The shortest way

About this video

Why does a builder pull a string tight between two sticks before laying a wall? This animation answers it with the first ideas of geometry. A point is a place, nothing more: a dot on a map has some size, but the point is only its exact middle, so the video shrinks a dot down to the place it marks and names it A.

Join two points and you get a straight path, which has three names depending on where it stops. A line segment has two ends, like the string between the sticks. A line goes on for ever in both directions, so we draw only a piece of it with an arrowhead at each end. A ray starts at one point and never stops, like a torch beam.

Then the video draws three paths from A to B, a wiggle, an arch and a straight line, and unrolls each into a bar to compare their lengths. The straight one is the shortest, which is why a string pulled tight shows a straight line. Last, it shows that through one point you can draw endless straight lines, but through two points only one, so two sticks are enough to fix the line of a wall. This video goes with the Points and Lines lesson of Geometry Level 1 on Knaph.

Transcript

1. 0:00A builder pulls a string tight between two sticks. Why tight?
2. 0:08Start with a point. It shows a place, and has no size at all.
3. 0:15Join two points, and you get a line segment. It has two ends.
4. 0:21A line goes on for ever, both ways.
5. 0:27A ray starts at a point and never stops.
6. 0:34Many paths join A and B. Unroll them and compare.
7. 0:41The straight path is the shortest. That is why the string is pulled tight.
8. 0:50Through one point, endless straight lines.
9. 0:55Through two points, only one. Two sticks fix the line.
10. 1:01Straight is shortest, and there is only one.