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In the mathematical field of Riemannian geometry, Toponogov's theorem (named after Victor Andreevich Toponogov) is a triangle comparison theorem.It is one of a family of comparison theorems that quantify the assertion that a pair of geodesics emanating from a point p spread apart more slowly in a region of high curvature than they would in a region of low curvature.
Nielsen–Schreier theorem (free groups) Orbit-stabilizer theorem (group theory) Schreier refinement theorem (group theory) Schur's lemma (representation theory) Schur–Zassenhaus theorem (group theory) Sela's theorem (hyperbolic groups) Stallings theorem about ends of groups (group theory) Superrigidity theorem (algebraic groups)
"At its heart is the leader's self-awareness, his progress toward self-mastery and technical competence, and his sense of connection with those around him. It's the inner core, the source, of a leader's outer leadership effectiveness." (Scouller, 2011). The idea is that if leaders want to be effective they must work on all three levels in parallel.
In Forsyth, the leadership substitute theory is defined as "a conceptual analysis of the factors that combine to reduce or eliminate the need for a leader." [1] A leader may find that behaviors focusing on nurturing interpersonal relationships, or coordinating tasks and initiating structure, are not required in every situation. A study by Kerr ...
Transformational leadership is a leadership theory in which a leader's behaviors influence their followers, inspiring them to perform beyond their perceived capabilities. . This style of leadership encourages individuals to achieve unexpected or remarkable results by prioritizing their collective vision over their immediate self-intere
Triangle inequality: If a, b, and c are the lengths of the sides of a triangle then the triangle inequality states that +, with equality only in the degenerate case of a triangle with zero area. In Euclidean geometry and some other geometries, the triangle inequality is a theorem about vectors and vector lengths :
Entrepreneurial leadership is (as per Roebuck's definition) "organizing a group of people to achieve a common goal using proactive entrepreneurial behavior by optimising risk, innovating to take advantage of opportunities, taking personal responsibility and managing change within a dynamic environment for the benefit of [an] organisation".
The following similar construction, which appears in certain possible definitions of Gromov-hyperbolicity, may be regarded as a limit case when .. For three points ,, in a metric space , the Gromov product of and at is half of the triangle inequality defect: (,) = ((,) + (,) (,)) Given a geodesic triangle in with vertices (,,), the comparison tripod for is the metric graph obtained by gluing ...