Analytic Geometry
On this page, two published papers:
Also:
- Analytic Geometry (a source for the above, and some additional notes)
- Conic Sections
See also Geometry notes.
“Thales and the Nine-point Conic”
Published in the De Morgan Gazette 8 no. 4 (2016), pages 27–78.
Latest revision (86 pages, size A5, 12 point type, March 14, 2018):
Previous revision (85 pages, size A5, 12 point type, July 25, 2017):
“Abscissas and Ordinates”
Published in Journal of Humanistic Mathematics 5 (2015), no. 1, 233–264. DOI: 10.5642/jhummath.201501.14 . Available at: http://scholarship.claremont.edu/jhm/vol5/iss1/14 .
Here my last submitted version: 38 pages, size A5, dated October 7, 2014 (some brief additions were made before the final publication above):
Older version (21 pages, size A5, June 2, 2014):
Abstract of the article:
In the manner of Apollonius of Perga, but hardly any modern book, we investigate conic sections as such. We thus discover why Apollonius calls a conic section a parabola, an hyperbola, or an ellipse; and we discover the meanings of the terms abscissa and ordinate. In an education that is liberating and not simply indoctrinating, the student of mathematics will learn these things.
The article is based on a part of the following:
“Analytic Geometry”
This is a report on the lack of rigor in analytic geometry as it is often taught, why this is a problem, and how it can be solved by reading mathematicians like Euclid and Descartes.
Current edition dated June 2, 2014, corrected and reformatted January 8, 2018. 113 pages, size A5, 12 point type.
I gave a related general
seminar talk, Geometry as made
rigorous by Euclid and Descartes,
October 31, 2013.
See also my published article, Model-theory of vector-spaces over
unspecified fields
(2009), for more on the technicalities of
interpretations, building on Descartes's interpretation of a field.
Also relevant is From Euclid to Descartes
(January 23, 2013)
and more, on the Geometry notes
page linked to above.
Meanwhile, here for the record is the edition of December 5, 2013 (75 pages, size A5) of the report:
“Conic Sections”
An article begun in the fall semester of 2006–7, when I was involved in teaching an analytic geometry course at METU. Apparently I finished in January, 2008. I edited the article more recently, mainly in accordance with my current stylistic practices for LaTeX; the document is now 31 pages of size A5:
Most of the article is a derivation of the equations and features of the so-called conic sections from the focus-directrix definition. There is some attempt to connected the curves to their original definition as sections of a cone. I did this more thoroughly in the Analitik Geometri course at Mimar Sinan in fall 2014–15.
