Bernhard Riemann

Học thuật
Thân thiện
Definition
  1. Proper noun:
    • Georg Friedrich Bernhard Riemann: A 19th-century German mathematician renowned for his foundational contributions to analysis, differential geometry, and number theory. He is a pioneer of non-Euclidean geometry, which studies spaces where Euclid's parallel postulate does not hold.
Usage Examples
  • Proper noun:
    • The theorems of Bernhard Riemann underpin much of modern physics.
    • Our class studied the Bernhard Riemann hypothesis in number theory.
Advanced Usage
  • "in the tradition of Riemann": Referring to work or ideas that follow the mathematical approaches established by Bernhard Riemann.
    • The physicist's work on manifold theory is firmly in the tradition of Riemann.
  • "Riemannian": An adjective derived from his name, used to describe concepts from his geometric work.
    • The concept of a Riemannian manifold is central to general relativity.
Variants and Related Words
  • Riemannian (adj): Pertaining to the geometry developed by Bernhard Riemann, especially Riemannian geometry.
    • Einstein's theory uses Riemannian geometry to describe spacetime.
  • Riemann surface (n): A one-dimensional complex manifold, a key concept he introduced.
    • The topology of a Riemann surface can be very complex.
Synonyms
  • Georg Friedrich Bernhard Riemann: The full name.
  • Riemann: The common shortened reference.
Related Phrases and Concepts
  • Riemann integral: A classical definition of the integral, though largely superseded by the Lebesgue integral.
    • The Riemann integral is taught in introductory calculus courses.
  • Riemann hypothesis: A famous, unproven conjecture in number theory concerning the zeros of the Riemann zeta function.
    • Solving the Riemann hypothesis is one of the great unsolved problems in mathematics.
  • Riemann curvature tensor: A fundamental object in Riemannian geometry that quantifies curvature.
    • The Riemann curvature tensor vanishes in flat space.
Related Idioms
    • It's not Riemann, but it's a clever piece of geometry. (Implies the work is not of the groundbreaking caliber associated with Riemann).
Noun
  1. pioneer of non-Euclidean geometry (1826-1866)

Từ đồng nghĩa

Từ chứa "Bernhard Riemann"