Desargues's theoremIn projective geometry, Desargues's theorem, named after Girard Desargues, states: Two triangles are in perspective axially if and only if they are in perspective centrally. Denote the three vertices of one triangle by a, b and c, and those of the other by A, B and C. Axial perspectivity means that lines and meet in a point, lines and meet in a second point, and lines and meet in a third point, and that these three points all lie on a common line called the axis of perspectivity.
Ancient Roman architectureAncient Roman architecture adopted the external language of classical Greek architecture for the purposes of the ancient Romans, but was different from Greek buildings, becoming a new architectural style. The two styles are often considered one body of classical architecture. Roman architecture flourished in the Roman Republic and to even a greater extent under the Empire, when the great majority of surviving buildings were constructed.
René DescartesRené Descartes (deɪˈkɑːrt or UKˈdeɪkɑːrt; ʁəne dekaʁt; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathematics was central to his method of inquiry, and he connected the previously separate fields of geometry and algebra into analytic geometry. Descartes spent much of his working life in the Dutch Republic, initially serving the Dutch States Army, later becoming a central intellectual of the Dutch Golden Age.
ColosseumThe Colosseum (ˌkɒləˈsiːəm ; Colosseo kolosˈsɛːo) is an elliptical amphitheatre in the centre of the city of Rome, Italy, just east of the Roman Forum. It is the largest ancient amphitheatre ever built, and is still the largest standing amphitheatre in the world, despite its age. Construction began under the emperor Vespasian (69-79) in 72 and was completed in 80 AD under his successor and heir, Titus (79-81). Further modifications were made during the reign of Domitian (81-96).
Parametric surfaceA parametric surface is a surface in the Euclidean space which is defined by a parametric equation with two parameters . Parametric representation is a very general way to specify a surface, as well as implicit representation. Surfaces that occur in two of the main theorems of vector calculus, Stokes' theorem and the divergence theorem, are frequently given in a parametric form. The curvature and arc length of curves on the surface, surface area, differential geometric invariants such as the first and second fundamental forms, Gaussian, mean, and principal curvatures can all be computed from a given parametrization.
Metric tensorIn the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold M (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows defining distances and angles there. More precisely, a metric tensor at a point p of M is a bilinear form defined on the tangent space at p (that is, a bilinear function that maps pairs of tangent vectors to real numbers), and a metric tensor on M consists of a metric tensor at each point p of M that varies smoothly with p.
Projective planeIn mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect at a single point, but there are some pairs of lines (namely, parallel lines) that do not intersect. A projective plane can be thought of as an ordinary plane equipped with additional "points at infinity" where parallel lines intersect. Thus any two distinct lines in a projective plane intersect at exactly one point.
EllipseIn mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by its eccentricity , a number ranging from (the limiting case of a circle) to (the limiting case of infinite elongation, no longer an ellipse but a parabola).
CurveIn mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that appeared more than 2000 years ago in Euclid's Elements: "The [curved] line is [...] the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which [...
CurvatureIn mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonical example is that of a circle, which has a curvature equal to the reciprocal of its radius. Smaller circles bend more sharply, and hence have higher curvature. The curvature at a point of a differentiable curve is the curvature of its osculating circle, that is the circle that best approximates the curve near this point.
Algebraic curveIn mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane curve can be completed in a projective algebraic plane curve by homogenizing its defining polynomial. Conversely, a projective algebraic plane curve of homogeneous equation h(x, y, t) = 0 can be restricted to the affine algebraic plane curve of equation h(x, y, 1) = 0.
ExerciseExercise is a body activity that enhances or maintains physical fitness and overall health and wellness. It is performed for various reasons, including weight loss or maintenance, to aid growth and improve strength, develop muscles and the cardiovascular system, hone athletic skills, improve health, or simply for enjoyment. Many individuals choose to exercise outdoors where they can congregate in groups, socialize, and improve well-being as well as mental health.
