Jensen Ackles Ass Equation 2.0

Abstract

I propose that a more accurate ass equation is y=-3.4088928e-019*x^9+6.9052649e-016*x^8-5.7819655e-013*x^7+2.5915691e-010*x^6-6.7602807e-008*x^5+1.0534899e-005*x^4-9.7423168e-004*x^3+4.9830296e-002*x^2-1.0748233*x+2.0046681e+002 (for 0<x<472). While an ugly equation, it works much better than the original Jensen Ackles Ass equation. A full copy of this paper (that includes the appendix) can be found here.

Definitions

The original Jensen Ackles Ass Equation: y = -(sin(x^(1.7/6)+4)+(1/x))+10 (for 1<x<12) [found here]

Most common Jensen Ackles Ass Equation picture:

Jensen Ackles Ass Equation 2.0

I decided to try my hand at deriving a Jensen Ackles Ass equation because the original equation uses a sine function, where in data analysis a polynomial function is typically used in non-repeating situations such as this one.

Upon further investigation, I found that I am unable to generate a graph of the original equation (in radians or degrees) that remotely resembles the desired shape. My failure is shown below.

Figure 1 - sin(degrees) in pink, sin(radians) in yellow

I don’t mean to belittle LiveJournal user Potthead’s work on the original equation – without it and their work I may never have begun this crazy quest – I simply mean to emphasize the need for a new/better equation.

As far as I can tell, the red line in the most common Jensen Ackles Ass Equaiton picture was drawn on by hand, because no equation I’ve gotten near can match it exactly.

With that in mind, I first used MATLAB and function “getpoints.m” (see appendix) to record the multiple data points along Jensen’s back/ass as shown in figure 2.

Figure 2 - Data points represented by blue “x"s

I then tried to fit the data to a 4th order polynomial because it has 3 obvious points of inflection. This result was acceptable, but the dip for the lower back was woefully misplaced. The next best order of polynomial is 6th, but that was still not ideal. A 9th order polynomial yields the best results. The 4th and 9th order polynomials can be seen in figure 3. All equations were acquired using appropriate variations of “find_line.m”.

Figure 3 - Comparison between 4th order and 9th order polynomial functions

The equation returned by “find_line.m” is as follows: y=-3.4088928e-019*x^9+6.9052649e-016*x^8-5.7819655e-013*x^7+2.5915691e-010*x^6-6.7602807e-008*x^5+1.0534899e-005*x^4-9.7423168e-004*x^3+4.9830296e-002*x^2-1.0748233*x+2.0046681e+002 (for 0<x<472).

Now, I am aware that I should have stuck with a 4th order polynomial because upper back/lower back/ass curve contains 3 points of inflection, but I decided that my main goal was to draw pretty pictures and not to be a perfect data analyst. The lovely 9th order curve can be seen in figure 4. Further proof that this is a robust equation can be seen in figure 5 where it is accurately rendered by my graphing calculator.