id: 06430685
dt: j
an: 2015c.00700
au: Park, Jungeun; Flores, Alfinio
ti: Fermat’s point from five perspectives.
so: Int. J. Math. Educ. Sci. Technol. 46, No. 3, 425-441 (2015).
py: 2015
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: G40
ut: Fermat point; Torricelli configuration; soap films; minimal sum of
distances
ci:
li: doi:10.1080/0020739X.2014.979894
ab: Summary: The Fermat point of a triangle is the point such that minimizes
the sum of the distances from that point to the three vertices. Five
approaches to study the Fermat point of a triangle are presented in
this article. First, students use a mechanical device using masses,
strings and pulleys to study the Fermat point as the one that minimizes
the potential energy of the system. Second, students use soap films
between parallel planes connecting three pegs. The tension on the film
will be minimal when the sum of distances is minimal. Third, students
use an empirical approach, measuring distances in an interactive
GeoGebra page. Fourth, students use Euclidean geometry arguments for
two proofs based on the Torricelli configuration, and one using
Viviani’s Theorem. And fifth, the kinematic method is used to gain
additional insight on the size of the angles between the segments
joining the Fermat point with the vertices.
rv: