id: 06560914
dt: j
an: 2016c.00761
au: Abboud, Elias
ti: Algorithms for drawing ellipses using GeoGebra.
so: Math. Comput. Educ. 49, No. 3, 183-193 (2015).
py: 2015
pu: MATYC Journal, Old Bethpage, NY
la: EN
cc: G70 G80 U70
ut: ellipses; geometric constructions; drawing; algorithms; mathematical
software; geometry software; analytic geometry; locus; distance;
circles; triangles; straight lines; intersection points; conic
sections; family of ellipses; quadratic curves; coverings
ci:
li:
ab: From the introduction: In this article we propose three algorithms for
drawing ellipses. The first algorithm aims to find the locus of points
in the plane whose distances to a given point are half their distances
to a given line. The second algorithm aims to find the locus of points
each of which divides, in the same ratio, the segment drawn from a
point on a given circle perpendicular to a line containing a fixed
chord of the circle, as the point moves along the circle. The third
algorithm is related to a new definition which states that the ellipse
is the locus of points which have a constant sum of squares of
distances from the sides of a given triangle. The first two algorithms
may be applied on any dynamic geometry software, while the last one
utilizes the unique features of the GeoGebra software. The outcomes of
the second and the third algorithms are families of ellipses, one of
which covers the interior of a circle and the other which covers the
plane with one hole. Summary: The article evaluates three algorithms
for drawing ellipses. Explored is the usage of the Compass tool on a
TI-92 graphing calculator as well as the link between geometry and
algebra through the GeoGebra. Analyzed is the algorithm on the locus of
points in the plane as well as the use of a dynamic geometry software
in determining a general point in the locus.
rv: