### Change of Plans?

Mar. 19th, 2019 09:40 amWe shall see.

Classes tomorrow. In History of Math, we're right on the cusp of calculus, with the work of John Wallis and Isaac Barrow. (Barrow was Newton's mentor, and actually discovered the relation between tangents and areas that we now call the Fundamental Theorem of Calculus.) In Abstract Algebra, we're just getting into Field Theory, and we'll get to the connection to straightedge-and-compass constructions pretty soon. In Linear Algebra, we've finally gotten to abstract vector spaces. (This course still stays pretty concrete - our primary clientele here consists of engineers and physics majors.)

It's been a good break, but I need to get back in harness.

### Crushing Under Heels Redux

Mar. 17th, 2019 08:00 amGorgo of Sparta approves of me.

### Mistaken Identity

Mar. 14th, 2019 10:57 amHope the pup gets back home!

### Unexpected Victory

Mar. 8th, 2019 10:42 amGilgamesh's city of Kish had had its walls blasted to rubble by a naval bombardment, and as soon as my land forces got there, they waltzed right in... at which point the game ended, in a Religious victory. I had already converted most of the cities in each of my remaining rivals.

Dammit, I was looking forward to grinding the entire world under my heel!

### Breakin' Good

Mar. 8th, 2019 09:51 amI figure on spending the week puttering around the house, mostly. I do intend a little shopping: the Chef's Shoppe for a new onion chopper (I've been avoiding recipes with onion since the old one broke, and that takes a deep cut out of my repertoire) and a new coffee filter cone (the old one's still more or less satisfactory, but it's chipped and ugly, and some undesirable things have been happening as well), and Target for a new laundry basket (the old one's crumbled and chewed to hellangone) and perhaps a few other household items.

Otherwise, I expect to spend my time playing Civ 6, working on my Finances database, and maybe writing the introduction and conclusion to Taxonomy II (and reading the galley proofs for Taxonomy I so I can give the journal the go-ahead to publish it). Perhaps I'll also do some "spring" cleaning. There are a few university duties I also have to attend to, but I can do them from home as well.

:stretches and yawns:

### Dogiversary

Mar. 6th, 2019 03:58 am:raises glass:

First off, an indication of the difficulties involved. Consider the quadrilateral with vertices A(0,0), B(1,1), C(1,0), D(0,1). This quadrilateral is shaped like a bow tie. What is its area? A natural answer might be the sum of the absolute areas of the two triangles it encloses, but that turns out to be an inconvenient choice mathematically.

The definition of area that I use rests on two declarations. First, the area of a triangle is the absolute area if the vertices are given in counterclockwise order; it's the negative of the absolute area if they are given in clockwise order. (This is related to the fact that a two-by-two matrix can have negative determinant, if you took and remember any linear algebra.) Second, if you have a polygon ABC..TU, its area may be computed by selecting a point Z and adding up the areas of the triangles ZAB, ZBC, ..., ZTU, ZUA. It turns out that the choice of Z makes no difference - the sum is the same, no matter where Z is.

For example, consider the triangle with vertices A(0,0), B(1,0), and C(0,1). The vertices ABC are given in counterclockwise order, so the area is the absolute area, which is 1/2. If you chose Z in the interior, all three of ZAB, ZBC, ZCA would also be counterclockwise, and obviously the area of ABC is the sum of the areas of those triangles. But what if you chose Z = (1,1)? Note that the triangles ZAB and ZCA are both counterclockwise, but ZBC is clockwise, so we get the sum of the absolute areas of ZAB (1/2) and ZCA (1/2), *minus* the absolute area of ZBC (1/2), so the area is 1/2 + 1/2 - 1/2 = 1/2. The same thing will happen for any choice of Z.

As for the bow-tie quadrilateral, the simplest choice of Z is at the intersection of AD and BC, (1/2, 1/2). Now ZAB is counterclockwise, but ZCD is clockwise, so the area is the absolute area of ZAB minus the absolute area of ZCD, or 1/2 - 1/2; the quadrilateral has area 0. (ZBC and ZDA are degenerate triangles, with area 0.)

If you want a challenge, work out the area of the hexagon whose vertices are A(0,0), B(1,0), C(1,1), D(1/3,1/3), E(2/3,1/3), and F(0,1).

### Memories...

Feb. 21st, 2019 07:10 pmThe family did come away with some souvenirs, including some linguistic ones, bastardized German phrases that became part of our family language. ("Idiolect" is the word for one's own specific habits of speech; there ought to be one for a family's.) One that I remember, we used with the meaning "It doesn't matter" or "I don't care"; I recall it as "mox nix", but of course that's a monoglot child's interpretation. Nowadays I know a little German, but not enough to confidently reconstruct the original. Presumably "machen" and "nicht", in some form or another, are involved.

I know there are people who follow me who know more German than I do. What could the original phrase have been, bitte?

### Mucho Machado!

Feb. 19th, 2019 06:15 pmI left San Diego in 1975. Since then, I have been to exactly one Padres game, during Khalil Greene's rookie year. (Shame what happened to him.)

I am nonetheless very excited to hear that the Padres have signed Manny Machado. Jumping-up-and-down excited, I am, and looking forward to that infield (Hosmer, Urias, Tatis, Machado. :drool:).

There is a strong chance this will be my last post on baseball this year. But for once there's a chance that it *won't*.

Does anyone a) know how to get decent docs for OO, or b) know of a decent, user-friendly, not-too-complicated DB environment, preferable as easy to work with as Access?

Most of the classes of quadrilateral I've worked with involve either the base parallelogram by itself, or the relationship between the perturbation and various special lines of the parallelogram. More about that later; but this construction is key to the way I study quadrilaterals.

(I tried to insert a pair of pictures illustrating the constructions, but it didn't seem to work. Sorry.)

### Walk Like a Pangolin!

Feb. 15th, 2019 09:29 amUntil today, I was unaware that pangolins are bipedal.