Interestingly, In[78]:= Arg[(((Sqrt[5] + 1)*(-Sqrt[Sqrt[17] - 3]* Sqrt[4*Sqrt[17] - 2*Sqrt[2*Sqrt[17] + 34]] + Sqrt[2*Sqrt[17] + 34] + Sqrt[17] + 1)/ 64) - ((Sqrt[5 - Sqrt[5]]* Sqrt[Sqrt[Sqrt[17] - 3]* Sqrt[2*Sqrt[2*Sqrt[17] + 34] + 4*Sqrt[17]] - Sqrt[2*Sqrt[17] + 34] + Sqrt[17] + 17])/16))* I + (((Sqrt[5] + 1)* Sqrt[Sqrt[Sqrt[17] - 3]* Sqrt[2*Sqrt[2*Sqrt[17] + 34] + 4*Sqrt[17]] - Sqrt[2*Sqrt[17] + 34] + Sqrt[17] + 17])/(16* Sqrt[2])) + ((Sqrt[ 5 - Sqrt[5]]*(-Sqrt[Sqrt[17] - 3]* Sqrt[4*Sqrt[17] - 2*Sqrt[2*Sqrt[17] + 34]] + Sqrt[2*Sqrt[17] + 34] + Sqrt[17] + 1))/(32*Sqrt[2]))] // FullSimplify // tim During evaluation of In[78]:= 9.430501 [seconds], 2 [multiplicands] Out[78]=π/170 is a constructible angle, whereas In[79]:= UnitConvert[Quantity[π/180, "Radians"], "Degrees"] /.n_Integer :> IntegerName@n Out[79]= Quantity["one", º] is not. —rwg -------- Original Message -------- Subject: Re: [math-fun] 170 Date: 2019-05-08 08:50 From: James Propp <jamespropp@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Reply-To: math-fun <math-fun@mailman.xmission.com> That's perfect! I see that in particular the Gray-code-based puzzle "The Brain Puzzler" takes 170 moves to solve: https://everything2.com/title/The+Brain+Puzzler Thanks, Michael! Jim On Wed, May 8, 2019 at 11:06 AM Michael Kleber <michael.kleber@gmail.com> wrote:
Membership in http://oeis.org/A000975 is definitely the way to go. The description of the sequence makes it clear that it's just saying 170 is 10101010 in binary, but the comments section offers plenty of examples of cool things about those alternating-0s-and-1s numbers.
--Michael
On Wed, May 8, 2019 at 10:41 AM Mike Stay <metaweta@gmail.com> wrote:
On Wed, May 8, 2019 at 8:29 AM James Propp <jamespropp@gmail.com> wrote:
I’ve agreed to host Carnival of Mathematics #170 next month, and I’m wondering whether the number 170 has any especially nice properties
that
might deserve mention.
The number 170 has its own Wikipedia page, but none of the mathematical properties listed there appealed to me.
I might say a little about writing numbers as sums of two squares, but I’d prefer something a little more exciting.
Jim Propp ________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush.