In modern schools, Geometry is often studied in 9th or 10th grade so that students get an introduction to the world of, well, proving things! In fact, modern students think that a "proof" is somehow unique to Geometry--a sign of how wacky modern education has become. Anyway, to Geometry, most schools add Trigonometry, which is nothing more than the Geometry of triangles, but it's presented as some sort of mystery science for "gifted" math students.
How far we've fallen from classical Geometry studied! Throughout history, the study of Geometry simply meant mastery of the Elements of Euclid. The study of Geometry wasn't thought to be beneficial only to math geeks, but to all students seeking to become wise men. Quintilian, teaching Rhetoric, praised the study of Geometry:
"Geometry arrives at its conclusions from definite premises, and by arguing from what is certain proves what was previously uncertain. Is not this just what we do in speaking? Again are not the problems of geometry almost entirely solved by the syllogistic method, a fact which makes the majority assert that geometry bears a closer resemblance to logic than to rhetoric? Again oratory sometimes detects falsehoods closely resembling the truth by the use of geometrical methods."
It is with a broad and healthy appreciation of the general benefits of this art in the pursuit of wisdom that the CLAA teaches Geometry.
Dr. Daniele Arcara
Classical Arithmetic, Geometry
Dr. Arcara works as assistant professor of mathematics at St. Vincent College, in Pennsylvania and serves as the primary author of the CLAA's Classical Mathematics program. Born and raised in Italy, Dr. Arcara received more of a "classical" mathematics education than American students do and this has allowed him to bring together the benefits of modern mathematical resources and the wisdom of the ancients. He earned his Bachelor of Science degree in mathematics from the Universita di Torino, Turin, Italy in 1996. He earned his Ph.D. in mathematics in 2003 from the University of Georgia. Dr. Arcara is Catholic husband and father with children studying in the Classical Liberal Arts Academy.
Mr. William Michael
Mr. Michael serves as the editor of the CLAA Mathematics courses (and all CLAA courses) and provides students with historical and philosophical background and practical applications of the concepts covered in CLAA Mathematics courses and works to maintain the coherence and simplicity of the entire CLAA program so that the students always understand how their new studies are derived from their past studies.