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390 Quick Answers 28 February

Reminder:  Diversity Summit tomorrow - discuss Friday, Annotated bibliography due Friday. 

Our class and connections to diversity and bias.

Exam in 2 weeks.  Topics?  Stronger essays also include a "why" component - cultural connections. 

Feedback:  Exam is not scary.  12 examples, either 2x6 or 3x4.  Only 12 examples.  Not everything (that would be crazy!).  Topics help keep the examples in mind.  I am happy to look over topics and lists of outlines during office hours.  Your topics _must_ be multicultural.  There are many ways to do this.  This course is different from a math course - do the work and you'll be fine so time spend is reward earned.  But, you must do the work.  I don't need enthusiasm for your reactions, but I do need sincere reflection. 

Our course materials include years for everything.  (If you disagree, tell me and I will put it in.) 

Crossword "Persian poet Omar"

Lecture Reactions

This being 2025 relates to Dionysius Exiguus computing Eastre backwards from his time a full 19x28 cycle before the dates that were known before him (up to what we now call 532).  He did not use different starting points for years, but he inspired Bede to use his work to define our starting point.  This is tedious work matching details together, not really something that would be extended indefinitely at the time.

There is a long history of unrealistic word problems - we've seen that.  It's worth questioning if they have value.  I think the answer is that they do as long as they are not claiming _to_ be realistic. 

Jordanus _is_ the first known to use variables in any way like we do.  The work before is all verbal.  And most of the work after is also.  I cannot emphasise this enough.  Please … hear this.  Oh, and it's not like magic when Jordanus starts.  They are generally not widespread.  We will see this in our original source work. 

Algebra is still heavily geometric for a while, although that is starting to fade.  It will fade more on Friday. 



Reading Reactions

Bonfils didn’t make my cut, not much there it seems, but he’s talking about astronomical events for the calendar, and astronomy _is_ different in different locations.  He did also do significant work with decimals.  That's noteworthy, but I'm struggling to find references for him. 

I’m not talking about ben Gerson’s trigonometry in lecture, so I’ll say something here.  We’ve seen (in Indian trigonometry) the work to get to 1 1/2° before.  Ok, some need reminders:  30° you know (I hope - from half of an equilateral triangle and the MCRTT).  18° comes from a pentagon.  We can use half-angle formulas to find sines for angles half of each of those.  Do that to get 15°.  Then we can use sine difference formulas to get 3°.  Then half again to 1 1/2°.  That’s not surprising.  ben Gerson then uses sine addition to get up to 16 1/2°.  Then half-angle six times to get 1/4 + 1/128°.  Similarly, since 15° = 16 - 1°, he uses half-angle six times to get 1/4 - 1/64°.  These can all be done exactly.  Then interpolate down to 1/4°.  We can know those exact values, and they are very close to 1/4°. 

Direct and indirect proof are both in Euclid, and we've seen many examples of them, in contrast to Induction.  

Until 1974, in England (10^6)^2 was a billion and 10^9 was a thousand million only.  Using the old system (10^6)^3 would be a trillion.  In the US and now the world 10^3 is a thousand, (10^3)^2 is a million, (10^3)^3 is a billion, and (10^3)^4 is a trillion.  The old English way seems more logical in a way.  Old way:  (10^6)^n = n-illion, US way:  (10^3)^(n+1) = n-illion.