Question

question 2 of 10

many of the constructions that the greeks thought impossible were later proven impossible in the 18th and 19th centuries.

a. true
b. false

Explanation:

Analyze the historical context of Greek constructions

The ancient Greeks proposed several geometric construction problems using only a compass and straightedge, such as doubling the cube, trisecting an angle, and squaring the circle. They suspected these constructions were impossible under the given constraints, but lacked the algebraic tools to prove it.

Identify the timeline of the proofs of impossibility

These problems were rigorously proven to be mathematically impossible in the 19th century using field theory and abstract algebra. Specifically, Pierre Wantzel proved the impossibility of doubling the cube and trisecting an angle in 1837, and Ferdinand von Lindemann proved the impossibility of squaring the circle in 1882 by showing that \(\pi\) is transcendental.

Determine the truth value of the statement

Since these proofs occurred in the 19th century, the statement "Many of the constructions that the Greeks thought impossible were later proven impossible in the 18th and 19th centuries" is historically accurate and true.

Answer:

• A. True (Correct answer)
• B. False