When we enter the geometric world of mathematics, it is like Su Shi stepping into Mount Lu. The charm of geometry lies inabstraction: it does not care what color a soccer ball is, only that it is a "sphere"; it does not care what a box contains, only that it is a "rectangular prism." By observing objects from different directions, we learn to use two-dimensional plane figures to precisely describe the three-dimensional world.
The Leap from Physical Objects to Geometric Figures
Some geometric figures (such as line segments, angles, triangles, circles, etc.) have all their parts in the same plane; they areplane figures (Plane Figure). Meanwhile, objects that occupy space, such as rectangular prisms, cylinders, and spheres, aresolids (Solid).
Through engineering drawing (three-view drawings) and surface unfolding, we can discover that:
- Solid figurescan be seen as being enclosed byplane figures.
- Dynamic transformation: a rectangle rotated around an axis forms a cylinder — this is "a surface moving to form a solid."
The viewing angle determines the plane shape we see, while the net is the "skin" that reveals the essential features of a geometric solid.
3D Solid (Solid) \xrightarrow{\text{Projection/Unfolding}} 2D Plane (Plane Figure)