The chapter discusses the possibilities modern IT opens for Mathematics and its applications to real life, in particular to Art – by an example of automated construction of caricatures. The research approach in math education which is based on computer modeling as a methodology of a competency approach is discussed as well as the future educational environment with free access to Internet resources and possibilities to operate software in distributive mode. Many examples are given – from simple illustrations to new math facts invented with original dynamic geometry package DG and proved with the help of computer algebra system Derive.

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