Merged No more algebra?

[psionl0]

Engineers don't like it when you ask "How do you correct for the fact that your walls are going to be at different angles, since they're on slightly different positions on the Earth's surface and you're using a plumb bob?"

Assuming a 100m wide building and an earth radius of curvature of 6350km, I calculate that the angle between the opposing walls (if plumbed) would be about 20 seconds of arc.

I doubt that this could be measured with any standard building tool.

 

[Careyp74]

By measuring with a micrometer/plumb bob, marking the uprights with chalk, and cutting with an ax.
I was observing a new building going up near here.. only two stories, but the bare structure looked askew.. leaning to the north.
Had to be an optical illusion, because the windows fit!

You need new shoes. One wore out faster than the other.

 

[Dinwar]

Assuming a 100m wide building and an earth radius of curvature of 6350km, I calculate that the angle between the opposing walls (if plumbed) would be about 20 seconds of arc.

I doubt that this could be measured with any standard building tool.

Yeah, that's why no one worries about it--at the scales we build to, there's no need to worry about it (a mile-high building may be a different story, but we don't build those). Honestly, I just do it to see engineers who've never given the matter any thought start shooting smoke out of their ears.

I was observing a new building going up near here.. only two stories, but the bare structure looked askew.. leaning to the north.
Had to be an optical illusion, because the windows fit!

I grew up in a house like that. Dad and I tried to put a door in once, and couldn't do it. We had to take a plain to it (well, we didn't HAVE to--Dad had a plain, and I had been a smart-mouth that week, otherwise we'd have used the power tools) to make it skewed just a bit. Fits perfectly now, and has the added advantage of holding itself in just the right position to be out of everyone's way, thanks to the slight incline.

The local hardware store once refused to sell us supplies until we brought in pictures of how screwy that house was. The owner thought we were lying to him...

 

[cwalner]

Yeah, that's why no one worries about it--at the scales we build to, there's no need to worry about it (a mile-high building may be a different story, but we don't build those). Honestly, I just do it to see engineers who've never given the matter any thought start shooting smoke out of their ears.

Yup. That's why Euclidean geometry still dominates, because despite the technical inaccuracy for being on a (roughly) spherical surface, the calculations in Euclidean geometry are simpler, and the error is below the threshold of significance so it works just fine.

However, when you go large scale (say finding the shortest route to fly a plane from Chicago to Tokyo or calculating how to steer a spacecraft to Saturn) we need non-Euclidean geometries to get the best answers.

 

[I Ratant]

You need new shoes. One wore out faster than the other.

.
I would have taken photos, as I do of everything, but this is the new police station, and photoing things like that are politically stupid now.

 

[psionl0]

(a mile-high building may be a different story, but we don't build those).

If the aforementioned building was a mile high then the base would be 100m wide and the top would be 100.01m wide - a difference of 1cm. This is measurable but would make no difference to the number of bricks you lay at the top compared to those at the bottom.

The local hardware store once refused to sell us supplies until we brought in pictures of how screwy that house was. The owner thought we were lying to him...

That sounds like a hardware store employee who doesn't get around much. This is hardly unusual at all.

At a house I once lived in the front door wouldn't even shut anymore. The reason was that the foundation pegs were sinking unevenly. The building manager had to use a truck jack to fix the problem.

 

[Ziggurat]

I thought cab meters ran according to the amount of time it took, not the mileage driven. So if you're stuck in a cab in traffic or ask the cabbie to wait on you, she's not getting paid? That seems unfortunate.

Typically fare is assessed as a combination of time and mileage. Sitting in a stationary cab for 10 minutes isn't free, but it is cheaper than sitting in a driving cab for 10 minutes.

Estimates based on mileage use some assumptions about the time it takes. If they didn't have to make an assumption about the time involved, then they wouldn't have to give you an estimate, they could give you a quote.

 

[xtifr]

What I find really amusing about this whole thread is that when it was pointed out to OP the many common cases where he(?) uses algebra day-to-day, he basically responded, oh, that's obvious--that's not algebra. Wrong! Basic algebra is simple and obvious. More simple and obvious, IMO, than basic arithmetic. I use algebra to convert my tip calculations from the tricky n x 0.15 to the much easier-to-do-in-my-head (n + 1/2n) / 10. I know the result is the same because...algebra!

I think the problem with algebra is not that it's difficult (it's not) but that it's taught poorly. You're expected to master basic arithmetic first, which is silly, and then it's presented as if it were the next, even-more-difficult step. It's not. You could start learning algebra as soon as you start learning to add. And, in fact, to some extent, you do, but it's so obvious and simple that nobody bothers pointing it out at that point.

 

[Dinwar]

That sounds like a hardware store employee who doesn't get around much. This is hardly unusual at all.

At a house I once lived in the front door wouldn't even shut anymore. The reason was that the foundation pegs were sinking unevenly. The building manager had to use a truck jack to fix the problem.

Sorry, was mixing two anecdotes. The time the owner refused to sell supplies to us was when we gutted the bathroom. We started talking about the different things wrong with it, and the guy simply refused to believe that a room could be that messed up and still standing (which was part of the reason we were gutting it--it was sloping pretty badly).

My grandfather's done the same thing to chicken coops. Does horrible things to the wire he uses when he does that trick to make it square; after the first time you don't use it for anything else, and after the second time it's junk.

 

[psionl0]

My grandfather's done the same thing to chicken coops. Does horrible things to the wire he uses when he does that trick to make it square; after the first time you don't use it for anything else, and after the second time it's junk.

Darn this curved earth's surface!

 

[Mark6]

What I find really amusing about this whole thread is that when it was pointed out to OP the many common cases where he(?) uses algebra day-to-day, he basically responded, oh, that's obvious--that's not algebra. Wrong! Basic algebra is simple and obvious. More simple and obvious, IMO, than basic arithmetic. I use algebra to convert my tip calculations from the tricky n x 0.15 to the much easier-to-do-in-my-head (n + 1/2n) / 10. I know the result is the same because...algebra!

I think the problem with algebra is not that it's difficult (it's not) but that it's taught poorly. You're expected to master basic arithmetic first, which is silly, and then it's presented as if it were the next, even-more-difficult step. It's not. You could start learning algebra as soon as you start learning to add. And, in fact, to some extent, you do, but it's so obvious and simple that nobody bothers pointing it out at that point.

Agree completely.

In Russian schools the concepts of "equation" and "unknown quantity" are introduced in first grade. Seven year olds learn that:

x + 4 = 6
x = 6 - 4
x = 2

That's a year before they learn multiplication table.

They do not call it "algebra" -- the word is not introduced until 5th or 6th grade, -- but they do learn it.

 

[Blue Mountain]

It can take you 90 minutes to travel 20 miles through Chicago, and then another 90 minutes to travel the next 100 miles south of Chicago. Miles aren't the relevant unit.

There's a highway in Illinois with a posted limit of 110 MPH (180 km/h)?

[I've rounded the numbers a bit]

 

[Hazel]

Agree completely.

In Russian schools the concepts of "equation" and "unknown quantity" are introduced in first grade. Seven year olds learn that:

x + 4 = 6
x = 6 - 4
x = 2

That's a year before they learn multiplication table.

They do not call it "algebra" -- the word is not introduced until 5th or 6th grade, -- but they do learn it.

I've been telling friends this for years but they just look at me crazy. They find it hard to believe anything that seems so complicated could be so simple. I am not a math genius. I am not a success at advanced math at all but I had no trouble with algebra. I keep wondering if I slept through most of it when I hear so many saying they flunked it. Now, geometry did slow me down. I got the basics and never went further. Thank goodness for grammar, literature and history.

 

[Marras]

[I've rounded the numbers a bit]

Perhaps a bit too much ...

 

[I Ratant]

In the late '50s, my aerodynamics professor Dr. Max Munk told us that the less capable in Germany were taught a binary arithmetic to do sums in the early 20th Century.
Mostly a number was divided by two until it was 1, 2, or 3. And the number of divisions were kept track of... if memory serves.

 

[xtifr]

There's a highway in Illinois with a posted limit of 110 MPH (180 km/h)?

[I've rounded the numbers a bit]

More than rounded. If it takes you an hour and a half to travel 100 miles, you were not traveling 110 MPH!

I think your problem may have been forgetting that there's only 60 minutes in an hour.

 

[Hazel]

There's a highway in Illinois with a posted limit of 110 MPH (180 km/h)?

[I've rounded the numbers a bit]

That's all right. The way people drive by here, I am quite certain it can be - and is being - done every day. Chicago is likely no different.

 

[AvalonXQ]

There's a highway in Illinois with a posted limit of 110 MPH (180 km/h)?

[I've rounded the numbers a bit]

This is, perhaps, the best argument so far in this thread that math education is important.

Please show your work as to how you got 110 miles per hour from covering 100 miles in 90 minutes. (Clue: the correct answer is just over 65 mph).

 

[Hazel]

This is, perhaps, the best argument so far in this thread that math education is important.

Please show your work as to how you got 110 miles per hour from covering 100 miles in 90 minutes. (Clue: the correct answer is just over 65 mph).

Or sticking with the term "miles" so people realize that miles are relevant.

 

[Rasmus]

(Clue: the correct answer is just over 65 mph).

Just by looking at it, you should understand that 110 miles in 90 minutes is "just a little something over a mile a minute".

I am posting this because I am not sure just how much actual math I needed for that, and how much more for the realisation how much that "little something" would actually be.