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In the theory of quadratic forms, the parabola is the graph of the quadratic form x 2 (or other scalings), while the elliptic paraboloid is the graph of the positive-definite quadratic form x 2 + y 2 (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form x 2 − y 2. Generalizations to more variables yield ...
The two Spains (Spanish: las dos Españas) is a phrase from a short poem by Spanish poet Antonio Machado. The phrase is the given name to the intellectual debate concerning the national identity of being Spanish , rising alongside regenerationism at the end of the 19th century.
A family of conic sections of varying eccentricity share a focus point and directrix line, including an ellipse (red, e = 1/2), a parabola (green, e = 1), and a hyperbola (blue, e = 2). The conic of eccentricity 0 in this figure is an infinitesimal circle centered at the focus, and the conic of eccentricity ∞ is an infinitesimally separated ...
In this position, the hyperbolic paraboloid opens downward along the x-axis and upward along the y-axis (that is, the parabola in the plane x = 0 opens upward and the parabola in the plane y = 0 opens downward). Any paraboloid (elliptic or hyperbolic) is a translation surface, as it can be generated by a moving parabola directed by a second ...
A parabola is the limit curve of a pencil of ellipses with a common vertex and one common focus, as the other focus is moved to infinity to the right, and also the limit curve of a pencil of hyperbolas with a common vertex and one common focus, as the other focus is moved to infinity to the left.
Tales of Count Lucanor (Old Spanish: Libro de los enxiemplos del Conde Lucanor et de Patronio) is a collection of parables written in 1335 by Juan Manuel, Prince of Villena. It is one of the earliest works of prose in Castilian Spanish. The book is divided into five parts.
It was later included in El Aleph under the title "Los dos reyes y los dos laberintos". It deals with a number of Borgesian themes: labyrinths, supposed obscure folk tales, Arabia, and Islam. [ 2 ] The story is itself referenced in-universe by characters of Borges' " Ibn Hakkan Al-Bokhari—Dead in His Labyrinth ", also found in The Aleph .
A parabolic segment is the region bounded by a parabola and line. To find the area of a parabolic segment, Archimedes considers a certain inscribed triangle. The base of this triangle is the given chord of the parabola, and the third vertex is the point on the parabola such that the tangent to the parabola at that point is parallel to the chord.