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*Algorithms* and *Polynomiography* for *Solving* *Quaternion* *Quadratic* *Equations*

"... Solving a quadratic equation P (x) = ax2 + bx+ c = 0 with real coefficients is known to middle school students. Solving the equation over the quaternions is not straightforward. Huang and So [2] give a complete set of formulas, breaking it into several cases depending on the coefficients. From a re ..."

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*Solving*a

*quadratic*

*equation*P (x) = ax2 + bx+ c = 0 with real coefficients is known to middle school students.

*Solving*the

*equation*over the

*quaternions*is not straightforward. Huang and So [2] give a complete set of formulas, breaking it into several cases depending on the coefficients. From a

###
*Solving* Cubic *Equations* By the *Quadratic* Formula

"... Let p(z) be a monic cubic complex polynomial with distinct roots and distinct critical points. We say a critical point has the Voronoi property if it lies in the Voronoi cell of a root θ, V (θ), i.e. the set of points that are closer to θ than to the other roots. We prove at least one critical point ..."

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by the Voronoi property, there is a solution c of p′(z) = 0 where Bm(c) converges to a root of p(z). The speed of convergence is dependent on the ratio of the distances between c and the closest and the second closest roots of p(z). This results in a different

*algorithm*for*solving*a cubic*equation*than### Proceedings�of�ISAMA�2009� Eighth�Interdisciplinary�Conference�of�The�International� Society�of�the�Arts,�Mathematics,�and�Architecture� University�at�Albany,�Albany,�New�York� June�22�25,�2009�

"... It is hard to believe the first art/math conference AM 92 was held here at the University at Albany seventeen years ago. Where does the time go?? This is already the eighth ISAMA conference since the founding of ISAMA in 1998. Looking back over the years, I have to thank all the people that helped c ..."

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It is hard to believe the first art/math conference AM 92 was held here at the University at Albany seventeen years ago. Where does the time go?? This is already the eighth ISAMA conference since the founding of ISAMA in 1998. Looking back over the years, I have to thank all the people that helped co-organize conferences, in particular Carlo Sequin, Javier Barrallo,

### Proceedings of ISAMA 2010 Ninth Interdisciplinary Conference of the International Society of the Arts, Mathematics, and Architecture

, 2010

"... It is a pleasure to return to my hometown Chicago, where Steve Luecking previously hosted a ..."

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It is a pleasure to return to my hometown Chicago, where Steve Luecking previously hosted a

### A Bibliography of Publications in Computers and Graphics

, 2013

"... Version 1.33 Title word cross-reference (n + 1) [SA87]. + [JHPhR11]. 1 [RPM97]. 2 [AA07, BDRV01, BPKG07, BD97, Dur89, ..."

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Version 1.33 Title word cross-reference (n + 1) [SA87]. + [JHPhR11]. 1 [RPM97]. 2 [AA07, BDRV01, BPKG07, BD97, Dur89,

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