Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Mean-Invariant Polynomial Intersections: A Case Study in Generalisation

Mean-Invariant Polynomial Intersections: A Case Study in Generalisation Tech Know Learn (2011) 16:183–192 DOI 10.1007/s10758-011-9185-y COMPUTER MA TH SNAPSH OTS - CO LUMN EDITOR: U RI W I LENSKY* Mean-Invariant Polynomial Intersections: A Case Study in Generalisation John Mason Published online: 13 October 2011 Springer Science+Business Media B.V. 2011 Anyone knowledgeable about cubics knows that they are symmetrical by rotation through 180 about their inflection point. Slightly less well known is that the tangent to a cubic at the midpoint of two of the roots, passes through the third root (see Horwitz undated). Indeed, Aude (1940) used this property in reverse to locate the real midpoint of a pair of complex roots of a cubic. Arne Amdal (private communication) reported the observation as arising spontaneously from a student in his high-school in Norway using dynamic geometry to explore cubics. Kaye Stacey (private communication April 2002) working with colleagues also found some of the results to be recorded here. 1 Tangent-to-a-Cubic Theorem The tangent to a cubic at the midpoint of two of the roots passes through the third root (Fig. 1). For example, taken from the internet: two people tackling the same specific problem, probably course work from the IB: https://nrich.maths.org/discus/messages/67613/68454.html and http://nrich.maths.org/ discus/messages/67613/69786.html. This column will http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Technology, Knowledge and Learning" Springer Journals

Mean-Invariant Polynomial Intersections: A Case Study in Generalisation

Mason, John
"Technology, Knowledge and Learning" , Volume 16 (2) – Oct 13, 2011
Download PDF
10 pages

Loading next page...
 
/lp/springer-journals/mean-invariant-polynomial-intersections-a-case-study-in-generalisation-RAXlozkIzk

References (8)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Science+Business Media B.V.
Subject
Education; Learning and Instruction; Mathematics Education; Educational Technology; Science Education; Creativity and Arts Education
ISSN
2211-1662
eISSN
1573-1766
DOI
10.1007/s10758-011-9185-y
Publisher site
See Article on Publisher Site

Abstract

Tech Know Learn (2011) 16:183–192 DOI 10.1007/s10758-011-9185-y COMPUTER MA TH SNAPSH OTS - CO LUMN EDITOR: U RI W I LENSKY* Mean-Invariant Polynomial Intersections: A Case Study in Generalisation John Mason Published online: 13 October 2011 Springer Science+Business Media B.V. 2011 Anyone knowledgeable about cubics knows that they are symmetrical by rotation through 180 about their inflection point. Slightly less well known is that the tangent to a cubic at the midpoint of two of the roots, passes through the third root (see Horwitz undated). Indeed, Aude (1940) used this property in reverse to locate the real midpoint of a pair of complex roots of a cubic. Arne Amdal (private communication) reported the observation as arising spontaneously from a student in his high-school in Norway using dynamic geometry to explore cubics. Kaye Stacey (private communication April 2002) working with colleagues also found some of the results to be recorded here. 1 Tangent-to-a-Cubic Theorem The tangent to a cubic at the midpoint of two of the roots passes through the third root (Fig. 1). For example, taken from the internet: two people tackling the same specific problem, probably course work from the IB: https://nrich.maths.org/discus/messages/67613/68454.html and http://nrich.maths.org/ discus/messages/67613/69786.html. This column will

Journal

"Technology, Knowledge and Learning" – Springer Journals

Published: Oct 13, 2011

There are no references for this article.