id: 05221281
dt: j
an: 2007e.00372
au: Harding, Ansie; Engelbrecht, Johann
ti: Sibling curves and complex roots 1: looking back.
so: Int. J. Math. Educ. Sci. Technol. 38, No. 7, 963-973 (2007).
py: 2007
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: H30 A30 F50 U70
ut: history of mathematics; fundamental theorem of algebra; quadratic
equations; cubic equations; algebraic equations; graphical methods;
visualization; graph of a function; polynomials
ci:
li: doi:10.1080/00207390701564680
ab: Summary: This paper, the first of a two-part article, follows the trail in
history of the development of a graphical representation of the complex
roots of a function. Root calculation and root representation are
traced through millennia, including the development of the notion of
complex numbers and subsequent graphical representation thereof. The
concepts of the Cartesian and Argand planes prove to be central to the
theme. We specifically pause to look at efforts of representing complex
roots of a function on the real plane, first, by superimposing the
Argand plane onto the Cartesian plane, and secondly, by keeping the
planes side by side and moving between the two, and thirdly, by taking
the modulus of the function value and hence eliminating one dimension
to enable drawing of the complex function as a surface in three
dimensions.
rv: