# Geometry: Quiz

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More interesting facts on Geometry

Question 1: It has made progress in the fields of threefolds, singularity theory and ________, as well as recovering and correcting the bulk of the older results.
Scheme (mathematics)Moduli spaceGeometric invariant theoryPicard group

Question 2: 300 BCE) was one of the most important early texts on geometry, in which he presented geometry in an ideal axiomatic form, which came to be known as ________.
Euclidean geometryTarski's axiomsAlfred TarskiEuclid's Elements

Question 3: The ________ is an open problem that has gradually taken its place as one of the major questions for mathematicians.
Alexander GrothendieckHodge conjectureMichael AtiyahRiemann hypothesis

Question 4: This played a key role in the emergence of ________ in the 17th century.
DerivativeIntegralCalculusDifferential calculus

Question 5: The field of algebraic geometry is the modern incarnation of the ________ of co-ordinates.
Cartesian coordinate systemAnalytic geometryVector spaceEuclidean vector

Question 6: The model of Euclid's Elements, a connected development of geometry as an ________, is in a tension with René Descartes's reduction of geometry to algebra by means of a coordinate system.
Set theoryMathematical logicAxiomatic systemGeorg Cantor

Question 7: Using ________, the classical groups give rise to finite groups, intensively studied in relation to the finite simple groups; and associated finite geometry, which has both combinatorial (synthetic) and algebro-geometric (Cartesian) sides.
Group (mathematics)Finite fieldRing (mathematics)Field (mathematics)

Question 8: Methods of algebraic geometry rely heavily on sheaf theory and other parts of ________.
Homology (mathematics)Group (mathematics)Homological algebraSheaf (mathematics)

Question 9: Geometry now is, in large part, the study of structures on manifolds that have a geometric meaning, in the sense of the principle of covariance that lies at the root of ________ theory in theoretical physics.
Introduction to general relativityGravitationBlack holeGeneral relativity

Question 10: The first, and most important, was the creation of analytic geometry, or geometry with coordinates and equations, by René Descartes (1596–1650) and ________ (1601–1665).
Pierre de FermatNumber theoryFranciscus VietaGottfried Leibniz