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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) Euclid
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 square root of -1
C) Ratio of a circle's circumference to its diameter
D) The area of a circle
  • 4. What famous problem in ancient mathematics was proved impossible by Lindemann's work on pi?
A) Placing a circle of equal area inside a square
B) Trisecting an angle
C) Doubling the cube
D) Squaring the circle
  • 5. In which century was it definitively proven that it is impossible to 'square the circle'?
A) 18th century
B) 19th century
C) 17th century
D) 20th century
  • 6. What is the term for a geometric construction that only uses a compass and straightedge?
A) Lindemann construction
B) Circle squaring
C) Curvilinear construction
D) Euclidean construction
  • 7. Who is credited for calculating a relatively accurate value of pi around 250 BC?
A) Thales
B) Euclid
C) Archimedes
D) Pythagoras
  • 8. 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
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