**** Here are the slides for my presentation "Gegenraum ... Auch für Physiker?" from February 28, 2018 at the Physiker Arbeitstagen at the Goetheanum.****

Charles Gunn's Resource Page for Projective Geometry

Welcome to the resource site associated to my projective geometry presentations. Here I hope you can find further inspiration to learn more about projective geometry. To begin with, for a more detailed introduction to projective geometry see my projective geometry blog. Please contact me (gunn at math.tu-berlin.de) if you have questions or suggestions regarding the content described in my talk and in these associated resources.

Here are some slides for a presentation on projective geometry at Urania in Berlin in November 2014, similar to the presentation I gave at Kangaru Mathecamp in August 2015. To shorten download times, the slides do not include any movies. These can be viewed using the following links:

Here you can find a photo album devoted to the Ames room construction.

Counter space. Here is an information sheet (in German) that gives references related to the subject of counter space, an important idea from projective geometry that I've been working with a lot recently (December, 2017). Also, here is an introductory article on this theme from 2014 (also in German). Finally, Here is a list of citations, in German, regarding counterspace mostly from the lectures of Rudolf Steiner, who introduced the idea into the scientific conversation about 100 years ago.

Below are links to the various applications I used in the presentation. They are all based on the programming language Java, and in particular on the 3D rendering package jReality, developed at the visualization group in the Mathematics Dept. of TU-Berlin. The first set of applications below use Java webstart, the others are Java applets.

Attention: Please consult this blog post on my projctive geometry blog if you encounter problems running the applets or the webstarts.

Java webstart applications

All Java webstart applications have on-line documentation, either in the left panel of the graphical user interface, or by clicking on the little '?' symbol in right corner of the title bar of the left panel. If these applications interest you, you can find more here.

Perspective Demo

This demo illustrates the principles of perspective drawing. The ingredients of central projection are shown: center, image plane, and world plane. A variety of objects are available. Additionally, the horizon line in the image plane is separately visualized.

Perspective Grid

This demo shows how a regular grid of lines in the plane is perspectively mapped onto another grid in which parallel lines meet in vanishing points on the horizon.

Ames Room

Learn how to build an Ames room, in which people can grow and shrink just by walking from one corner to the other.

Stereographic projection demo

This application allows you to play around with stereographical projection. Dragging over the sphere rotates the sphere; dragging over the plane rotates the whole world.

Rendering Spherical Panoramas

This application allows you to play around with spherical panoramas, the kind used in the PhotoSphere feature of Android mobile OS. It uses conformal curvilinear perspective to render different views in real time -- creating "tiny planet" images among many other possibilities.

Dynamic Geometry Demos

The following links are dynamical geometry demos which run as Java applets in your browser. They are all based on the Java Zirkel package.

Desargues Theorem

Desargues Theorem, one of the fundamental theorems of projective geometry, asserts the when two triangles are perspective in a point, then also in a line, and vice-versa.

Projective Generation of Conics

This demo demonstrates how with projective geometry curves can be called into being without recourse to any numerical or algebraic techniques, purely through intersection and joining of a given set of points and lines.

Pascal's Theorem

From projective generation of conics it is a short step to Pascal's celebrated theorem (discovered when he as 16!), that says that the meeting points of opposite sides of a hexagon inscribed in a conic section are collinear.