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trapezoidal triglycerides
Jun. 9th, 2014 11:23 amGood news today on both those fronts. In the latter, mine are down (though not yet enough), and all my other (less) iffy blood numbers improved too. In the former, I was able to figure out the answer to this question the formal way after the guesstimate method wasn't working for me:
Parallel side length A plus parallel side length B multiplied by height and divided by 2. Or, (A+B)h/2: This is the mathematical formula for the area of what shape?
I had to start from "Hmm, what shapes have parallel sides" and what the "height" of a parallelogram and a trapezoid are (more the width, as I was drawing them), and what they might mean by A & B in the cases of each of those shapes (seems it'd be different). Then my toy examples with sizes that wouldn't be likely to promote coincidences (so 3, 7, etc.) didn't work sufficiently fast+conclusively, and that failure was the key to my having (to have) the real fun of trying to figure the geometry of them. I made a boneheaded glitch at one stage (on the area of a rectangle within!) it took me a while to catch (d'oh!), and I had to keep doing little experimental asides to remember/confirm rules of arithmetic/fractions/roots, etc. (cuz I don't seem to be able to remember much of that at all with authority), but I got there. Eventually I got a formula that is equiv to (A+B)h/2, and, terribly minor though it is, it felt good to derive/prove it myself. The key is in getting rid of the two extraneous variables that don't appear in that final formula by using their definitions in terms of others. When I finally got the glimmer that I'd be able to ditch my - Dh/2 + Dh/2, I was exclamation-point-ly tickled.
In the sung words of Oliver Twist & co.: small pleasures, small pleasures--- who would deny us these?
Parallel side length A plus parallel side length B multiplied by height and divided by 2. Or, (A+B)h/2: This is the mathematical formula for the area of what shape?
I had to start from "Hmm, what shapes have parallel sides" and what the "height" of a parallelogram and a trapezoid are (more the width, as I was drawing them), and what they might mean by A & B in the cases of each of those shapes (seems it'd be different). Then my toy examples with sizes that wouldn't be likely to promote coincidences (so 3, 7, etc.) didn't work sufficiently fast+conclusively, and that failure was the key to my having (to have) the real fun of trying to figure the geometry of them. I made a boneheaded glitch at one stage (on the area of a rectangle within!) it took me a while to catch (d'oh!), and I had to keep doing little experimental asides to remember/confirm rules of arithmetic/fractions/roots, etc. (cuz I don't seem to be able to remember much of that at all with authority), but I got there. Eventually I got a formula that is equiv to (A+B)h/2, and, terribly minor though it is, it felt good to derive/prove it myself. The key is in getting rid of the two extraneous variables that don't appear in that final formula by using their definitions in terms of others. When I finally got the glimmer that I'd be able to ditch my - Dh/2 + Dh/2, I was exclamation-point-ly tickled.
In the sung words of Oliver Twist & co.: small pleasures, small pleasures--- who would deny us these?
