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390 Quick Answers 24 February


Reminder:  7 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.  

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. 

Again please pay attention to the relative dates.  At least 5.2 and 5.3 are chronologically consecutive.  

Lecture reactions

Usually work is worth numbers and words at this point.  Sometimes the words are not written repeatedly. 

.  The arithmetic triangle is used for combinations and binomial coefficients. 

Something to remember about Hindu Arabic numerals and their introduction in the west … polynomials _are_ actually conceptually simpler.  There's no regrouping and the places are labeled.   And, Hindu-Arabic numerals had been used for a while before this in Islamic mathematics.  Yes, these are the numbers you use today.  Please also remember the role of zero - having a symbol for nothing is boring, unimportant, and probably around forever.  Using it for a place holder is huge progress.  It's interesting that we don't know if the Indians had zero, but … Fibonacci seems to think they didn't. 

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

I chose to not mention it then, but the finger reckoning dates back to abu'l Wafa. 

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. 

The only thing that Jeff is crediting Gerbert for with numeration is writing them in groups of three, as we separate with commas.  This is not a big step forward. 

A sestina can be analysed using modern group theory.  No one did so at the time.

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 Ï€ = 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.