One of these two things is required in Napoleon's problem, while the Mohr-Mascheroni and Poncelet-Steiner theorems suggest that, under certain conditions, only one of them is necessary. Pierre Wantzel provided proofs determining the solvability of several problems involving these two things. One of these things can be made more robust by replacing it with a neusis. If the odd prime factors of a number n are distinct Fermat primes, then these things can be used to produce a (*) polygon with n sides. The fact that these two things cannot generate the square root of pi means that one cannot use them to produce a square with the same area as a given circle. They also cannot be used to double a cube or trisect an angle. For 10 points, name these two physical objects used in construction problem
One of these two things is required in Napoleon's problem, while the Mohr-Mascheroni and Poncelet-Steiner theorems suggest that, under certain conditions, only one of them is necessary. Pierre Wantzel provided proofs determining the solvability of several problems involving these two things. One of these things can be made more robust by replacing it with a neusis. If the odd prime factors of a number n are distinct Fermat primes, then these things can be used to produce a (*) polygon with n sides. The fact that these two things cannot generate the square root of pi means that one cannot use them to produce a square with the same area as a given circle. They also cannot be used to double a cube or trisect an angle. For 10 points, name these two physical objects used in construction problems from classical Greek geometry.
One of these two things is required in Napoleon's problem, while the Mohr-Mascheroni and Poncelet-Steiner theorems suggest that, under certain conditions, only one of them is necessary.