Saturday, October 15, 2011

Ingenious Batman Equation

Saw this on Facebook, and I thought it's fake.

But out of curiosity, I went to google 'Batman equation", and found that somebody actually solve it!!
These people are brilliant...
And the prof who came out with this equation is genius.


Solution taken from HERE:




The ellipse (x7)2+(y3)21=0 looks like this:
ellipse
So the curve (x7)2x3x3+(y3)2y+3337y+33371=0 is the above ellipse, in the region where |x|>3 and y>333/7:
ellipse cut
That's the first factor.

The second factor is quite ingeniously done. The curve x2(3337)112x23+1(||x|2|1)2y=0 looks like:
second factor
This is got by adding y=x2(3337)112x23, a parabola on the positive-x side, reflected:
second factor first term
and y=1(||x|2|1)2, the upper halves of the four circles (||x|2|1)2+y2=1:
second factor second term

The third factor 9((1x)(x.75))(1x)(x.75)8|x|y=0 is just the pair of lines y = 9 - 8|x|:
Third factor without cut
truncated to the region 0.75<|x|<1.

Similarly, the fourth factor 3|x|+.75((.75x)(x.5)(.75x)(x.5))y=0 is the pair of lines y=3|x|+0.75:
fourth factor without cut
truncated to the region 0.5<|x|<0.75.

The fifth factor 2.25(.5x)(x+.5)(.5x)(x+.5)y=0 is the line y=2.25 truncated to 0.5<x<0.5.

Finally, 6107+(1.5.5|x|)(610)144(|x|1)2y=0 looks like:
sixth factor without cut
so the sixth factor 6107+(1.5.5|x|)x1x1(610)144(|x|1)2y=0 looks like
sixth factor

As a product of factors is 0 iff any one of them is 0, multiplying these six factors puts the curves together, giving: (the software, Grapher.app, chokes a bit on the third factor, and entirely on the fourth)
Wholly Batman

4 comments:

Max said...

siao

GES said...

but very impressive, no?

Max said...

coz i dont need it, so didnt impress me..

GES said...

Then let's ask the math teacher.