Problem of duplicating the cube

The "Problem of Duplicating the Cube" is a famous challenge from ancient Greece. It asks: given a cube with a known volume, how can you construct a new cube with exactly twice that volume using only a straightedge and compass? The core issue is whether such a construction is possible with classical tools. Mathematically, it translates to solving a cubic equation. The problem was eventually proven impossible using only these tools, revealing fundamental limits in geometric construction and deepening understanding of mathematics.