When drawing a triangle, you might start at one vertex (corner) and proceed to draw three straight, connected lines, such that you return to the starting vertex with the third line drawn. If you were to try to communicate what you were doing to someone unable to see your pad, but who is able to draw on their own pad, you might say something like, "starting with the pencil at one point on the pad, move in a straight line toward the top-center of the pad for about one inch, then continue toward the lower-right corner for another inch without lifting the pencil. etc." These instructions provide the listener with a loosely defined rule that can be used to reconstruct your shape.
Instructions like this, however, are not very precise. If our goal is to be able to draw a wide range of different shapes and if we want to be able to draw them on any piece of paper, then we need to be more systematic in the directions that we give. The directions ought to be clear and unambiguous and they must offer an adequate range of alternatives -- as many directions as we are likely to require to draw the shapes that interest us.
When drawing a triangle, you might start at one vertex (corner) and proceed to draw three straight, connected lines, such that you return to the starting vertex with the third line drawn. If you were to try to communicate what you were doing to someone unable to see your pad, but who is able to draw on their own pad, you might say something like, "starting with the pencil at one point on the pad, move in a straight line toward the top-center of the pad for about one inch, then continue toward the lower-right corner for another inch without lifting the pencil. etc." These instructions provide the listener with a loosely defined rule that can be used to reconstruct your shape.
Instructions like this, however, are not very precise. If our goal is to be able to draw a wide range of different shapes and if we want to be able to draw them on any piece of paper, then we need to be more systematic in the directions that we give. The directions ought to be clear and unambiguous and they must offer an adequate range of alternatives -- as many directions as we are likely to require to draw the shapes that interest us.
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