From Prisms to Polyhedra: A Practical Solid Geometry Handbook

Overview

A concise, application-focused textbook covering 3D Euclidean geometry: definitions, properties, and problem-solving techniques for prisms, pyramids, cylinders, cones, spheres, and polyhedra.

Target readers

High-school students, math contest participants, and self-learners seeking clear explanations and worked problems.

Key chapters

Foundations: points, lines, planes, angles, cross-sections
Prisms & Pyramids: surface area, volume, nets, coordinate methods
Cylinders, Cones & Spheres: formulas, derivations, slicing techniques
Polyhedra: Platonic, Archimedean solids, Euler’s formula, duals
Transformations & Symmetry: reflections, rotations, nets, tessellations
Advanced tools: vector and coordinate methods, barycentric coordinates, analytic geometry in 3D
Problem-solving strategies: common tricks, inequality techniques, extremal problems
Competition-style problems with full solutions (graded by difficulty)
Appendices: formulas, reference tables, notation, solution hints

Features

Clear derivations of volume and area formulas.
Step-by-step worked examples and practice problems.
Visual aids: diagrams, cross-sections, and nets (described textually).
Problem sets for drills and contest prep.
Summary tables of formulas and key theorems.

Sample problem (with solution sketch)

Problem: Find the volume common to two perpendicular unit cylinders whose axes cross at their centers (Steinmetz solid).
Sketch: Use cylindrical coordinates and integrate the region where x^2 + y^2 ≤ 1 and y^2 + z^2 ≤ 1; result = ⁄₃ – 8√2/3 ≈ 2.228.

Why read it

Practical, compact, and focused on building intuition and exam-ready techniques for 3D geometry.

Related search suggestions:

From Prisms to Polyhedra: A Practical Solid Geometry Handbook