PARALLEL POSTULATE Meaning and
Definition
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The parallel postulate is a foundational principle in Euclidean geometry that states: if a line intersects two other lines and the interior angles on one side of the transversal sum up to less than two right angles, then the lines, when extended indefinitely, will intersect on that same side of the transversal. Alternatively, if the interior angles sum up to exactly two right angles, the lines will be parallel and never intersect. This postulate essentially describes the concept of parallel lines and their relationship to a transversal line.
The parallel postulate dates back to the work of the ancient Greek mathematician Euclid, who formulated it as one of the five postulates in his book "Elements." It distinguishes itself from the other postulates by being more complex and less self-evident. Euclid's inability to derive the parallel postulate solely from the other four postulates led to centuries of attempts and investigations into its nature.
The parallel postulate has been a subject of great interest and controversy in the history of mathematics. It was eventually discovered that the parallel postulate is independent of the other four postulates, which means that it cannot be proven or derived from them. This realization led to the development of non-Euclidean geometries in the 19th century, where alternate versions of the parallel postulate were proposed, resulting in a new understanding of space and geometry.
Etymology of PARALLEL POSTULATE
The word "parallel" originated from the Latin word "parallelos", which is derived from the Greek word "parallēlos". It means "beside one another" or "alongside".
The term "postulate" comes from the Latin word "postulare", meaning "to demand" or "to request". In mathematics, a postulate is an assumption or a basic statement that is accepted without proof.
Therefore, the phrase "parallel postulate" refers to a statement that is accepted as true without proof, concerning the properties of parallel lines. This postulate was introduced by Euclid in his work "Elements", and it played a significant role in establishing the foundations of Euclidean geometry.
