BOLYAI AND LOBACHEVSKY

Where did János Bolyai spend most of his life?

• France

• Germany

• Transylvanian mountains of modern-day Romania

• England

What was the fundamental principle of geometry that János Bolyai became obsessed with?

• Fermat's Last Theorem

• Euclid's fifth postulate

• Pythagorean theorem

• Pascal's Theorem

In hyperbolic space, what do apparently parallel lines do?

• Overlap

• Diverge

• Remain parallel

• Converge

What did János Bolyai call the geometry of curved spaces on a saddle-shaped plane?

• Spherical geometry

• Euclidean geometry

• Hyperbolic geometry

• Elliptic geometry

Who also worked on developing a geometry in which Euclid's fifth postulate did not apply?

• Archimedes

• Plato

• Pythagoras

• Nikolai Lobachevsky

What is the early non-Euclidean geometry often referred to as?

• Euclidean geometry

• Spherical geometry

• Elliptic geometry

• Lobachevskian geometry

What was the method developed by Nikolai Lobachevsky for approximating the roots of algebraic equations?

• Newton's method

• Dandelin-Gräffe method

• Bisection method

• Secant method

What did János Bolyai leave behind when he died?

• 20,000 pages of mathematical manuscripts

• 15,000 pages of mathematical manuscripts

• 10,000 pages of mathematical manuscripts

• 25,000 pages of mathematical manuscripts

Who refused to take on János Bolyai as a student?

• Plato

• Archimedes

• Fermat

• Gauss

What did János Bolyai become obsessed with to the extent that his father warned him about it?

• Algebraic equations

• Euclid's fifth postulate

• Complex numbers

• Trigonometry