|
|
|
Operations |
|
We use a ruler and a compass; the ruler can be used only to draw the line through two given points and the compass can be used only to draw the circle with a given center and through a given point. We use the following seven operations: Operation 1. Given two points. Using the straightedge, construct (=draw) a line (or a ray, or a line segment) through the points. Operation 2. Given two points. Center the compass at the first point and construct (=draw) a circle (or an arc) through the second point. Operation 3. Given a point and a line segment. Center the compass at the given point and construct (=draw) a circle (or an arc) with radius the given line segment. Operation 4. Given two intersecting lines. Construct (=label) the point of intersection. Operation 5. Given two intersecting circles. Construct (=label) the point(s) of intersection. Operation 6. Given intersecting line and crcle. Construct (=label) the point(s) of intersection. Operation 7. Construct (=choose) a point.
Constructions A construction consists of a sequence of the above seven operations. A length of a construction is the number of operations in the sequence.
Notations
|
