- Dear fellow geometrophiles,
This message is a preliminary announcement of
a new electronic journal devoted to classical
euclidean geometry and related areas.
The tentative title is FORUM GEOMETRICORUM.
The publication of this journal is sponsored
by Florida Atlantic University, and is free to
readers in the internet community. This is an
electronic journal only in the sense that
papers are published in pdf and a few other
downloadable formats, and that communications
between authors and editors are expedited by
emails as much as possible. Papers submitted
for publication are refereed. The first papers
are expected to be published in early 2001.
Papers published in each calendar year will be
collected into a volume, and issued in the form
of a CD, along with supplementary materials.
Depending on the success of the journal,
arrangement for paper editions shall be made.
FORUM GEOMETRICORUM is intended to be a meeting
place of things geometrical, interesting to
professional mathematicians and amateurs alike.
As editor in chief, I invite you to submit papers
to us. I hope the journal will turn out to be
a forum you will most enjoy. Its success, however,
truly depends on your support, as authors and
I am appending a tentative statement of purpose
of the journal, and a list of mathematicians
who have agreed to serve as advisors and editors.
If you want to know more about this venture, or
want to offer more help, please feel free to
Department of Mathematical Sciences
Florida Atlantic University
Boca Raton, Florida, 33431-0991
Statement of Purpose
FORUM GEOMETRICORUM, an electronic journal of
classical euclidean geometry and related areas,
is intended to bring to a wide, international
readership the beauty, elegance, and usefulness
of Elementary Geometry, in research and in teaching.
Papers shall be published in English only.
FG shall focus on concrete but challenging problems
of euclidean geometry and related areas, that can
be conducted by mathematicians, professional and
amateur alike. Papers will also feature the long
and interesting history of the subject. We shall
also strive to incorporate beautiful illustrations
made possible by contemporary technology. In this
way, the editors of FG intend to influence in a
profoundly positive way the instructions of
geometry, and mathematics in general, up to the
college level. We sincerely hope that participation
in this forum, as editors, authors, and readers,
will make teachers better scholars, and scholars
FORUM GEOMETRICORUM covers the following areas listed
in the Mathematics Subject Classification 2000:
Primary: 51Mxx, 51Nxx, 51Axx, 51-02,03,04.
Secondary: 11D04,09,25,41,99; 15-XX; 01-XX.
It shall comprise of the following departments.
(1) MAIN ARTICLES on themes and problems in
elementary geometry and related areas, historical
or pedagogical. Articles should be mainly
mathematical and discussions on pedagogical
issues should be tangential but constructive.
(2) SHORT NOTES on interesting problems and new
insights on old theorems. The quality of the short
notes should be comparable to the Notes in the
American Mathematical Monthly.
(3) GEOMETRIC CONSTRUCTIONS on the use of dynamic
softwares on ruler and compass constructions.
(4) LETTERS to the EDITORS welcomes constructive
criticisms on papers published in FG, especially
relevant bibliographical (and biographical)
informations that escape the attentions of authors,
referees, and editors.
(5) SUPPLEMENTS in yearly CD-editions consisting
of computer programs, and/or longer instructional
The decisions of several mathematicians pending,
the following have kindly agreed to serve as
advisors and editors.
Julio Gonzalez Cabillon, Montevideo, Uruguay
Richard Guy, Calgary, Alberta, Canada
Clark Kimberling, Evansville, Indiana, USA
Kee Yuen Lam, Vancouver, British Columbia, Canada
Tsit Yuen Lam, Berkeley, California, USA
Frederick Richman, Boca Raton, Florida, USA
Paul Yiu, Boca Raton, Florida, USA
Clayton Dodge, Orono, Maine, USA
Roland Eddy, St. John's, Newfoundland, Canada
Jean-Pierre Ehrmann, Paris, France
Lawrence Evans, La Grange, Illinois, USA
Rudolf Fritsch, Munich, Germany
Bernard Gibert, St Etiene, France
Antreas P. Hatzipolakis, Athens, Greece
Michael Lambrou, Crete, Greece
Floor van Lamoen, Goes, Netherlands
Daniel B. Shapiro, Columbus, Ohio, USA
Man Keung Siu, Hong Kong, China
Peter Woo, La Miranda, California, USA
Peter Yff, Oak Lawn, Illinois, USA
Yuandan Lin, Boca Raton, Florida, USA
Aaron Meyerowitz, Boca Raton, Florida, USA
Xiaodong Zhang, Boca Raton, Florida, USA
Frederick Hoffman, Boca Raton, Florida, USA
Stephen Locke, Boca Raton, Florida, USA
Heinrich Niederhausen, Boca Raton, Florida, USA
- The following paper has been published in Forum Geometricorum. It can be viewed at
Paul Yiu, On the conic through the intercepts of the three lines through the centroid and the intercepts of a given line,
Forum Geometricorum, 13 (2013) 87--102.
Abstract. Let L be a line intersecting the sidelines of triangle ABC at X, Y, Z respectively. The lines joining these intercepts to the centroid give rise to six more intercepts on the sidelines which lie on a conic Q(L,G). We show that this conic (i) degenerates in a pair of lines if L is tangent to the Steiner inellipse, (ii) is a parabola if L is tangent to the ellipse containing the trisection points of the sides, (iii) is a rectangular hyperbola if L is tangent to a circle C_G with center G. We give a ruler and compass construction of the circle C_G. Finally, we also construct the two lines each with the property that the conic Q(L,G) is a circle.
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