When we step into the world of geometry in mathematics, it’s like Su Shi entering Mount Lu. The charm of geometry lies inabstraction— it doesn’t care about the color of a football, only that it is a ‘sphere’; it doesn’t care what a box contains, only that it is a ‘rectangular prism’. By observing objects from different directions, we’ve learned to precisely describe three-dimensional solid worlds using two-dimensional plane figures.
Bridging the Gap from Physical Objects to Geometric Shapes
Some geometric figures (such as line segments, angles, triangles, circles, etc.) have all their parts lying in the same plane; they areplane figures (Plane Figure). While three-dimensional objects such as rectangular prisms, cylinders, and spheres occupy space, they aregeometric solids (Solid).
By engineering drawings (three views) and surface unfolding, we can discover:
- solid figurescan be seen as being formed byplane figuressurrounding them.
- dynamic transformation: When a rectangle rotates around an axis, it forms a cylinder — this is known as 'a surface moving to form a solid'.
The viewing angle determines the plane shape we see, while the net diagram reveals the essential characteristics of a geometric solid — its 'skin'.
Three-dimensional Solid \xrightarrow{\text{Projection/Unfolding}} Two-dimensional Plane Figure