I will try to return the GREAT day papers first - I hope for Friday for
those who turned in on Monday, to advise with those people.
Remember your presentations are two weeks from yesterday.
Unfortunately, I have another exam tomorrow evening and so will be
doing virtual office hours again (remember JohannesOhrs on
AOLIM). Also, I will be unavailable in all capacities a week from
tomorrow 4p ->. Therefore, esp. for those presenting, please
don't hesitate to schedule meetings with me outside of office
hours. This is important, and I do want to be available to you in
spite of my scheduling challenges.
§8.3.4-
We'll talk about other (more familiar) work of Monge, but he did project 3d objects on to the xy, yz and xz planes.
Gauß's 17-gon was notable because it was the first regular
polygon constructed in millennia. His long discussion is
precisely for Gauß's construction. We'll look at it.
This has nothing to do with Gaußian elimination, or any other
results of Gauß. Such constructions in practice
aren't commonly performed today in research mathematics. Part of
this is because the ancient construction problems are almost entirely
solved. There are plenty of other ways to construct things.
Impossibilities are proven by contradiction.
Surely there are many contributions of Gauß - as typical for us -
we will only consider one aspect, which Suzuki has found valuable.
Germain used a pseudonym to hide her gender. She communicated to Gauß thru letters.
There are still always things omitted. Fourier got slighted here
with Poisson. This will only get worse. As always, please
explore the things that interest you elsewhere.
Gauß's childhood summing story probably is not true - at least it's difficult to verify.
I think Gergonne's satement about communication says that it is
important to make new ideas understandable to the public. I agree
to a point - if we assume a highly educated passer-by.
We cannot discuss Germain's proof - too difficult and too
obscure. Germain only spoke up for Gauß's safety out of
academic respect.
Poisson made significant contributions to probability - those are
probably his most famous. Also appears in differential equations,
theoretical physics,
"How does Suzuki know that the students were incapable of appreciating
Lagrange's work?" There are records of his students' reactions,
and information about how he presented the material. Combining
that with knowing the background at the time we can come to such
conclusions.
Repeated square roots are definitely constructible. Wantzel
proved things like this by considering the coordinates that would
appear as intersections in constructions.
Suzuki emphasises professors to distinguish them from readers and examiners.
Projective geometry was clearly "in the air"....is this the same thing
as saying something is "up in the air?" No, it was an idea that
many had at the time.
"I think it was very bold of Poisson to say that "Life is good for only
two things: to study mathematics, and to teach it". It made me
wonder if you agree with the statement or disagree and I personally
think you would agree." Hm. Ask me about some of the other
things that I'm passionate about some other time.