Geometry is the study of shapes. We limit our definition to this, because for hundreds of years Geometry was a field of mathematics with only one author, Euclid. Much of what is taught in Modern Geometry is the result of the work of Descartes.
We wish for the student to have some time experiencing Geometry as it was seen by Euclid, because once the ideas of Descartes are added to the story, it is difficult to think about Geometry with a “Euclid only” mindset.
Anything that can be done or made using a Straightedge and a Compass is a part of Euclidean Geometry. This includes concepts for length and angle, half, and concepts of multiples such as double, triple, etc.
Work by Descartes is considered an advancement to Geometry and it is also considered to be the uniting of Algebra and Geometry. We don’t want to say too much about what Descartes brings, but we will mention Graph Paper.
Rob Sterling 