0.8440935944…

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

Oh, whoops! I forgot I removed the word “whopping” when I submitted the paper — feeling a bit nervous I guess. If I’d been clever, I would have re-inserted it in the final version.

]]>• 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.

]]>Sarcastically, like us?

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

]]>Thanks for giving me the Mathematica notebook and a printout that people can read without using the software:

• 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.

]]>Wow, that’s *amazing!* You’re the first person outside the team to actually check our work.

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.

]]>