Meeting times?

[Natasha]

Hi UNR math group,

I've been wanting to attend meetings, but I've been busy. I work at the bookstore on campus. Can someone remind me when/where meetings are at? I would really appreciate it! [:

thanks!!

Natasha

[Ben Hutchins]

Same thing for me~

Cheers!
-Ben Hutchins

[Sam Breen]

We meet every other Friday, and will be meeting this Friday!

Our meeting location is the physics lounge, I believe the room number
is LP118 (or 119).

Do you guys think that right triangles can have legs longer than its
hypotenuse in the complex plane?

BreenEggsAndSam

[Elliot Koontz]

Sam, TJ totally answered that... there is no order on the complex plane, no < or >, so theoretically you could have hypotenuses which are "shorter" than a leg a triangle, but on the complex plane that doesn't really make sense. 

[Sam Breen]

But it makes enough sense to get the right answer using the
pythagorean theorem instead of using complex exponentials. Might just
be the coincidence we need!

[xander]

The issue is not complex numbers, but what you mean by a "right
triangle" and what you mean by the "length of a leg or hypotenuse."
Under the usual Euclidean metric (which measures the lengths of
things) and the usual understanding of what is meant by a right angle
(i.e. viewing C as a two-dimensional vector space, two vectors are
orthogonal if their inner product is zero), right triangles in the
complex plane obey the normal laws of right triangles.

Change the metric or change the inner product, and you may get other
interesting results. You can also get interesting results by
replacing the axiom on parallel lines with another (Euclidean geometry
assumes that given a line and a point not on the line, there is a
unique parallel to the line through the point---Klein and Poincare,
among others, constructed geometries where 0 or infinitely many
parallels are possible---see, for instance, spherical geometry or the
Klein disk).

For an example of a right triangle with legs longer than its
hypotenuse, you might try to think of something coming from spherical
geometry. Take two lines (where lines on the sphere are great
circles) that meet at the north pole at a right angle, and a third
line that intersects the first two somewhere near the south pole. The
"legs" (the segments that meet at the north pole) will be very long
relative to the hypotenuse (the segment near the south pole).

xander