The Golden Helmet

''—that this piece we have now before us, which this worthy gentleman has in his hands, not only is no barber's basin, but is as far from being one as white is from black, and truth from falsehood; I say, moreover, that this, although it is a helmet, is not a complete helmet.''

—Cervantes, Don Quixote

''The Golden Helmet'' is a 32-page funny animal comic book adventure story written, drawn, and lettered by Carl Barks.

—Wikipedia, The Golden Helmet

Linkblog: Two curious integrals

Aug 25, 2016

H. Schmid: Two curious integrals and a graphic proof. Elem. Math. 69 (2014)., via Simo Kivelä’s math blog [in Finnish].

Tl;dr.

$\int_0^\infty \prod_{k=0}^n \mathrm{sinc} \left( \frac{t}{2k+1} \right) dt = \frac{\pi}{2},$

but only for $n=1, \dots, 6.$ At $n = 7$ , value of the integral is $< \pi / 2$ , which someone might consider puzzling.

Nice application of convolutions and Fourier transforms. Grokking the proof looks like a doable exercise in functional analysis.