| Abstrakt: |
Geometry–Do is a textbook about plane geometry. It will be divided into two volumes, Geometry without Multiplication: White through Red Belt, and Geometry with Multiplication: Blue through Black Belt. The white- and yellow-belt chapters are neutral geometry; the remainder of Volume One and all of Volume Two is Euclidean geometry. It is primarily intended to teach geometry from the ground up, starting with the postulates and citing only already-proven theorems. It trains mathletes for competition, but it is not the usual grab-bag of unproven theorems chosen haphazardly and solely because they appeared in past exams. The early chapters prepare students for jobs in construction, architecture, surveying, graphic arts, and military defense. The later chapters teach geometry needed by engineers and military officers. In this lecture, the White Belt chapter is presented. I will address these people: Pure Mathematicians Moise derides the “lighthearted use of the word let.” I prove the crossbar theorem and other foundations not usually taught in high school, and I discuss Hilbert’s Foundations of Geometry. High-School Teachers Randomly assigning letters to points is what makes geometry confusing. I have special symbols for midpoints, perpendicular feet, and infeet (where the angle bisector cuts the opposite side of a triangle) and exfeet. Administrators I present clear distinctions between Geometry–Do and Common Core with examples that concerned parents can understand. Construction Workers I invent the Aguilar A-Frame, give detailed instructions on squaring a basement foundation wider than a tape measure without exiting the rectangle, and discuss how building with wood differs from steel construction. Military Officers I discuss troop positioning along a frontier that is plagued with cross-border raids, which assumes that friendly and enemy troops move at the same speed, and a parabola is the set of points equidistant from the focus and the directrix. [ABSTRACT FROM AUTHOR] |
