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The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels.
Social capital is a concept used in sociology and economics to define networks of relationships which are productive towards advancing the goals of individuals and groups. [1] [2] It involves the effective functioning of social groups through interpersonal relationships, a shared sense of identity, a shared understanding, shared norms, shared values, trust, cooperation, and reciprocity.
Depending on how the line segment is defined, either of the two end points may or may not be part of the line segment. Two or more line segments may have some of the same relationships as lines, such as being parallel, intersecting, or skew, but unlike lines they may be none of these, if they are coplanar and either do not intersect or are ...
Make networking a priority, even in a virtual world. The old adage, “It’s not what you know, it’s who you know” has been proven time after time in corporate America. Education, talent and ...
Assume that we want to find intersection of two infinite lines in 2-dimensional space, defined as a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0. We can represent these two lines in line coordinates as U 1 = (a 1, b 1, c 1) and U 2 = (a 2, b 2, c 2). The intersection P′ of two lines is then simply given by [4]
Graph theory is also widely used in sociology as a way, for example, to measure actors' prestige or to explore rumor spreading, notably through the use of social network analysis software. Under the umbrella of social networks are many different types of graphs. [17] Acquaintanceship and friendship graphs describe whether people know each other.
Earlier, the topological properties of the real plane had been introduced via ordering relations on the affine lines, see, e.g., Hilbert, [3] Coxeter, [4] and O. Wyler. [5] The completeness of the ordering is equivalent to local compactness and implies that the affine lines are homeomorphic to R {\displaystyle \mathbb {R} } and that the point ...
Next to the intersecting chords theorem and the tangent-secant theorem, the intersecting secants theorem represents one of the three basic cases of a more general theorem about two intersecting lines and a circle - the power of point theorem.