Properties of One Remarkable Quartic Curve

摘要：

This contribution aims to report on the experiences and results gained by the author through the incorporation of historical issues into the teaching of geometry to prospective mathematics teachers.An unexpected and until now not described quartic plane curve emerged in the course of solving a locus problem from an 18th century Latin book of geometrical exercises using dynamic geometry software.This algebraic curve of a remarkable shape which resembles a pretzel (see Figure 1) has the algebraic equation x4 + x2y2 + 2ax2y + 2ay3-a2x2 + 3a2y2 =0, where a is a positive real number.

关键词： Algebraic curve Geometry teaching Rational parametrization Polar equation Properties of a curve

作者: Roman Ha(s)ek

作者单位: University of South Bohemia,Czech Republic

会议类型: 国际会议

会议名称: The 17th International Conference on Geometry and Graphics(ICGG2016)(第17届几何与图学国际会议)

会议地点: 北京

会议语种:英文

页码: 310-311

在线出版日期: 2016-08-04（万方平台首次上网日期，不代表论文的发表时间）