euclid's postulate

Học thuật
Thân thiện
euclid's postulate

A student draws a diagram illustrating Euclid's postulate on a chalkboard.

Definition

Noun: 1. A foundational axiom in Euclidean geometry: Any one of the five basic, self-evident statements about points, lines, and planes from which the theorems of Euclidean geometry are logically derived. These postulates are assumed to be true without proof.

Examples of Usage
  • Noun:
    • The parallel postulate is the most famous of Euclid's postulates.
    • For centuries, mathematicians tried to prove that Euclid's fifth postulate could be derived from the other four.
    • The entire structure of classical geometry rests upon Euclid's postulates.
Advanced Usage
  • "Challenge a postulate": To question or attempt to prove a fundamental assumption.
    • Attempts to challenge Euclid's fifth postulate eventually led to the discovery of non-Euclidean geometries.
  • "Based on Euclid's postulates": Describing a geometric system or proof that uses these axioms as its foundation.
    • The proof is valid because it is based solely on Euclid's postulates and previously established theorems.
Variants and Related Words
  • Euclidean axiom (n): A synonym for Euclid's postulate.
    • The study began with a review of the fundamental Euclidean axioms.
  • Postulate (n): A statement assumed to be true as the basis for reasoning. "Euclid's postulate" is a specific instance.
    • Every logical system must start with some basic postulates.
  • Non-Euclidean geometry (n): A type of geometry that does not hold Euclid's parallel postulate to be true.
    • The geometry on a curved surface is an example of non-Euclidean geometry.
Synonyms
  • Euclidean postulate
  • Euclidean axiom
  • Geometric axiom (when referring specifically to Euclid's set)
Related Phrases
  • The five postulates of Euclid: The complete set, often listed as:
    • A straight line segment can be drawn joining any two points.
    • Any straight line segment can be extended indefinitely in a straight line.
    • Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.
    • All right angles are congruent.
    • The parallel postulate: If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side.
euclid's postulate

A student draws a diagram illustrating Euclid's postulate on a chalkboard.

Noun
  1. (mathematics) any of five axioms that are generally recognized as the basis for Euclidean geometry

Từ đồng nghĩa