Circular segment Circular segment In geometry, a circular segment (symbol: ⌓) is a region of a circle which is "cut off" from the rest of the circle by a secant or a chord. More formally, a circular segment is a region of two-dimensional space that is bounded by an arc (of less than 180°) of a circle and by the chord connecting the endpoints of the arc. Let "R" be the radius of the circle, "θ" the central angle in radians, α is the central angle in degrees, "c" the chord length, "s" the arc length, "h" the sagitta (height) of the
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