This PreMath channel on YouTube reminds me of how much I've forgotten. I fail to solve most of the problems on the channel, but every once in a while, an easy one like this pops up, and I can feel temporarily proud.
Sometimes, being "good at math" is simply a matter of common sense, but sometimes, it's more about remembering certain algebraic and geometric properties so you can shortcut your way to a solution.
In the above case, they give the circle's radius as 3√2. Imagine that radius going from one corner of the square to the center, then from the center to the diagonally opposite corner of the square. This gives you double the radius of the circle, i.e., the diameter. It also gives you the length of the square's diagonal: 6√2.
That diagonal divides the square into two right triangles, but not just any right triangles: these are 45-45-90 right triangles. This means that, if the leg length of such a triangle is x, then the diagonal (the hypotenuse) has to be x√2.
Work that logic backward. If the hypotenuse is 6√2 (which we know), then the leg length must be 6. So now, you know the length of the side of the square. To calculate the square's area, just multiply 6 by 6: 36. QED.
Algebra was torture for me in school, I somehow managed to pass the required course in college, but did not retain anything I'd "learned" after the final exam.
WHAT CORN AND PEANUTS ARE HIDDEN IN THE WARM AND STEAMING PILE? Vapid cultural commentary, pungent reviews, sundry Korea-related musings, fartological/scatological humor, political flatulence, and nondualistic Zen excretions in prose or poetry form.
Got a beef? Write the Hominid at bighominid@gmail.com, and put "HAIRY CHASMS" in the subject line, or your mail will be automatically trashed by Satan, my beautiful but deadly spam filter. Assume your mail will be published (editing at my discretion), unless you specify otherwise. Welcome to my backside.
BLOGROLLING POLICY: I don't do mutual linkage, and I have no problem with asymmetrical linkage: I link to bloggers who don't link back, and that's fine by me. Please DO NOT ask to be linked. Please DO NOT expect linkage just because you've linked to me. Also, if I don't link to you, please do not assume I think your blog sucks.
COMMENTS POLICY: My blog is my house; I'm responsible for keeping my dwelling clean. Commenters are guests, and guests of this blog will be civil, succinct, and relevant. All comments are subject to approval; I reserve the right to publish or not publish—in a pristine or altered form—all comments (and emails intended as comments) that I receive. Act like an asshole on my turf, and I'll make you look like the asshole you are. Be cool, and we won't have a problem. Simple, yes? And before I forget:
NO ANONYMOUS COMMENTS. Take responsibility for what you say. Screen names are OK, but no sock puppetry. Use the same SN consistently.
3 comments:
If there is one thing I am worse at than grammar and punctuation, it is math. My brain just isn't wired that way.
This PreMath channel on YouTube reminds me of how much I've forgotten. I fail to solve most of the problems on the channel, but every once in a while, an easy one like this pops up, and I can feel temporarily proud.
Sometimes, being "good at math" is simply a matter of common sense, but sometimes, it's more about remembering certain algebraic and geometric properties so you can shortcut your way to a solution.
In the above case, they give the circle's radius as 3√2. Imagine that radius going from one corner of the square to the center, then from the center to the diagonally opposite corner of the square. This gives you double the radius of the circle, i.e., the diameter. It also gives you the length of the square's diagonal: 6√2.
That diagonal divides the square into two right triangles, but not just any right triangles: these are 45-45-90 right triangles. This means that, if the leg length of such a triangle is x, then the diagonal (the hypotenuse) has to be x√2.
Work that logic backward. If the hypotenuse is 6√2 (which we know), then the leg length must be 6. So now, you know the length of the side of the square. To calculate the square's area, just multiply 6 by 6: 36. QED.
Easy for you to say.
Algebra was torture for me in school, I somehow managed to pass the required course in college, but did not retain anything I'd "learned" after the final exam.
Post a Comment