667 per centimeter

Merry Newtonmas tomorrow! On finding the area of the Batman Shape using Monte Carlo integration

It’s Newtonmas 2017 tomorrow!

What better way to celebrate than talk about integration!

The Batman Shape (sometimes called the Batman Curve, somewhat erroneously, I think) looks like this:

You can find details about it at Wolfram MathWorld, including its area in closed form. What’s interesting is integrating it without algebra, numerically. Quadrature would be difficult and a lot of work. Monte Carlo integration, not so much. What’s interesting is the relation between that and use of Monte Carlo integration for Bayesian computation, such as in Markov Chain Monte Carlo and slice sampling.

I was going to do the area of the Batman Shape using Monte Carlo integration and compare it with the exact value, but Jame Schloss has already done that. I might come back and do it using slice sampling, which will be a little interesting since it’s a two-dimensional figure. I’ll append that below if I do.

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  1. Sampling: Rejection, Reservoir, and Slice | Hypergeometric

    […] Third, the discussion surrounding the Python code Professor Rahul offers is a bit weak, particularly regarding the multimodal case. This is unfortunate, because that’s the interesting one. This suggests I’m talking myself into doing a tutorial on slice sampling in R some time down the road, remedying these problems. When I do so, I should really include finding the area of the Batman shape as previously promised. […]

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Sophia Bennett is an art historian and freelance writer with a passion for exploring the intersections between nature, symbolism, and artistic expression. With a background in Renaissance and modern art, Sophia enjoys uncovering the hidden meanings behind iconic works and sharing her insights with art lovers of all levels. When she’s not visiting museums or researching the latest trends in contemporary art, you can find her hiking in the countryside, always chasing the next rainbow.