What Is Non-Euclidean Geometry?
By: Shawn Donovan Non-Euclidean geometry should be a familiar term to anyone who’s taken an advanced math class. Like most sciences, the field of geometry is broken down into subfields. Euclidean geometry refers to the mathematics pioneered by the Ancient Greek scholar Euclid. This is probably the geometry that you’re most accustomed to seeing. It deals with lines and angles on a tw-dimensional plane or in three dimensions. It was the only kind of geometry that was taught for around 2,000 years. However, in the 19th century, breakthroughs in mathematics lead to the discovery of modern geometry that wasn’t based on Euclid’s theories. The two geometries that arose are referred to as hyperbolic and elliptical. Alternate Spaces What makes these modern forms of geometry different? Picture a line drawn horizontally across a page. Now picture a dot somewhere on that page above the line. If you were to draw lines through the dot at any angle, there would only be one (a parallel line) that woul
