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Batman Curve

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BatmanCurve

The Batman curve is a piecewise curve in the shape of the logo of the Batman superhero originally posted on reddit.com on Jul. 28, 2011. It can be written as two functions, one for the upper part and the other for the lower part, as

f(x)=(h-l)H(x+1)+(r-h)H(x-1)+(l-w)H(x+3)+(w-r)H(x-3)+w
(1)
g(x)=1/2[|1/2x|+sqrt(1-(||x|-2|-1)^2)-1/(112)(3sqrt(33)-7)x^2+3sqrt(1-(1/7x)^2)-3][sgn(x+4)-sgn(x-4)]-3sqrt(1-(1/7x)^2),
(2)

where H(x) is the Heaviside step function and

w=3sqrt(1-(x/7)^2)
(3)
l=1/2(x+3)-3/7sqrt(10)sqrt(4-(x+1)^2)+6/7sqrt(10)
(4)
h=1/2[3(|x+1/2|+|x-1/2|+6)-11(|x+3/4|+|x-3/4|)]
(5)
r=1/2(3-x)-3/7sqrt(10)sqrt(4-(x-1)^2)+6/7sqrt(10)
(6)

(J. M. 2011).

Its area can be computed exactly as

A=(955)/(48)-2/7[2sqrt(33)+7pi+3sqrt(10)(pi-1)]+21[cos^(-1)(3/7)+cos^(-1)(4/7)].
(7)

Here cos^(-1) denotes the inverse cosine with values in radians. The area is approximately 48.4244 square units.

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References

Gramberg, H. Jul. 31, 2011. https://groups.google.com/g/comp.soft-sys.math.mathematica/c/P8t_EHJ3e1c/m/R0X5i_xhmiQJ.i_luv_ur_mom. Jul. 28, 2011. https://www.reddit.com/r/pics/comments/j2qjc/do_you_like_batman_do_you_like_math_my_math/.J. M. Aug. 7, 2011. https://math.stackexchange.com/questions/54506/is-this-batman-equation-for-real/56150#56150.Numberphile. "Batman Equation." Jul. 30, 2012. https://www.youtube.com/watch?v=M-yAgyrzGdo.

Referenced on Wolfram|Alpha

Batman Curve

Cite this as:

Weisstein, Eric W. "Batman Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BatmanCurve.html

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