Wentworth's Plane and Solid Geometry · Introduction, §§ 1–17 · Book 1: Introduction
1. Solids, surfaces, lines and points
Goal: Your student can explain what a geometric solid, surface, line and point are, and how many dimensions each has.
You'll need
- The book, open to these pages
- A box or block of wood
- Pencil and a notebook
What's in the book
The opening pages start from a cut block of wood and work down to surfaces, lines and points, then define Geometry, Plane Geometry and Solid Geometry.
The lesson, step by step
Start with a real block
Hand your student a box, a book or a block of wood.
SayHow many flat faces does it have? Where two faces meet, what do you see? Where three edges meet?
Let them find the faces, edges and corners. The book does exactly this with a block of wood (Fig. 1).
Read the definitions together
Read §§ 1–8 aloud, taking turns. Stop after each and ask your student to say it in their own words.
The key sentences:
A surface has only two dimensions, length and breadth.
A line has only one dimension, length.
A point has no dimension, but denotes position simply.
Ideal, not real
Read § 9. A pencil line has some width, but a geometric line has none. We draw lines only to help our thinking.
SayIf a line has no width, can you ever really see one? (No; the drawing only stands for it.)
Motion makes figures
Read §§ 12–14. A moving point traces a line, a moving line sweeps out a surface, a moving surface sweeps out a solid.
Demonstrate: drag a pencil point across paper (a line); slide a ruler flat across the table (a surface).
What geometry is
Read §§ 15–17 and copy the definition into the notebook:
Geometry is the science which treats of position, form, and magnitude.
Ask: Is a drawing on this page plane or solid geometry? Is a cube?
Wrap up
Your student explains, without the book, the difference between a solid, a surface, a line and a point, and gives a real-life example of each.
Afterwards
Begin a geometry notebook with a page of definitions. Add to it every session.
Tip
The author says the first fourteen pages should simply be read in class with discussion. Keep it relaxed: talk, do not drill.