Geometry Studies

Like all realms of Mathematics, Geometry is an endless landscape where new roads and new interconnections between those roads and older roads are perpetually being introduced by some very clever people who seem to relish such activities. Their work, to most, is beyond the scope of interest. But to those who are interested, it can be absorbing. It is easy to understand why many do not give Geometry any attention. It is definitely not something that will pay the bills unless you happen to be a bit exceptional in the mathematical realm. As deep and extensive as the realm is, it is not widely known and it is not easily accessible for the less than determined. The originalists in the field are often remarkably clever and intellectually determined. For those who enjoy bending their brains a bit in the pursuit of understanding the properties and interrelationships of abstract objects (abstracted from real world objects to which the properties then apply), Geometry in rich in possibility. Almost everyone is introduced to the fundamentals of Geometry in school. Even those who are not particularly drawn to mathematics often find Geometry interesting because it does relate to familiar objects. Unfortuantely, for most, that taste of geometry they get in school is all they get. Even for those who go on to study more math after high school for engineering or science or computer science, etc, further studies of Geometry is not always part of their curriculum. So it is only a subset of even the small set of people who do study mathematics that get to experience the joys of this realm. The paper Geometry Studies takes the reader on a short trip into this realm. It is meant as another taste that many never got. It follows the flow of Chapter 2 in Howard Eves' "A Survey of Geometry, Volume 1". By working the exercises of that chapter in detail, the paper offers some insights for those who might get get their foot caught in some brambles on the side of the road.