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Squaring the circle
  • 1. Who proved that it is impossible to 'square the circle' using only a compass and straightedge?
A) Pythagoras
B) Archimedes
C) Ferdinand von Lindemann
D) Euclid
  • 2. Which ancient civilization tried to construct a square equal in area to a given circle?
A) Egyptians
B) Mesopotamians
C) Ancient Greeks
D) Romans
  • 3. What is the mathematical constant frequently denoted by the Greek letter pi (Ď€)?
A) The square root of -1
B) Ratio of a circle's circumference to its diameter
C) The base of natural logarithms
D) The area of a circle
  • 4. Who is credited for calculating a relatively accurate value of pi around 250 BC?
A) Archimedes
B) Thales
C) Euclid
D) Pythagoras
  • 5. What famous problem in ancient mathematics was proved impossible by Lindemann's work on pi?
A) Doubling the cube
B) Placing a circle of equal area inside a square
C) Squaring the circle
D) Trisecting an angle
  • 6. What theorem states that pi is a transcendental number?
A) Cauchy's Mean Value Theorem
B) Fermat's Last Theorem
C) Lindemann–Weierstrass theorem
D) Pythagorean theorem
  • 7. In which century was it definitively proven that it is impossible to 'square the circle'?
A) 19th century
B) 18th century
C) 20th century
D) 17th century
  • 8. What is the term for a geometric construction that only uses a compass and straightedge?
A) Circle squaring
B) Curvilinear construction
C) Lindemann construction
D) Euclidean construction
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