So this week we learned about one of the great troubles in math, having to estimate. I personally really don't like the idea of estimating, because if we are estimating, we don't have a definite answer, and if we don't have a definite answer, then what's the point? I realize that estimating is a big part of math and that most math done in real life is about estimation, but I just don't see the point in it.
When we first started doing the exercises that involve estimating the area of something, I immediately thought of making a grid. Now this obviously takes a lot more time than making rectangles, but it could possibly be more accurate, depending on how small you make the squares. Technically, you could make the squares very small, and then the accuracy would be increased greatly. But who has the time to do that? And then we learned about the rectangles. In a way, the rectangles are much like a grid. While grids are made of squares, the rectangles are made of... well, rectangles. The cool thing about the rectangles is that you can make them as tall as the curve is, which makes them pretty accurate. The only problem is that you can't make them have curved tops, so there will always be more or less area than there actually is (which is why they are just estimates).
Estimating the area under a curve isn't particularly one of my favorite subjects, but that's okay. I like the idea of having different kinds of ways to estimate the area under the curve (these include RRAM, MRAM, and LRAM). Even though I know some work better than others (MRAM tends to work better than LRAM when the graph is increasing), it is nice to know that there are multiple ways to do it.
When we first started doing the exercises that involve estimating the area of something, I immediately thought of making a grid. Now this obviously takes a lot more time than making rectangles, but it could possibly be more accurate, depending on how small you make the squares. Technically, you could make the squares very small, and then the accuracy would be increased greatly. But who has the time to do that? And then we learned about the rectangles. In a way, the rectangles are much like a grid. While grids are made of squares, the rectangles are made of... well, rectangles. The cool thing about the rectangles is that you can make them as tall as the curve is, which makes them pretty accurate. The only problem is that you can't make them have curved tops, so there will always be more or less area than there actually is (which is why they are just estimates).
Estimating the area under a curve isn't particularly one of my favorite subjects, but that's okay. I like the idea of having different kinds of ways to estimate the area under the curve (these include RRAM, MRAM, and LRAM). Even though I know some work better than others (MRAM tends to work better than LRAM when the graph is increasing), it is nice to know that there are multiple ways to do it.