Distinguishing factors between Euclidean and non- Euclidean spaces: The space we inhabit cannot solely be determined by a priori
Hassanah Smith
Professor Mandik
Philosophy of space and time There are a plethora of ways to distinguish the differences between Euclidean and non- Euclidean geometries. Understanding both geometries can help one determine our physical space rather than inferring because of past experiences, or in this instance postulates of geometry. Euclidean geometry studies planes and solid figures based on a number of axioms and theories. This is explained using flat spaces, hence the usage of paper, and dry erase boards in classrooms, and other flat planes to illustrate these geometrical standards. Some of Euclid’s concepts are 1. The shortest distances between two points is a straight line. 2. The sum of all angles in a triangle equals one hundred eighty degrees. 3. Perpendicular lines are associated with forming right angles. 4. All right angles are equal 5. Circles can be constructed when the point for the center and a distance of the radius is given.
But Euclid is mostly recognized for the parallel postulate. This states that through a point not on a line, there is no more than one line parallel through the line. (Roberts, 2012) These geometries went unchallenged for decades until other forms of geometry was introduced in the early nineteen hundreds, because Euclid’s geometry could not be applied to explain all physical spaces, this gave rise to non- Euclidean geometry. Non Euclidean geometry are in correspondence with axioms when metric geometry or the parallel postulate is replaced, in other words non Euclidean geometry negates Euclid’s parallel postulate. Some popular non Euclidean geometry is hyperbolic or the saddle which states If L is any line and P is any point not on L, then there exists at least