Gorgeous couple, cutiehead sleeping toddler

Annabel is mowing her way through a slice of pepperoni pizza. I never know what to expect when I give her foods these days.

The "pining for the fjords" sketch is on Monty Python on BBC America.

I hope I can get through the conference this weekend without my head exploding. In a possible bout of insanity, I volunteered to do the same job next year....

"This is an ex-parrot!"

How do you inscribe a triangle within a parabola? One point in the peak, one at each x-axis crossing? (assuming it's a parabola with exactly two real solutions)

Heh. Math geekery.

Oh, sorry, did I say that? It's meant to be a parabolic segment and its inscribed triangle, so I've said, basically, wherever the line is which cuts off the segment, move the segment so that line is at the x-axis and the segment is above it (so yes, the points of the triangle will be at the x crossings and at the vertex).

T:P is 3:4 right? That's a fun problem.

My method is below, all whitefonted for those that hate math (infidels!): Yeah, all parabolic segments can be defined by an upside-down (negative a) parabola with one of the solutions at (0,0) (so c=0). Then our parabola is of the form y = ax^2 + bx, with a < 0. Our key triangle points are the solutions to y=0: (0,0) and (-b/a, 0) and the peak, which is directly between them and turns out to be (-b / 2a, -b^2 / 4a) (can be found just by plugging x = -b/2a, the midpoint, or using derivative first to be sure). T = 1/2 * b * h, then, is b^3 / 8a^2

To find the area of the parabola segment, just need to integrate ax^2 + bx from 0->-b/a, which isn't too bad, and gives b^3 / 6a^2, so T:P = 3:4

I think this may have been a problem on the AP calc exam my senior year, actually. I've def' seen it somewhere. Figuring out the representation trick you did is definitely the crucial step.

Okay, so where were you two days ago when this would have saved me six pages?!

Also, why isn't it online anywhere? I googled parabola area inscribed triangle, but they all want to talk about Diophantus's proof, which is lovely but not what I need!

OMG, CASH! You're all such pretty people!

I like Cash's hair.

My mother just forwarded my grandmother's obituary. It reads kind of strange to me, but I guess it may just be inescapably weird to read a summary like that of someone you know. I found this particularly weird:

Her husband, parents, brother, and an infant grandson preceded her in death.

I know it's traditional, but... it's weird. Also, depressing. Which, in an obituary, is sort of gilding the lily, don't you think?

(The obituary I can find online -- maybe a different paper? -- just says "She was preceded in death by an infant grandson" which, actually, may be worse.)

Cash - you look so elegant ! No wonder Buffista babies are so cute.

Hey VW - hopeing things are going well enough so you can stay home. A step back is ok... we can help hold you up.

and I am jealous because you have a frosty.