Protractor Protractor A protractor is a measuring instrument, typically made of transparent plastic or glass, for measuring angles. Most protractors measure angles in degrees (°). Radian-scale protractors measure angles in radians. Most protractors are divided into 180 equal parts. Some precision protractors further divide degrees into arcminutes. They are used for a variety of mechanical and engineering-related applications. One common use is in geometry lessons in schools. Some protractors are simple half-discs. More advanced protractors, such as the bevel protractor, have one or two swinging arms, which can be used to help measure the angle. A bevel protractor is a graduated
Semi-invariant of a quiver the coefficients of the characteristic polynomial In case Q has neither loops nor cycles the variety "k"[Rep(Q,d)] has a unique closed orbit corresponding to the unique d-dimensional semi-simple representation, therefore any invariant function is constant. Elements which are invariants with respect to the subgroup SL(d) := ∏ SL(d("i")) form a ring, SI(Q,d), with a richer structure called ring of semi-invariants. It decomposes as where A function belonging to SI(Q,d) is called semi-invariant of weight "σ". Consider the quiver Q: Fix d = ("n","n"). In this case "k"[Rep("Q",("n","n"))] is congruent to the set of square matrices of size "n": "M"("n"). The