Concepts 10
... If two angles and a ___________________ side of a triangle are congruent to two angles and the non included side of another triangles, then the triangles are congruent. ...
... If two angles and a ___________________ side of a triangle are congruent to two angles and the non included side of another triangles, then the triangles are congruent. ...
Uniform hyperbolicity of the curve graphs
... depending on a constant, K, in the hypotheses. The three clauses (1), (2) and (3) of those hypotheses were verified respectively by Lemma 4.10, Proposition 4.11 and Lemma 4.9. These respectively gave K bounded by 4D, 18D and 2D, which we can now replace by 80, 280 and 40. In particular, we have show ...
... depending on a constant, K, in the hypotheses. The three clauses (1), (2) and (3) of those hypotheses were verified respectively by Lemma 4.10, Proposition 4.11 and Lemma 4.9. These respectively gave K bounded by 4D, 18D and 2D, which we can now replace by 80, 280 and 40. In particular, we have show ...
Interactive Chalkboard
... • A tangent is a line in the plane of a circle that intersects the circle in exactly one point. Line j is a tangent. • A secant is a line that intersects a circle in two points. Line k is a secant. A secant contains a chord. ...
... • A tangent is a line in the plane of a circle that intersects the circle in exactly one point. Line j is a tangent. • A secant is a line that intersects a circle in two points. Line k is a secant. A secant contains a chord. ...
Riemann–Roch theorem
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles. It relates the complex analysis of a connected compact Riemann surface with the surface's purely topological genus g, in a way that can be carried over into purely algebraic settings.Initially proved as Riemann's inequality by Riemann (1857), the theorem reached its definitive form for Riemann surfaces after work of Riemann's short-lived student Gustav Roch (1865). It was later generalized to algebraic curves, to higher-dimensional varieties and beyond.