Don’t Get the Polywobbles Shifting Quartics? — It’s Simpler With a ‘Designer Ratio’!

Author(s): Greg Oliver

Originally published on Towards AI.

Simplifying Quartic Shifts using a ‘Designer Ratio’Now You ‘B‘ Me. Now You Don’t!

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It can give you the Polywobbles trying to get your head around the fact that moving any Polynomial around the X-Y Grid can change its formula markedly without any change of shape. Most of us are ok with straight up and down moves due to Constant term changes, but lateral shift formula changes are a bit harder to grasp.

The Quartic y=Ax⁴+Bx³+Cx²+Dx+E shown in black in the Header Graph is shifted laterally until its 2 Inflection Points +-Ip(x) equally straddle the Y-Axis. The now ‘Home-based’ function shown in red, y=Ax⁴+cx²+dx+e has no Bx³ term and different x^n Coefficients and Constant e, but its shape and size have not changed.

Many students will be familiar with lateral shifts referred to as ‘Depressing’ which Cardano adopted to eliminate the Bx² term with his Cubic roots solution and Ferrari the Bx³ term in deriving the Quartic roots solution. I think the term can be a little misleading because there is no change to the functional architecture, it simply has a new address.

Furthermore if shifting to random locations, these terms change but are not necessarily eliminated. So while this… Read the full blog for free on Medium.

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Published via Towards AI