## Thursday, September 9, 2010

### Distances, Part III

This blog  talks about how adults use the concepts and skills we learn in elementary math class.

What is needed to measure a distance? There are lots of ways to do it.

1. We need to know how large a distance we are measuring. That seems sort of impossible, doesn't it? I want to know how far it is from X to Y and you ask me to decide first how far it is? That's right. But only in general terms. Is it from your elbow to your fingertip, or is the distance across town or between planets? That sort of thing.

2. We need to chose a unit of measure. Will we need feet, or meters, or miles or what? In case you are tired of the normal choices, here's a list of units of measure for distance.

3. We need to know the level of precision required. This is related to the unit of measure. If we are going to be flying across an ocean, we'll want to be sure we have enough fuel. If we're walking around the neighborhood, our needs are simpler. Precision doesn't really come into it. If our surgeon is measuring the distance between two nerves in our spine, precision is expected!

4. Now we need to know the route. If it's from your fingertip to your elbow, you will have to decide which finger, then is your wrist going to be twisted so the points lay in a straight line, or will we measure around the forearm in a curve? In many cases there is more than one route to choose from. And you might need to contemplate the options. Here's a nifty site with some distance calculators.

Some of the calculators show the most likely routes for global flights. From Phoenix to India you may want to go EAST, but from San Diego to India you may want to go WEST. When you are walking, you may take a short-cut across a grassy field, but you can't take a short-cut across a lake. An airplane doesn't care about either of those options, but will need to be careful of high mountains or "unfriendly airspace".

5. Now we can choose our measuring tool and get to work. Ruler, tape measure, odometer, or what? We can measure ourselves, or we can estimate using conversation with friends, we can do internet research, look at a map, etc.

Here's a typical measurement scenario -

I am moving to a new house and I want to know how far it is to work.

Using an online mapping system, I check a group of possible routes. I select some alternatives based on how easy or hard it is to get through freeways in the morning rush hour traffic:

Route 1 - 21.8 miles, 31 minutes
Route 2 - 20.6 miles, 32 minutes
Route 3 - 22.0 miles, 35 minutes
Route 4 - 21.9 miles, 34 minutes
Route 5 - 23.5 miles, 37 minutes
Route 6 - 23.3 miles, 32 minutes
Route 7 - 26.0 miles, 35 minutes

Each of these routes uses a different on-ramp. I will travel on 2 or 3 of 5 different highways and a number of surface streets. Several of the alternative routes allow me to pass my bank either going to or from work. None is so far out of the way that I would resent going that route once in a while.

In summary, the distance is about 20-25 miles and will take about 30-35 minutes.