Basic Geometry

Geometry is one of the most elegant fields in mathematics. It deals with visual shapes that we know from everyday life. This book is intended for use by a parent (or a teacher) and a child. It is recommended that the parent have some familiarity with geometry, but this is not necessary. The parent can simply read the chapter before teaching the child and then learn it together.

The classic book about geometry is Euclids Elements. This book helped teach geometry for hundreds of years, so we feel that writing this book based on the Elements is a correct step.

We will adapt parts of the book for children and modify the order of some topics in order to make the book clearer.

The learning will be based on constructions and proofs. A construction is a method of creating a geometric object (such as a triangle) using a set of tools. In the case of this book, the tools we will be using are a compass and a ruler. A proof is a logical trail where we can prove one fact by starting with some given information and make a series of conclusions based on that information. Oftentimes it is more difficult to prove a result than to simply find the result.

The constructions are useful for letting the child experience geometric ideas and get visual results.

The proofs are a good way to understand geometry and are a good basis for future study of logic.

Since the book is for children, we omit some of the proof details and use intuition instead of precise definition. On the other hand, we insist on correct and elegant proofs. Precise definitions and exact proofs can be found in regular geometry books and can be used to extend to material to some of the children.