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