In the previous chapter space was studied through coordinates: equations, vectors, formulae. Here instead we approach it with synthetic geometry: axioms, relations between lines and planes and, above all, the solids — the three-dimensional figures that can be measured in terms of volume and surface area. We start from perpendicularity between a line and a plane and from the theorem of the three perpendiculars, move on to dihedral angles, then to polyhedra (prisms, parallelepipeds, pyramids) and to solids of revolution (cylinder, cone, sphere), studying their volumes and surface areas. The chapter closes with the similarity of solids together with Thales’ theorem in space, the five Platonic solids and Euler’s formula.
Sezioni
- Perpendicularity between lines and planes
- Dihedral angle
- Prisms and parallelepipeds
- Pyramids
- Similarity of solids and Thales’ theorem
- The cylinder
- Cone
- The sphere
- Platonic solids and Euler’s formula