Last week, in Number Sense 002, we took a look at counting on a number line, by ones, twos, threes and more. This week we will look at things from a different angle.
The grizzled veteran addresses a tactics class at infantry officer candidate school.
The fresh faced rookie asks: “Sir, why do we have to be the first to run at the enemy, waving our sword and yelling 'Follow Me!'? Couldn't we just, say, point at the enemy and yell, 'Go Git Um!'”
“Son,” replies the grizzled veteran, “You ever try to push a string?”
An interesting thing happens when you pull a string though...
...the part you pull on becomes straight.
The interesting thing is that bit of geometry, that straight line, does not appear in nature (the exception being the horizon line – over an ocean, large lake or a very flat portion of the earth.) Essentially, all straight lines are created by human beings.
Now, if we put our stretched out straight piece of string next to a number line, we discover something else we can use numbers for, other than counting.
We can measure the length of the string. Notice that, as with counting, our measuring also begins at zero, rather than one.
This is possibly the simplest connection between geometry (Ie: earth measurement, or surveying, in ancient days undoubtedly done mainly with lengths of string) and mathematics. The Greeks later developed geometry into more of an abstract discipline, proving theorems and constructing figures using only a straight edge and a compass. Of course, string can substitute for both the straight edge, as shown above, and for the compass, by holding one end of the string in place then stretching the string out and moving the other end to trace out an arc of a circle.
By stretching the string we ensure that we have got the shortest length of string between point A (at one hand) and point B (at the other)
Even the tiniest bit of slack (as shown with the blue string) means the unstretched string is longer, since we could, if we wanted, move our hands further apart to take the slack out of the blue string. So only the straight string, the stretched string, is the shortest distance between our two points, A and B.
This is, more or less, the definition of a straight line, or, strictly speaking, a straight line segment, since “lines” in geometry don't have ends, but go on in the same direction forever.
A line (an arrowhead means it keeps going in that direction)
A line segment (it ends where it ends.)
Have fun in the comments