390 Quick
Answers 23 February
Reminder:
4 March Annotated Bibliography. Yes, following _all_ the
details in the citation example matter. Yes, it is your job
to see them.
Reminder:
Diversity summit Tuesday. Participate. We’ll talk
about it before class Friday. Be prepared.
Feedback:
Names and dates are on our main course information, so they appear
on the screen. It's ok or even great to say "I'm
confused about this one specific point in reading or
lecture". It's less ok to say "I don't understand anything"
(mostly because it's not true. If you're concerned about
your project, please come talk to me about it. I
will now point to the different places that clarifying comments
are scattered. Finally: masking options.
Again please pay attention to the relative dates. At least
5.2 and 5.3 are chronologically consecutive.
Lecture
reactions
Radians are a long way off. I don't think anyone at the time
notices that Khayyami's solution is close to one radian.
In
division 1/x = x^(-1) and we’re just using coefficients.
This was the first example of polynomial long division that I know
of. al-Sama'wal is not finishing with a remainder, but
continuing to divide to get what we would now call a Laurent power
series - with negative powers. This is deeper than a
remainder, and replicates non-terminating decimals, but with
polynomials.
al-Mu'taman's work related to a problem in optics.
I found more about ibn Mun'im's Arabic labels.
What was the cause of the dark ages? Ask a historian, but
over-expansion of the Roman empire lead to vulnerability and decay
inside, then pillaging from without which seemed to continue
throughout Europe. That's my naïve impression.
Having worked on translations, I do think it requires knowledge of
the mathematics to do it in any meaningful way.
Did Fibonacci see ancient Egyptian work, or something descended
from it? Seems hard to imagine not.
Don’t
feel bad about not recognising Fibonacci, Suzuki clearly had
some reason to hide it. I don’t at all know what his
reason is. But he was intentionally doing so. This
is not an accident.
Reading
reactions
A sestina can be analysed using modern group theory. No one
did so at the time.
Gerbert's
abacus is a poorly designed manipulative. It's just grabbing
digits and putting them in their places.
Alcuin’s area formulas are both shockingly
inaccurate. I think the quadrilateral formula only works
for rectangles (where it’s silly), and his circle formula
would be true if π = 4 … wow!
Someone in another class may have told you a fictional story
about Gauß as a child finding the sum of the first 100
numbers. It’s cute. I know where it’s from.
It’s almost surely not true. Alcuin’s work is authentic
and verifiable.
Sometime
I would love to work with someone to play Rithmomachy. I
did order a book to the library about it years ago (the first
time I taught out of Jeff’s book). For what it’s worth,
chess originated from the two-player Indian war game, Chatarung,
which dates back to 600 A.D. In 1000 A.D, chess spread to Europe
by Persian traders. So, comparable time, at least.
Sacrobosco
listed digits in natural order … from right to left … starting
with the most familiar and ending with the most exotic.