A ‘Back of Envelope Sketch’ for Quintic Design
Last Updated on August 29, 2025 by Editorial Team
Author(s): Greg Oliver
Originally published on Towards AI.
Using the ‘Extended Quadratic Equation’ For Approximating Quintic Architecture
Unlike Quadratics, Cubics and Quartics, Quintic Polynomial architecture y=Ax⁵+Bx⁴+Cx³+Dx²+Ex+F generally produces more ‘polywobbles’ making visualisation less intuitive. While the x Coefficient E and Constant F reveal the gradient and constant at x=0 and though the overall shape replicates a similarly signed +- Cubic from a distance, additional inside Turning Points Tp’s can complicate things a little.
This article explores the complexities of Quintic Polynomial architecture by introducing a method to sketch typical Quintics using the Extended Quadratic Equation. It delves into the use of genetic tracers to improve visualization and understanding of the polynomial shape and behavior, highlighting the importance of internal turning points and their significance in mathematical modeling. The author also encourages experimentation with polynomial functions, particularly in applications related to robotics design, to foster a deeper comprehension of higher order polynomials and their practical uses.
Read the full blog for free on Medium.
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