other uses. If you use the results of this applet, we encourage you to reference the paper that describes how it works:

**Stirling Chow and Peter Rodgers. Extended Abstract: Constructing
Area-Proportional Venn and Euler Diagrams with Three Circles. Presented at
Euler Diagrams Workshop 2005. Paris.**

Also, if you use this applet, we would like you email us the details. Knowing that it is in use makes the effort of working on it more worthwhile, and we might even be persuaded to improve it.

- Ellipses allow exact area-proportionality most of the time: EulerAPE.
- Diagrams with some zero areas can often be drawn with circles: Euler 3 Applet.
- If you want to always draw Venn-3 diagrams with exact area-proportionality use the Convex Venn-3 applet
- If you want to draw two circle Venn diagrams (with exact area-proportionality) use the DrawVenn applet.
- Constructing these sorts of diagram is a fascinating problem. For more information on Venn Diagrams (diagrams where all zones appear) see the Venn Diagram Survey.
- For more information on Euler Diagrams (diagrams where not all zones have to appear) see the Euler Diagrams Workshop 2004, and the Euler Diagrams Workshop 2005.

- Firstly, typically, the areas are approximate, in that they are not exactly proportional to their population. This is because the exact solution is not possible for most populations when circles are used to represent the sets. To get an exact solution for every possible combination of populations, concave shapes must be used.
- Zero values for zones will cause problems. We suggest using very small values in this case. Diagrams with zones that have zero area would often look better with different layouts from the 3 circle intersection in the applet above. We may get around to dealing with these cases.

Stirling Chow, University of Victoria, Canada

Peter Rodgers, University of Kent, UK (email)