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Line (geometry): Quiz


Question 1: In ________, a ray in a space X is a continuous embedding R+X.
TopologyMathematicsManifoldAlgebraic topology

Question 2: Any collection of lines partitions the plane into convex polygons; this partition is known as an ________.
K-set (geometry)Arrangement of linesSylvester–Gallai theoremVector space

Question 3: In coordinate geometry, lines in a ________ can be described algebraically by linear equations and linear functions.
Spherical coordinate systemCartesian coordinate systemCylindrical coordinate systemParabolic coordinates

Question 4: Glossary of Riemannian and metric geometry#R for its meaning in ________.
Ricci curvatureDifferential geometryRiemannian geometryManifold

Question 5: When geometry was first formalised by ________ in Elements, he defined lines to be "breadthless length" with a straight line being a line "which lies evenly with the points on itself".

Question 6: In two dimensions, the characteristic equation is often given by the ________:
Quartic functionPolynomialLinear equationCubic function

Question 7: In modern geometry, a line is simply taken as an undefined object with properties given by ________.
Set theoryAxiomatic systemMathematical logicAxiom

Question 8: ________, including Plane (geometry)#Distance from a point to a plane, which generalizes the distance from a point to a line.
Stereographic projectionPlane (geometry)ManifoldComplex plane

Question 9: In ________ Rn (and analogously in all other vector spaces), we define a line L as a subset of the form
Metric spaceDimensionEuclidean spaceMathematics

Question 10: ________, just as two points determine a line
Five points determine a conicEnumerative geometryCayley–Bacharach theoremVeronese surface


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