Math and geometry software to create instructional videos

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I am looking into starting an amateur project for online tutoring. I need a math/geometry program that I can use to create shapes, graph functions, and create animation. I know of many types of software (such as geogebra) but they have restrictions for commercial use. In other words, I can't use the material or features (even screenshots) to gain a profit. Does anyone know of any programs/ software that I can use for my project?

Note: I don't mind software or programs that I can purchase for a one time fee.

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1) Contact the geogebra support people; there may be some provision to pay a fee for the right to distribute-for-profit screenshots or animations produced.

2) See if Mathematica meets your needs -- but this is not a cheap solution, the commercial cost is about $2500. However, Mathematica is a truly professional, well-made tool and the time it saves you might be worth the cost.

PS- Don't be biased by lack of features in Wolfram Alpha: That is emphatically not like the full-blown Mathematica.

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You can take a look at GNU Dr. Geo a free software of mine, there is no commercial limitation and you can even redistribute it along your work.

You can do classic interactive geometry with: Mouse and clic construction

Or you can use its programming features to design very original sketches: Programmed chaotic sequence

More over, it is very easy to modify Dr. Geo from itself, in case of need!