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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 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[f(|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)

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References

Gramberg, H. http://groups.google.com/group/comp.soft-sys.math.mathematica/msg/249a61fc8bf94547.Jul. 31, 2011.i_luv_ur_mom. http://www.reddit.com/r/pics/comments/j2qjc/do_you_like_batman_do_you_like_math_my_math/. Jul. 28, 2011.J. M. https://math.stackexchange.com/a/56150/. Jul. 29, 2011.

Cite this as:

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

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