# Constructible polygon: Quiz

Question 1: that are nested, each in the next (a composition series, in group theory terms), something simple to prove by induction in this case of an ________.
Group (mathematics)Group homomorphismSimple groupAbelian group

Question 2: This number lies in the n-th cyclotomic field — and in fact in its real subfield, which is a totally real field and a rational ________ of dimension
Vector spaceGroup (mathematics)Matrix (mathematics)Hilbert space

Question 3: It is straightforward to show from ________ that constructible lengths must come from base lengths by the solution of some sequence of quadratic equations.
Cartesian coordinate systemVector spaceAnalytic geometryEuclidean vector

Question 4: ________ proved the constructibility of the regular 17-gon in 1796.
Isaac NewtonCarl Friedrich GaussBenjamin FranklinJean le Rond d'Alembert

Question 5: This theory allowed him to formulate a ________ for the constructibility of regular polygons:
Necessary and sufficient conditionMatrix (mathematics)AlgebraSet (mathematics)

Question 6: Constructions for the regular pentagon were described both by Euclid (Elements, ca 300 BC), and by Ptolemy (________, ca AD 150).
AlmagestPytheasPosidoniusHipparchus

Question 7: It should be stressed that the concept of constructibility as discussed in this article applies specifically to ________ construction.
Compass and straightedge constructionsAngle trisectionField (mathematics)Heptagon

Question 8: In mathematics, a constructible polygon is a ________ that can be constructed with compass and straightedge.
Regular polygonPentagonHexagonOctagon

Question 9: In the light of later work on ________, the principles of these proofs have been clarified.
Group theoryField (mathematics)Symmetric groupGalois theory