Contents

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.
- Calculate roots of polynomials for various degrees; uses Maple

Contents