Before proving a theorem, mathematicians must be able to find something to prove. They must see patterns, explore them, test for many cases, and make conjectures and generalization. The final part of the process is the proof.

Mathematicians during the early times rely only pencil and paper in investigating patterns. Today, hundreds of free and commercial software are available and accessible, even for high school students like you. Below are some of the free programs that you can use to explore patterns and improve your skills in mathematical proofs. Use these programs to investigate future problems here in **Proofs from the Book**.

**1. GeoGebra**. GeoGebra is an excellent mathematics software that joins algebra, geometry, calculus, and spreadsheet. It is free and open-source and very student friendly. If you want to learn about GeoGebra, visit Math and Multimedia’s GeoGebra Tutorial Series with more than 50 step by step tutorials. There are also more than 20000 applets in GeoGebraTube that you can explore.

**2. Spreadsheet**. Every student who wants to learn about mathematical proofs must learn how to use a spreadsheet. Spreadsheets can be used to easily spot number patterns, perform quick computations, and generate graphs. The OpenOffice Calc and the LibreOffice Calc are two of the most famous free spreadsheets that you can use.

**3. Wolfram Alpha**. Wolfram Alpha is a computational search engine capable of generating calculations based on user search. Unlike ordinary search engines, Wolfram alpha generates mathematical results instead of listing websites from queries. To know more about Wolfram Alpha, visit the Wikipedia page.

**4. Microsoft Mathematics**. Microsoft Mathematics is a powerful graphing calculator with the capability of a Computer Algebra System. The software is capable of graphing in 2 and 3 dimensions and can be used for mathematical and scientific calculations.

**5. Wolfram Demonstrations**. Wolfram Demonstration is another repository of animations (called demonstrations) for verifying and exploring mathematical relationships. Some of the demonstrations include the proofs. You should be able to make conjectures based on the demonstrations, or study the included proofs.