Topology of Quartic Loci in 2D and 3D Inspired by A College Entrance Exam

We explore with technological tools on some problems that originated from a college practice entrance question (see [12]). The problems involve an affine transformation whose image is a locus based on lines passing through a fixed point (see Figure 1(a) or 1(b)), which has been explored in ([17], [1...

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Published inThe electronic journal of mathematics & technology Vol. 19; no. 1; pp. 1 - 14
Main Authors Yang, Wei-Chi, Kovacs, Zoltan, Dana-Picard, T
Format Journal Article
LanguageEnglish
Published Mathematics and Technology, LLC 01.02.2025
Subjects
College entrance achievement tests
College entrance examinations
Entrance examinations
Influence
Locus (Geometry)
Tests, problems and exercises
Topological spaces
Universities and colleges
China
Online AccessGet full text
ISSN1933-2823
1933-2823

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Summary:We explore with technological tools on some problems that originated from a college practice entrance question (see [12]). The problems involve an affine transformation whose image is a locus based on lines passing through a fixed point (see Figure 1(a) or 1(b)), which has been explored in ([17], [18], [19], [20]) by using parametric equations. We are interested in the topological structures for the shapes of image curves or surfaces when the scaling factor s vary. We found the value for s which affects the topological structures for the loci in 2D first, and we extend the results to 3D based on the arguments in 2D. Finally, we include an exploration on the topological structure for the locus ellipsoid when scaling factor s and the fixed point A approach to infinity.
ISSN:1933-2823
1933-2823