A PLANE INTERSECTING A TRIANGULAR PYRAMID
- Jack D. Gittinger
Just as a line is made of an infinite number of points, a plane is made of an infinite number of lines that are right next to each other. A plane is flat, and it goes on infinitely in all directions. A sheet of paper represents a small part of one plane. But actually a sheet of paper is much thicker than a plane, because a plane has no thickness. It is only as thick as a point, which takes up no space at all. So a plane is like an imaginary sheet of paper, infinitely wide and long, but with no thickness. When we talk about a triangle or a square, these shapes are like pieces cut out of a plane, as if you had cut them out of a piece of paper. But is there another way to create these polygons? Some geometers are very interested what happens when a plane intersects or cuts a 3-Dimensional shape. Examine the GeoGebra workspace. The light blue-green rectangle represents, like a piece of paper, a small part of a plane. The dark green shape represents the polygon that would be formed if the plane actually cut the triangular pyramid. You can use the slider to MOVE THE PLANE forwards and backwards. The ROTATE THE VIEW point can be used to look at the pyramid from different angles. Experiment with these tools. Observe what polygons are created when a plane slices through a triangular pyramid. What shapes did you observe?