You've all heard kids say it before in a lesson.

"When am I ever going to use that in real life?"

And this applies to lots of things where there's a formula or a bit of algebra and some abstract thinking.

Well, yesterday was Sunday and I was looking to find a church somewhere in San Francisco that I wanted to visit. I found it on a map. It is called the City Church on Sutter St - great church by the way if you're looking for somewhere.

Anyway, looking at the map, I had a few choices. I could go straight down Jones Street until I hit Sutter Street and then turn right (the red line).

Or I could take the hypotenuse (the green line) - much shorter!

This wasn't some clever mathematical calculation - it is just common sense. The hypotenuse is going to be shorter.

But how much shorter?

Well, if each of the other sides is about 2.5kms, then....

a

^{2}+ b^{2}= c^{2}
2.5

^{2}+ 2.5^{2 }= c^{2}
c

^{2}= 6.25 + 6.25
c

^{2}= 12.5
c = 3.5

So I saved myself about 1.5km but cutting along the hypotenuse.

Of course, I couldn't exactly go straight along the green line - there were houses and things in the way. My path looked a bit more like this:

Still, pretty sure it saved me some time. I got there 45 minutes before it started - which was good because I hadn't written down the exact address so I needed to walk around a bit to find the actual building.

*Well, who would have thought to look in the Russian Centre building?*

## POSTSCRIPT:

After posting this story, there was a certain frenzy on Twitter with several astute minds asking about the conclusions I had drawn - thanks ~~@~~mathinyourfeet ~~@~~ddmeyer ~~@~~nathankraft1 ~~@~~smithnj ~~@~~tieandjeans ~~@~~emilyrolsen ~~@~~mauidoe ~~@~~fawnpnguyen ~~@~~ajm2035 and any others I forgot to mention.

The concerns raised were specifically:

- Was the green route actually any shorter? - because it looks like it has the same vertical and horizontal distances as the red lines
- If I was driving, did I take into account the number of left hand turns I would need to do that might slow me down
- Were there any red lights I had to stop for?
- And how much stopping and starting would you do if you had to make all those turns?
- And what would that do with your mileage?

Well, I was walking and got to cut a few corners but I take the point. Even though the green path is fractionally shorter when you walk it (by cutting the corners etc), it certainly isn't the same as going in a straight line.

And I certainly didn't save 1.5kms by doing it.

Oh, for the wings of a dove....

I really like this visual and you're comment that the path you took felt much shorter is a very interesting one. I would probably posit my students:

ReplyDelete"Which one is faster? Which one is shorter?"

Of course, a great thing to show them after that discussion is that the real-life hypotenuse is the exact (about) length of just taking the two legs and then see if they can come up with the reason they are exactly the same is that all the small streets being parallel to one of the legs. Great visual, thanks!

Ooh, and I forgot to comment that if you're driving the "hypotenuse" would almost assuredly be a much longer (time-wise) trip since you're making all left hand turns! So many angles to take with those visuals!

ReplyDeleteI did manage to "cut" a few corners in my zig-zag path and thus saved several minutes I'm sure. Of course, there were those hills to consider as well - they also determine how quickly you get there. The countryside is not as flat as the piece of paper on which it is drawn.

ReplyDeleteGreen should be shorter because at each intersection you have two options for the walk signal. Obviously you cross where the walk signal is an option, then by the time you reach that corner, the other needed walk signal should light up. If you stay on the red path, you will sometimes get lucky with walk signals, and sometimes be waiting for a while.

ReplyDeleteHonestly, this is very fascinating -- something very quantitative vs. qualitative about it all. And the great thing, everyone's right! :-) Here's one of my very first blog posts that speaks to this very issue: http://mathinyourfeet.blogspot.com/2010/10/map-is-not-territory.html?view=magazine

ReplyDelete