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Discover Lill's method, a surprisingly simple and visual approach to solving polynomial equations using turtles and lasers. Explore stunning applications including elegant solutions for quadratic equations using ruler and compass, and cubic equations with origami. Delve into Horner's form, synthetic division, and a newly discovered incarnation of Pascal's famous triangle. Learn through step-by-step explanations, from the basic principles to advanced concepts, accompanied by visual demonstrations and real-world examples. Gain insights into the historical context and mathematical significance of this method, referencing original papers and modern interpretations. Enhance your problem-solving skills and deepen your understanding of polynomial equations through this innovative and visually engaging approach.