
05221281
j
2007e.00372
Harding, Ansie
Engelbrecht, Johann
Sibling curves and complex roots 1: looking back.
Int. J. Math. Educ. Sci. Technol. 38, No. 7, 963973 (2007).
2007
Taylor \& Francis, Abingdon, Oxfordshire
EN
H30
A30
F50
U70
history of mathematics
fundamental theorem of algebra
quadratic equations
cubic equations
algebraic equations
graphical methods
visualization
graph of a function
polynomials
doi:10.1080/00207390701564680
Summary: This paper, the first of a twopart 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.