page_title: Foundations of geometry
section_title: School geometry
hierarchical_section_title: Foundations of geometry / Euclidean geometry / School geometry
caption_attribution_description: English: American mathematician George Bruce Halsted (November 25, 1853 – March 16, 1922).
context_page_description: Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries. These are fundamental to the study and of historical importance, but there are a great many modern geometries that are not Euclidean which can be studied from this viewpoint. The term axiomatic geometry can be applied to any geometry that is developed from an axiom system, but is often used to mean Euclidean geometry studied from this point of view. The completeness and independence of general axiomatic systems are important mathematical considerations, but there are also issues to do with the teaching of geometry which come into play.
context_section_description: Whether or not it is wise to teach Euclidean geometry from an axiomatic viewpoint at the high school level has been a matter of debate. There have been many attempts to do so and not all of them have been successful. In 1904, George Bruce Halsted published a high school geometry text based on Hilbert's axiom set. Logical criticisms of this text led to a highly revised second edition. In reaction to the launching of the Russian satellite Sputnik there was a call to revise the school mathematics curriculum. From this effort there arose the New Math program of the 1960s. With this as a background, many individuals and groups set about to provide textual material for geometry classes based on an axiomatic approach.
caption: George Bruce Halsted
exif: {}