id: 06269298
dt: j
an: 2014b.00555
au: Hodgson, Ted; Gore, Joe
ti: A historical excursion: Carlyle’s geometric solution to the quadratic
equation.
so: Ohio J. Sch. Math. 2009, No. 59, 6-11 (2009).
py: 2009
pu: Ohio Council of Teachers of Mathematics (OCTM), Columbus, Oxford, OH
la: EN
cc: H30 G70 A30
ut: quadratic equations; circles; geometric solution; Carlyle’s technique
ci:
li:
ab: Summary: A study of the history of mathematics offers rich learning
opportunities for students. In this article, we present a process for
constructing geometric solutions to the quadratic equation that was
developed by one 19th century mathematics student (Thomas Carlyle). In
particular, Carlyle discovered that the $x$-intercepts of a particular
circle (which we define as the Carlyle circle) corresponds to the
solutions of quadratic equations of the form $x^2+bx+c=0$. With
advances in technology, Carlyle’s geometric solution to quadratics
could now be considered an historical curiosity. As this article
demonstrates, however, Carlyle’s solution offers an effective context
for deepening and connecting students’ understanding of both algebra
and geometry.
rv: