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Contemporary interpretation of a historical locus problem with the use of computer algebra. (English) Zbl 1395.51004
Kotsireas, Ilias S. (ed.) et al., Applications of computer algebra, Kalamata, Greece, July 20–23, 2015. Cham: Springer (ISBN 978-3-319-56930-7/hbk; 978-3-319-56932-1/ebook). Springer Proceedings in Mathematics & Statistics 198, 191-205 (2017).
Summary: This paper deals with the joint use of computer algebra and the dynamic geometry features of the mathematics software GeoGebra to solve a locus problem. Through a generally unknown problem from an eighteenth century Latin book of geometry exercises the use of the computer algebra features of GeoGebra will be presented on the one hand as a means of automatic computation of the locus equation and on the other hand as an environment to realize the symbolic step-by-step derivation of the equation. The core principles of the effective implementation of computer algebra functions within the dynamic geometry system will be presented. An enhanced approach to solving the problem, inspired by the findings from the use of the computer to investigate the locus, will cause the appearance of an unexpected and until now not described curve.
For the entire collection see [Zbl 1379.13001].

MSC:
51-04 Software, source code, etc. for problems pertaining to geometry
68W30 Symbolic computation and algebraic computation
01A05 General histories, source books
51-03 History of geometry
Software:
GeoGebra; Giac; SINGULAR; Xcas
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References:
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