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The Platonic solids are the only five convex regular polyhedra: a regular polyhedron has congruent regular polygonal faces and the same number of faces meeting at each vertex. The five solids are the tetrahedron (4 faces), cube (6 faces), octahedron (8 faces), dodecahedron (12 faces), and icosahedron (20 faces). Their symmetry and properties have been…
The Euler characteristic is a topological invariant, a number that describes a topological space’s structure or shape regardless of how it is bent. For polyhedra, it is defined by the formula chi = V – E + F[/latex], where V, E, and F are the number of vertices, edges, and faces, respectively. For a sphere,…
A fundamental theorem in topology and geometry stating that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) are related by the formula V – E + F = 2[/latex]. This value, 2, is the Euler characteristic of a sphere, revealing a deep topological property independent of the polyhedron’s specific…
The Gauss-Bonnet theorem connects the geometry of a compact two-dimensional surface to its topology. It states that the integral of the Gaussian curvature K[/latex] over the entire surface M[/latex] is equal to 2pi[/latex] times the Euler characteristic chi(M)[/latex] of the surface. The formula is int_M K , dA = 2pi chi(M)[/latex].
The Pythagorean theorem is a fundamental relation in Euclidean geometry among the three sides of a right-angled triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. The formula…
It is impossible to simultaneously know with perfect accuracy certain pairs of complementary physical properties of a particle. The most common example is the position x[/latex] and momentum p[/latex]. The principle states that the product of their uncertainties, Delta x[/latex] and Delta p[/latex], must be greater than or equal to a specific value: Delta x…
نموذج "من عميل إلى عميل" (C2C) هو نموذج أعمال يتاجر فيه المستهلكون مع بعضهم البعض مباشرة، وعادةً ما يتم تيسيره من خلال منصة إلكترونية تابعة لجهة خارجية. يتناقض هذا النموذج مع نماذج الأعمال بين الشركات والمستهلكين (B2C) والأعمال بين الشركات (B2B). لا يكون مزود المنصة هو البائع، بل هو وسيط يُمكِّن المعاملة، مما يخلق سوقًا للسلع المستعملة أو السلع المصنوعة يدويًا أو المقتنيات.
The C2C model has two primary implementations: online marketplaces and classifieds. Marketplaces, like eBay, are highly integrated, providing payment processing, structured listings, and reputation systems. They are active intermediaries. In contrast, classifieds platforms, like Craigslist, act more as simple connectors, providing a venue for listings but typically leaving the payment and transaction logistics entirely up…
Digital trust and reputation systems are critical mechanisms that facilitate cooperation between strangers in online P2P platforms. They quantify and display the past behavior of users, typically through ratings, reviews, and endorsements. This creates a form of social collateral, reducing transaction uncertainty and risk, which is essential for the functioning of the sharing economy where…
B2B business models are often categorized as either vertical or horizontal. A vertical B2B model focuses on a single industry or ‘vertical,’ providing specialized products and services tailored to that sector’s unique needs (e.g., software for dentists). In contrast, a horizontal B2B model offers a product or service that is applicable across multiple industries (e.g.,…
