Showing posts with label proportion. Show all posts
Showing posts with label proportion. Show all posts

Tuesday, August 02, 2016

Daily Regents: Similar Triangles are Proportional (August 2015)

Even though the title says "Daily", I won't be doing them daily any more, until the exams get closer. But they will be frequent.

Geometry, August 2015, Question 27

27. To find the distance across a pond from point B to point C, a surveyor drew the diagram below. The measurements he made are indicated on his diagram.

Use the surveyor’s information to determine and state the distance from point B to point C, to the nearest yard

There are two right triangles. Right angles are congruent.
Both triangles contain angle A. Reflexive Property says angle A is congruent to itself.
Therefore, triangle ABC ~ ADE
If the triangles are similar, then their corresponding sides are proportional.

AE = 230, AC = 230 + 85 = 315. DE = 120. BC corresponds to DE.

Set up a proportion: AE / DE = AC / BC
230/120 = (230 + 85) / x
230 x = (120)(315)
230 x = 37800
x = 164.3478...
x = 164 yards

The distance from point B to point C is 164 yards.


Tuesday, December 30, 2014

Two Taylor Swifts and a Sliding Yardstick

I've come to realize that as of this month of December, I am currently exactly 2 Taylor Swifts in age. That's really not so bad when I think about it because when You Belong With Me hit the charts (in 2009), I was 2.25 Taylorswifts. So i guess it's getting better. I could continue, figure out when I'll be only 1.5 Taylorswifts, but it would start to sound like an old Abbott & Costello routine. (Not that there's anything wrong with that.)

I had the thought recently about sliding yardsticks (or sliding metrics). What if you're measuring something, and the unit that you're measuring against changes along the way. It would be a great way to obscure (or hide) data.

What brings this up, without getting political, are all the political postings I see on different social platforms by people who should be smart enough to know better. (Scary thought: they are smart enough, but they assume we're all dumb enough.)

You don't judge a book by its cover and you don't evaluate major chunks of the economy based on a graphic containing a pithy quote and carefully selected factoids(*) underlined with a "witty" applause line, wrapped up in 140 characters, meant to be repeated and reported by people using the phrase "Alls I knows is...".

(*) factoid - Not a "little fact", but something that "looks like a fact", but isn't. This could be extended to the presentation of facts in a way that they seem related but are really not.

If that's all you know, you need to be more educated. Look beyond the numbers. Check those that confirm your biases and those you dismiss out of hand as made-up lies (What other kind are there?). However, when the fact-checking doesn't happen, a low-information individual is created -- someone who doesn't know all the facts, who knows that they don't have all the facts, but believes that every fact and factoid that they do have is enough, and no other piece could possibly make a difference. Any other data is obviously wrong, and if not, needs to be ignored, you Fill-In-The-Blank-ist Bad-Noun!

Oddly, though no piece of information can sway them, they are shocked that their one piece of information hasn't yet swayed you.

What spurs this on?

Comparisons of budgets and deficits and debts and prices and any number than can (and did) fluctuate wildly, so that specific highs and lows can be picked out and averaged or compared or manipulated alongside the assignment of blame or credit, regardless of the merit of that assignment. Is the latest increase big or tiny? Is it bigger or tinier than that other guy's? And what percent increase in the load was the straw that broke the camel's back?

Are these things appropriate fodder for debate? Absolutely, as long as that debate is longer than a sentence and the rebuttal is more than "You're a butthead. Neener. Neener!"

Shouting down your opponent doesn't mean you've won the argument. It means you're rude and willing to stay ignorant of facts you don't have.

My entire class can ignore me when I say that 0! = 1. They can all insist that it should be 0, and maybe even argue why. but they'll be wrong in class and wrong on every test after.

As for me, I've given way too much thought to it. I'll be exactly 1.5 Taylorswifts old when (T + 25)/T = 1.5

Yes, I can calculate it. No, I don't want to. Unlike Costello, I know that she isn't going to catch me. The answer is that the ratio is getting smaller, but I'm still getting old.

Monday, December 01, 2014

Blog: 31 Posts of December? There's Proportionality in There Somewhere

I didn't write a novel in November, like many set out to do each year, and I didn't successfully tackle my goal of 100,000 words in the past year or so (before hitting a landmark birthday), but I did think that I could challenge myself to author another 31 blog posts this month.

And that almost fell apart on Day 1. It's late in the evening, and I'm exhausted. So I've punted and given you an introduction post announcing my intent without actually getting started. I've fulfilled the obligation with more noise and less content.

Noise and content, as we know, are inversely proportional in blog posts, as well as message boards and other forums. The more of one, the less of the other. Bob McAllister, host of the old -- old -- kid show Wonderama, used to sing "The more you Fingel, the less you Heimer, The less you Heimer, the more you Fingel" when he introduced his character, Professor Fingelheimer. That was probably my first real exposure to the concept of inverse proportion even though it didn't mean a fingel-thing!

With noise and content, you really can't have one without the other. Well, you can, theoretically, but 100% content is boring and bland while 100% noise would be ... should I name names? You know which blogs those are: lists of 20 random things required 72 clicks to get through.

So this is mostly noise and nostalgia, and tomorrow will be some wonderfully thought out piece about inequalities that might even merit a second draft.

Unless a comic comes to me in the next hour or so that just can't wait. Or my work schedule demands a little bit more of me.

Which would leave you with a little bit less of me.