[math-fun] Another experimental multiple choice
Trying to minimize math jargon. gosper.org/Dragon Screen Shot.png Fair question? --rwg
ie, http://gosper.org/Dragon%20Screen%20Shot.png On Sat, Aug 30, 2014 at 12:19 PM, Bill Gosper <billgosper@gmail.com> wrote:
Trying to minimize math jargon. gosper.org/Dragon Screen Shot.png Fair question? --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
I tweaked it. gosper.org/Screen Shot <http://gosper.org/Screen%20Shot%20Dragon.png>Dragon <http://gosper.org/Screen%20Shot%20Dragon.png>.png <http://gosper.org/Screen%20Shot%20Dragon.png> . --rwg On Sat, Aug 30, 2014 at 12:19 PM, Bill Gosper <billgosper@gmail.com> wrote:
Trying to minimize math jargon. gosper.org/Dragon Screen Shot.png <http://gosper.org/Screen%20Shot%20Dragon.png> Fair question? --rwg
On Sat, Aug 30, 2014 at 2:10 PM, Bill Gosper <billgosper@gmail.com> wrote:
I tweaked it. gosper.org/Screen Shot <http://gosper.org/Screen%20Shot%20Dragon.png> Dragon <http://gosper.org/Screen%20Shot%20Dragon.png>.png <http://gosper.org/Screen%20Shot%20Dragon.png> . --rwg
Did anyone (besides a helpful private respondent, who mentions that the figure remains vertically squished despite my struggles with (hypersucky) OpenOffice) find this too easy or too hard? If you solved it, did you use any prior or outside knowledge about Dragons? --rwg
On Sat, Aug 30, 2014 at 12:19 PM, Bill Gosper <billgosper@gmail.com> wrote:
Trying to minimize math jargon. gosper.org/Dragon Screen Shot.png <http://gosper.org/Screen%20Shot%20Dragon.png> Fair question? --rwg
PS, pure evil:
https://mail.google.com/mail/?ui=2&ik=97b2a014c7&view=att&th=1481fbf0be9db9f... (Problem (4).) Subject: [math-fun] fib(1/2) Binet's and another formula give Sqrt[1/5 - (2 I)/5] and ((1 - I) (Cosh[ArcCsch[2]/2] + I Sinh[ArcCsch[2]/2]))/Sqrt[5] This is that "other formula". Axel Vogt raised a good point: In[730]:= MinimalPolynomial[((1 - I) (Cosh[ArcCsch[2]/2] + I Sinh[ArcCsch[2]/2]))/Sqrt[5], z] Out[730]= 1 - 2 z^2 + 5 z^4 I don't know why FullSimplify didn't try this. FullSimplify[TrigToExp[2*I^(n - 1)/Sqrt[5] Sin[n*ArcSec[2*I]]],n\[Element] Integers] comes within hailing distance of Binet.
Gosper, I was already familiar with dragons, so I knew that in the tail chains each connected piece has half the area of the next (except for one weird joint in the middle). So I was able to get the right answer (assuming I did). On Sun, Aug 31, 2014 at 4:26 PM, Bill Gosper <billgosper@gmail.com> wrote:
On Sat, Aug 30, 2014 at 2:10 PM, Bill Gosper <billgosper@gmail.com> wrote:
I tweaked it. gosper.org/Screen Shot <http://gosper.org/Screen%20Shot%20Dragon.png> Dragon <http://gosper.org/Screen%20Shot%20Dragon.png>.png <http://gosper.org/Screen%20Shot%20Dragon.png> . --rwg
Did anyone (besides a helpful private respondent, who mentions that the figure remains vertically squished despite my struggles with (hypersucky) OpenOffice) find this too easy or too hard? If you solved it, did you use any prior or outside knowledge about Dragons? --rwg
On Sat, Aug 30, 2014 at 12:19 PM, Bill Gosper <billgosper@gmail.com> wrote:
Trying to minimize math jargon. gosper.org/Dragon Screen Shot.png <http://gosper.org/Screen%20Shot%20Dragon.png> Fair question? --rwg
PS, pure evil:
https://mail.google.com/mail/?ui=2&ik=97b2a014c7&view=att&th=1481fbf0be9db9f... (Problem (4).)
Subject: [math-fun] fib(1/2)
Binet's and another formula give Sqrt[1/5 - (2 I)/5] and ((1 - I) (Cosh[ArcCsch[2]/2] + I Sinh[ArcCsch[2]/2]))/Sqrt[5]
This is that "other formula". Axel Vogt raised a good point:
In[730]:= MinimalPolynomial[((1 - I) (Cosh[ArcCsch[2]/2] + I Sinh[ArcCsch[2]/2]))/Sqrt[5], z]
Out[730]= 1 - 2 z^2 + 5 z^4
I don't know why FullSimplify didn't try this.
FullSimplify[TrigToExp[2*I^(n - 1)/Sqrt[5] Sin[n*ArcSec[2*I]]],n\[Element] Integers]
comes within hailing distance of Binet. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
-
Allan Wechsler -
Bill Gosper -
Thane Plambeck