Which angle can't be trisected?
- Ku, Yin Bon (Albert)
To show that an angle cannot be trisected, it suffices to show that is not a constructible angle. Let's consider . Then . Now we use the following trigonometric identity: Let , we have It can be shown that is irreducible over . Therefore, the degree of over is and hence by the Main Theorem, is not a constructible number. In other words, is not a constructible angle, which in turn implies that cannot be trisected.