Name: Secrets to measuring a piece of paper - Numberphile
Uploaded: 2020-03-27T18:02:47.000Z
Duration: 5 min 35 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Past simple

Modal verbs - A2

The principal said "Oh Cliff, you can teach exactly as you wish." So my idea in teaching is,

every day have the kids go home and do an experiment. And, first thing I did was say, okay,

Measure the area of this sheet of paper. Use metric units and show your work. And, by the way, here's a ruler for you.

So, I don't know, what's the area of this sheet of paper?

Just go do it. Bring it in tomorrow. So the obvious thing to do is you take your ruler, you measure across here, 20 centimeters

You go across this way, you measure up and down, 26 centimeters this way. 20 centimeters times 26 centimeters should be around

520 square centimeters. Okay, that much you would do, I'd do. What my students didn't realize is, of course,

that has lots of wrinkles and difficulties. For example,

oh, what do you mean by the area of this sheet of paper?

The front side, or the front plus the back? Or maybe just the back side?

the circles that have been knocked out? Do they count as part of the area? Worse than that.

did you realize that its height over here

over here? Let's put this piece of paper onto a square sheet of paper.

Oh, this isn't a rectangular piece of paper. In other words,

multiplying height times width doesn't work. You're gonna have to do

at least some kind of outer product or an integral perhaps. The rulers that I gave to my students

9 10 11 12 13 14 15 16 17 17 18 19 centimeters.

Uh, there's something wrong with Theophilus Measure Company.

It's an Imperfecto. In other words, this is a comment about doing science

Always examine the assumptions that you're making whenever you make a measurement.

Hey! Look for the places where you have ambiguous statements. What's the area of this sheet of paper?

Good science does not mean getting the perfect answer.

Good science means figuring out what could go wrong.

BRADY: "How did your students do? How many of these

embedded tricks did your students pick up on?"

Oh, so, I had two classes, fifteen sixteen people in each class.

One kid right away picked up. Hey, there's these holes in it.

I'll have to subtract the holes, if, you know, pi r squared, he figured,

and he subtracted from it. Another kid said, wait a second,

I don't know what you mean by area. In fact, two or three kids said,

oh, there's a front side, or front plus back, or was just the back side?

And the shape? Nobody really saw that. Nobody saw this coming,

Brady, people write to me and say I'm thinking of going to college. How do I write an essay?

People write to me and say I'm trying to get into grad school, what should I say on my application?

who's got to figure things out, who says "I don't know now, but I got to know!"

somebody who's got enthusiasm. Not somebody who's boring or puts me to sleep.

Brady: "Cliff, is that natural? Do you learn that or does it come naturally?"

Does it come naturally? Who knows? I mean,

I want to know things. I gotta know things.

Wait wait wait wait wait wait what's the mathematician, the German mathematician?

"We must know, we will know", What's his epitaph? What was his name? Uh hell, come on. You must know. Oh.

Hold on. We must know we must know. I'm gonna look him up real fast. I'll take a second.

Well, he's curious. He's gone off to find out who the mathematician is.

Brady: "I didn't think you'd be an iPhone guy."

Hilbert! It was David Hilbert! On his grave it says,

...1894 1895 in Switzerland, came up with an absolutely wonderful device.

This device - check this out - this will not only ... hey! Go over here, over here...

Subtitles ListPlay Video

Secrets to measuring a piece of paper - Numberphile

absolutely

obvious

recognize

figure