## Towards an intelligent and dynamic geometry book.(English)Zbl 1425.97002

Summary: The pursuit of an Intelligent and Dynamic Geometry Book should involve the study of how currently developing methodologies and technologies of geometry knowledge representation, management, deduction and discovery can be incorporated effectively into future education. Just as Doron Zeilberger pointed out in [Plane geometry: an elementary textbook by Shalosh B. Ekhad XIV (circa 2050) downloaded from the future, http://sites.math.rutgers.edu/~zeilberg/PG/nis.html] a geometry book from the future would be a computer program, in which all the theorems can be automatically discovered (and of course proved) by computer and beautiful illustrations can be automatically generated and dynamically modified. Such a prospect motivates studies on how to represent and manage digitised geometric knowledge on computer. The geometry book of the future (the $$\mathcal{I}$$nt$$\mathcal{D}$$yn$$\mathcal{G}$$eo$$\mathcal{B}$$ook) should be adaptive, collaborative, visual and intelligent. Adaptive because the contents should adapt itself to the curricula and readers. It will allow collaborative work and its contents would be collaboratively formed using a knowledge base open to contributions. Statements and proofs should be en-lighted by dynamic geometry sketches and diagrams, and the correctness of the proofs should be ensured by computer checking. The book will be intelligent, the reader should be able to ask closed or open questions, and can also for proof hints. The book should also provide interactive exercises with automatic correction. Such a cloud platform, freely available in all standard computational platforms and devices, collaborative, adaptive to each and every user’s profiles, should bring together a whole new generation of mathematical tools with impact in all levels of education. To realise such a book, a network of experts must be built, increasing the connections between several research communities, such as: mathematical knowledge management; computer theorem proving and discovery; education, aggregating expertise in areas such as Proofs in a Learning Context; Interfaces and Searching; Tools Integration; Learning Environments in the Cloud. In this paper the author tries to make the case for such an endeavour.

### MSC:

 97U50 Computer-assisted instruction, e-learning (aspects of mathematics education) 68T05 Learning and adaptive systems in artificial intelligence 68T15 Theorem proving (deduction, resolution, etc.) (MSC2010) 68T30 Knowledge representation 97G10 Comprehensive works on geometry education
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