0.8440935944…

This is an improvement of 2.178245 × 10^{-5} over our earlier work—roughly equal to our improvement over Hansen.

• John Baez, Karine Bagdasaryan and Philip Gibbs, The Lebesgue universal covering problem, *Journal of Computational Geometry* **16** (2015), 288-299.

The referees caught a number of mistakes, so if you ever got ahold of an earlier version of this paper, and if you care, please get the new one. The journal is open-access, so it’s free.

]]>(I’m not sure I’ll have the guts to include this when we submit the paper for publication.)

]]>• Greg Egan, Gibbs–Bagdasaryan–Baez reduction: Mathematica notebook.

• Greg Egan, Gibbs–Bagdasaryan–Baez reduction: Mathematica printout.

I’ve updated our paper to refer to these.

]]>Thanks for catching those stupid typos. Those are my fault, and it goes to show (yet again) that errors easily creep in when copying things by hand—a lesson I should have learned by now.

But thanks much more for redoing Philip’s calculation! That’s truly heroic! Could you mail me the Mathematica program? I guess you can send it to me as a “notebook”. I can put it on my website and include a link to it in the paper, saying you used it to check our work. That way a referee of the paper, or any other interested party, will have another way to check our work.

]]>I reconstructed the geometry for your final cover in Mathematica, and I get the same results for area as a function of the angle σ as you do.

Using high-precision arithmetic (2000 digits working precision), I found a valid σ of:

1.294389444703601012°

giving an area for the cover of:

0.844115297128419059…

There are a couple of typos in the paper. In the second inequality on page 2, you give Sprague’s area as:

0.8441377708435

but I believe the correct value is:

0.844137708435

i.e. there’s a triple 7 in the paper where it should be just a double 7.

Also, when you quote your final bound on page 10, you go from:

0.8441153768593765

which I agree with, to:

0.844411538

where the double 4 has become a triple 4.

]]>