Geometric Series Fun!

I'm excited about an upcoming lesson about applying geometric series. In fact, I am excited about it enough to be writing about it in way advance. :) (I'm not getting around to it until late next week. But, anyway, it's making me feel very OCD to be pretty much finished with planning for all 3 classes all the way through next week! I am kind of really in love with my job.)

Here it is. I love problem #1, because it brings up the idea of a summation approaching a particular value! If you keep constructing new rectangles at half size (adding counterclockwise each time), you'll see that they just fill in the middle portions and the overall geometric series approachs 2*(original area). YEAH! Chivisimo.




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In other news, Geoff's and my car broke down on the way back from the beach on Sunday. :( --OUR FIRST BREAKDOWN!! The mechanic has been sending us emails with estimated costs, and I just want to know which parts of the car are not broken, because it sounds like he's going to have to replace everything that I either did or did not know existed in a car!! (Fun fact: Our car was spilling oil all over the engine area after having spontaneously broken down on the side of the road, an hour away from our house, when it was already getting dark! It was a bit nerve-wracking, and it even started to rain just as we were waiting on the side of the road. Our friend Greg got out of the car, peeked under the hood, and said seriously, "You guys got a fire extinguisher?" ...Thank goodness we've got awesome friends who live near the beach, who arrived within 15 minutes with a tow truck to drag us all the way back to the city!!)

So, that's gonna be fun... I learned some key words recently from dealing with all the miraculous breakdowns in our lives: grua means tow truck, and calentador is the water heater at our house (whose thermostat broke because of electric current fluctuations that are a side effect of the heavy rains that we had over the summer). Really fun stuff.