Projective geometryIn mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, for a given dimension, and that geometric transformations are permitted that transform the extra points (called "points at infinity") to Euclidean points, and vice-versa.
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 [...
Cartesian ovalIn geometry, a Cartesian oval is a plane curve consisting of points that have the same linear combination of distances from two fixed points (foci). These curves are named after French mathematician René Descartes, who used them in optics. Let P and Q be fixed points in the plane, and let d(P, S) and d(Q, S) denote the Euclidean distances from these points to a third variable point S. Let m and a be arbitrary real numbers. Then the Cartesian oval is the locus of points S satisfying d(P, S) + m d(Q, S) = a.
Baroque architectureBaroque architecture is a highly decorative and theatrical style which appeared in Italy in the early 17th century and gradually spread across Europe. It was originally introduced by the Catholic Church, particularly by the Jesuits, as a means to combat the Reformation and the Protestant church with a new architecture that inspired surprise and awe. It reached its peak in the High Baroque (1625–1675), when it was used in churches and palaces in Italy, Spain, Portugal, France, Bavaria and Austria.
Affine connectionIn differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space. Connections are among the simplest methods of defining differentiation of the sections of vector bundles.
Power toolA power tool is a tool that is actuated by an additional power source and mechanism other than the solely manual labor used with hand tools. The most common types of power tools use electric motors. Internal combustion engines and compressed air are also commonly used. Tools directly driven by animal power are not generally considered power tools. Power tools are used in industry, in construction, in the garden, for housework tasks such as cooking, cleaning, and around the house for purposes of driving (fasteners), drilling, cutting, shaping, sanding, grinding, routing, polishing, painting, heating and more.
Garden toolA garden tool is any one of many tools made for gardening and landscaping, which overlap with the range of tools made for agriculture and horticulture. Garden tools can be divided into hand tools and power tools. Hand tool Today's garden tools originated with the earliest agricultural implements used by humans. Examples include the hatchet, axe, sickle, scythe, pitchfork, spade, shovel, trowel, hoe, fork, and rake. In some places, the machete is common. The earliest tools were made variously of wood, flint, metal, tin, and bone.
Defensive wallA defensive wall is a fortification usually used to protect a city, town or other settlement from potential aggressors. The walls can range from simple palisades or earthworks to extensive military fortifications with towers, bastions and gates for access to the city. From ancient to modern times, they were used to enclose settlements. Generally, these are referred to as city walls or town walls, although there were also walls, such as the Great Wall of China, Walls of Benin, Hadrian's Wall, Anastasian Wall, and the Atlantic Wall, which extended far beyond the borders of a city and were used to enclose regions or mark territorial boundaries.
Synthetic geometrySynthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic method for proving all results from a few basic properties initially called postulate, and at present called axioms. The term "synthetic geometry" has been coined only after the 17th century, and the introduction by René Descartes of the coordinate method, which was called analytic geometry.
Hand toolA hand tool is any tool that is powered by hand rather than a motor. Categories of hand tools include wrenches, pliers, cutters, , striking tools, struck or hammered tools, screwdrivers, vises, clamps, snips, hacksaws, drills, and knives. Outdoor tools such as garden forks, pruning shears, and rakes are additional forms of hand tools. Portable power tools are not hand tools. Hand tools have been used by humans since the Stone Age when stone tools were used for hammering and cutting.
MachiningMachining is a process in which a material (often metal) is cut to a desired final shape and size by a controlled material-removal process. The methods that have this common theme are collectively called subtractive manufacturing, which utilizes machine tools, in contrast to additive manufacturing (3D printing), which uses controlled addition of material. Machining is a part of the manufacture of many metal products, but it can also be used on other materials such as wood, plastic, ceramic, and composite material.
BaroqueThe Baroque (UKbəˈrɒk, US-ˈroʊk; baʁɔk) or Baroquism is a style of architecture, music, dance, painting, sculpture, poetry, and other arts that flourished in Europe from the early 17th century until the 1750s. It followed Renaissance art and Mannerism and preceded the Rococo (in the past often referred to as "late Baroque") and Neoclassical styles. It was encouraged by the Catholic Church as a means to counter the simplicity and austerity of Protestant architecture, art, and music, though Lutheran Baroque art developed in parts of Europe as well.
