The ancient Greeks struggled with three very challenging geometric problems. One of them, "Using only a compass, and a straightedge trisect an angle?". Research this problem and discuss it? Is it possible? If yes or no, explain?

Question

The ancient Greeks struggled with three very challenging geometric problems.  One of them, "Using only  a compass, and a straightedge trisect an angle?".  Research this problem and discuss it? Is it possible? If yes or no, explain?

Noah Atkinson · Accepted Answer

Solution to this problem does not exist.

Read explanation at https://tutor.hix.ai

Parker Allen · Answer

undefined Trisecting an angle using only a compass and straightedge was one of the three classical geometric problems that puzzled ancient Greeks. The problem involves dividing an angle into three equal parts using only the two aforementioned tools. However, it was proven impossible to achieve using only a compass and straightedge. This impossibility is demonstrated by the fact that trisecting an angle results in a geometric construction that involves constructing lengths that are not expressible as finite combinations of additions, subtractions, multiplications, divisions, and square roots of the lengths determined by the compass and straightedge. This limitation is known as the angle trisection problem, and it has been rigorously established through mathematical proofs, particularly using field theory and Galois theory in modern mathematics. Therefore, trisecting an angle with just a compass and straightedge is not possible.