The basic technology explored in this paper is represented in the interactive roots of polynomials interface. It is used in a variety of instances to illustrate points made in the paper. Several different images of the roots of polynomials are also available for large degree ( d > 20 ) showing details in the complex plane.

• Basic roots of polynomials interface

• Roots of polynomials
  Calculate roots of polynomials for various degrees; uses Maple

  Figure 1

  roots of polynomials with 0/1 coefficients for degree 12; uses interface

  Figure 2

  close up portion of Figure 1; uses interface

  Figure 3

  shows zeros of polynomials for degrees < 33 in small area; scanned image

  Figure 4

  shows a portion of in detail; scanned image

  Figure 5

  shows a portion of in detail; scanned image

  Figure 6

  shows a portion of in detail; scanned image

  Zero finding software

  Algorithm (in C) due to Weirstrass, with Gauss-Siedel style updates

  Averaging

  shows roots of 0/1 polynomials with averages included; uses interface

  Coefficients of -1,1

  shows roots of polynomials with -1/1 coefficients up to degree 12; uses interface

  Limiting curves C1 and C2

  shows limiting curves for 0/1 roots, overlaid on roots up to degree 6; uses Maple

  Mandelbrot and Julia set

  are demonstrated via a user interface; uses remote resource

  Spike along negative real axis

  shows line of roots along negative real axis of complex plane for 0/1 polynomials up to degree 24.