If you would like to enhance your geometric drawings, then Google Sketchup is one software that I would recommend. Google Sketchup is 3-dimensional modeling software designed for architects, engineers, filmmakers and game developers, and other related professionals (Wikipedia).  It is now used to create models in Google Earth.

What makes Google Sketchup advantageous over other 3d software is that  it is a lot easier to use.  Some of the examples below are the figures I created after only watching several of their video tutorials.

Figure 1 shows the model in perspective showing symmetries of a right rectangular prism.

Figure 1 - Symmetries of a right rectangular prism.

Figure 2 shows the painted cube problem my Introduction to the Concept of Functions post. In the diagram, a big cube is painted yellow and cut into smaller cubes. The problem is to investigate the number of painted faces.

Figure 2 - Cube painted yellow and cut into smaller cubes.

Figure 3 shows different face styles of a cuboctahedron.

Figure 3 - Cuboctahedron in different view types.

Google Sketchup is free, and you can pay if you want a professional version. There are basic, intermediate and advanced video tutorials in its website.

You may also want to read my post on Using Google Sketchup in Teaching Mathematics.

## Free Geometry and Topology Ebooks

Below are free Geometry and Topology ebooks. Most of these books are in PDF format. Some of the links point to a website containing the ebooks, while some directly links to the pdf files. All of these ebooks are downloadable and free.

1. CK-12 Geometry by V. Cifarelli, A. Gloag, D. Greenberg, J. Sconyers, B.
2. Geometry for Elementary School by Wikibooks
3. The Elements by Euclid

College Geometry and Beyond

1. A First Course in Topology: Continuity and Dimension by John McCleary
2. A Tour of Triangle Geometry by Paul Yiu
3. Algebraic and Geometric Topology by Andrew Ranicki, Norman Levitt, Frank Quinn
4. Algebraic Curves: an Introduction to Algebraic Geometry by William Fulton
5. Algebraic geometry and projective differential geometry by Joseph M. Landsberg
6. Algebraic Geometry by J.S. Milne
7. An Introduction to Differentiable Manifolds and Riemannian Geometry by William M. Boothby
8. An Introduction to Riemannian Geometry by Sigmundur Gudmundsson
9. Classical Geometry by Danny Calegari
10. Computational Geometry
11. Course of Differential Geometry by Ruslan Sharipov
12. Elementary Topology O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
13. Fractal Geometry by Michael Frame, Benoit Mandelbrot, Nial Neger
14. Fundamentals of Geometry by Oleg A. Belyaev
15. Geometric Asymptotics
16. Geometry and Billiards by Serge Tabachnikov
17. Geometry and Group Theory
18. Geometry and Quantum Field Theory by Pavel Etingof
19. Geometry Formulas and Facts by Silvio Levy
20. Geometry study guide
21. Geometry of Surfaces Nigel Hitchin
22. Geometry of the Sphere by John C. Polking
23. Geometry, Topology, Geometric Modeling by Jean Gallier
24. Geometry Unbound Kiran S. Kedlaya
25. Intrinsic Geometry of Surfaces by A. D. Aleksandrov and V. A. Zalgaller
26. Introduction to Symplectic and Hamiltonian Geometry by Ana Cannas da Silva
27. Natural Operations in Differential Geometry Ivan Kolar, Peter W. Michor, Jan Slovak
28. Non-Euclidean Geometry by Henry Manning
29. Open Problems in Topology by Jan Van Mill, George M. Reed
30. Projective and Polar Spaces by Peter J. Cameron
31. Projective Differential Geometry Old and New by V. Ovsienko, S. Tabachnikov
32. Projective Geometry by Nigel Hitchin
33. Riemann surfaces, dynamics and geometry Course Notes
34. The Eightfold Way: The Beauty of Klein’s Quartic Curve editedy by Silvio Levy
35. The Foundations of Geometry by David Hilbert
36. The Geometry and Topology of Three-Manifolds William P Thurston
37. The Geometry of Iterated Loop Spaces by J. P. May
38. Topics in Finite Geometry: Ovals, Ovoids and Generalized Quadrangles by S. E. Payne
39. Topology and Geometry for Physics by H. Eschrig
40. Topology Without Tears by Sydney A. Morris

You may also want to view my list of Free Algebra and Free Calculus ebooks.

## Free Whiteboard Software

If you are using computers during lectures, or fond of screencasting, you would probably need a software where you could scribble.  You would need a blackboard or a whiteboard software. There are several free software that you could use – you could use PaintBrush or Flash Player.

One of my latest internet dig, however, would also be a good choice. It is called  Classic WhiteBoard. It is available in Windows, Linux and Mac platform. Its screenshot is shown below.

What I love about this software is that it is very easy to use (click here to view screencast tutorial) and it really looks like a whiteboard.  It works very much like PaintBrush.  One of the disadvantages, though, is that it has only four colors.

Update: I have uploaded a better whiteboard software added with math tools such as compass, straightedge, triangle and protractor here.