It's unknown whether any region in R^n described by a set of algebraic equations has a volume of 6/pi^2. (In particular, if you take the Cartesian product with the circle x^2 + y^2 = 1/6, then the resulting shape has a volume of 1/pi, which is not known to belong to the Ring of Periods.) https://en.wikipedia.org/wiki/Ring_of_periods So it's an unsolved problem, unless there's a particular non-existence proof which works in dimension 2 but not in dimension n. Best wishes, Adam P. Goucher
Sent: Thursday, January 19, 2017 at 4:53 AM From: "David Wilson" <davidwwilson@comcast.net> To: 'math-fun' <math-fun@mailman.xmission.com> Subject: [math-fun] Analytic geometry question
Is there a planar figure describable whose boundary is a polynomial in x and y, and whose area is 6/pi^2?
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