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Extended Base
In geometry, a base is a Edge (geometry), side of a polygon or a face (geometry), face of a polyhedron, particularly one oriented perpendicular to the direction in which Height#In mathematics, height is measured, or on what is considered to be the "bottom" of the figure. This term is commonly applied in plane geometry to triangles, parallelograms, trapezoids, and in solid geometry to Cylinder (geometry), cylinders, Cone (geometry), cones, Pyramid (geometry), pyramids, parallelepipeds, Prism (geometry), prisms, and frustums. The side or point opposite the base is often called the ''apex (geometry), apex'' or ''summit'' of the shape. Of a triangle In a triangle, any arbitrary side can be considered the ''base''. The two endpoints of the base are called ''base vertices'' and the corresponding angles are called ''base angles''. The third vertex opposite the base is called the ''apex''. The extended base of a triangle (a particular case of an extended side) is the line (geometry), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pyramid Coloured Base (geometry)
A pyramid () is a Nonbuilding structure, structure whose visible surfaces are triangular in broad outline and converge toward the top, making the appearance roughly a Pyramid (geometry), pyramid in the geometric sense. The base of a pyramid can be of any polygon shape, such as triangular or quadrilateral, and its surface-lines either filled or stepped. A pyramid has the majority of its mass closer to the ground with less mass towards the pyramidion at the Apex (geometry), apex. This is due to the gradual decrease in the cross-sectional area along the vertical axis with increasing elevation. This offers a weight distribution that allowed early civilizations to create monumental structures.Ancient Civilization, civilizations in many parts of the world pioneered the building of pyramids. The largest pyramid by volume is the Mesoamerican Great Pyramid of Cholula, in the Mexican state of Puebla. For millennia, the List of largest buildings in the world, largest structures on Earth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apex (geometry)
In geometry, an apex (: apices) is the vertex which is in some sense the "highest" of the figure to which it belongs. The term is typically used to refer to the vertex opposite from some " base". The word is derived from the Latin for 'summit, peak, tip, top, extreme end'. The term apex may be used in different contexts: * In an isosceles triangle, the apex is the vertex where the two sides of equal length meet, opposite the unequal third side. * In a pyramid or cone In geometry, a cone is a three-dimensional figure that tapers smoothly from a flat base (typically a circle) to a point not contained in the base, called the '' apex'' or '' vertex''. A cone is formed by a set of line segments, half-lines ..., the apex is the vertex at the "top" (opposite the base). In a pyramid, the vertex is the point that is part of all the lateral faces, or where all the lateral edges meet. References Parts of a triangle Polyhedra {{elementary-geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parts Of A Triangle
Part, parts or PART may refer to: People *Part (surname) * Parts (surname) Arts, entertainment, and media * Part (music), a single strand or melody or harmony of music within a larger ensemble or a polyphonic musical composition * Part (bibliography), a sub-division of a volume or journal * ''Parts'' (book), a 1997 children's book by Tedd Arnold *Character (arts), in acting, a person or other being in a performed narrative Transportation * Pottstown Area Rapid Transit (PART), Pennsylvania, U.S. * Putnam Area Rapid Transit (PART), New York, U.S. * Piedmont Authority for Regional Transportation (PART), North Carolina, U.S. Other uses * Part (mathematics) or Mereology, the study of parts and the wholes they form * Part-of, the semantic relation of a part to the whole specific to linguistics *Spare part, an interchangeable part used for repair *Part number, identifier of a particular part design in engineering * Part (haircut), a hairstyle * Parts of Lincolnshire, geographic divisio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York City
New York, often called New York City (NYC), is the most populous city in the United States, located at the southern tip of New York State on one of the world's largest natural harbors. The city comprises five boroughs, each coextensive with a respective county. The city is the geographical and demographic center of both the Northeast megalopolis and the New York metropolitan area, the largest metropolitan area in the United States by both population and urban area. New York is a global center of finance and commerce, culture, technology, entertainment and media, academics, and scientific output, the arts and fashion, and, as home to the headquarters of the United Nations, international diplomacy. With an estimated population in 2024 of 8,478,072 distributed over , the city is the most densely populated major city in the United States. New York City has more than double the population of Los Angeles, the nation's second-most populous city. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volume
Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The definition of length and height (cubed) is interrelated with volume. The volume of a container is generally understood to be the capacity of the container; i.e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces. By metonymy, the term "volume" sometimes is used to refer to the corresponding region (e.g., bounding volume). In ancient times, volume was measured using similar-shaped natural containers. Later on, standardized containers were used. Some simple three-dimensional shapes can have their volume easily calculated using arithmetic formulas. Volumes of more complicated shapes can be calculated with integral calculus if a formula exists for the shape ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Area
Area is the measure of a region's size on a surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an open surface or the boundary of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analogue of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). Two different regions may have the same area (as in squaring the circle); by synecdoche, "area" sometimes is used to refer to the region, as in a " polygonal area". The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (written as m2), which is the area o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Locus (geometry)
In geometry, a locus (plural: ''loci'') (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.. The set of the points that satisfy some property is often called the ''locus of a point'' satisfying this property. The use of the singular in this formulation is a witness that, until the end of the 19th century, mathematicians did not consider infinite sets. Instead of viewing lines and curves as sets of points, they viewed them as places where a point may be ''located'' or may move. History and philosophy Until the beginning of the 20th century, a geometrical shape (for example a curve) was not considered as an infinite set of points; rather, it was considered as an entity on which a point may be located or on which it moves. Thus a circle in the Euclidean plane was defined as the ''locus'' of a point that is at a given distance of a fixed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Area Of A Triangle
In geometry, calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is T=bh/2, where ''b'' is the length of the ''base'' of the triangle, and ''h'' is the ''height'' or ''altitude'' of the triangle. The term "base" denotes any side, and "height" denotes the length of a perpendicular from the vertex opposite the base onto the line containing the base. Euclid proved that the area of a triangle is half that of a parallelogram with the same base and height in his book ''Elements'' in 300 BCE. In 499 CE Aryabhata, used this illustrated method in the '' Aryabhatiya'' (section 2.6). Although simple, this formula is only useful if the height can be readily found, which is not always the case. For example, the land surveyor of a triangular field might find it relatively easy to measure the length of each side, but relatively difficult to construct a 'height'. Various methods may be used in practice, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intersection
In mathematics, the intersection of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously. For example, in Euclidean geometry, when two lines in a plane are not parallel, their intersection is the point at which they meet. More generally, in set theory, the intersection of sets is defined to be the set of elements which belong to all of them. Unlike the Euclidean definition, this does not presume that the objects under consideration lie in a common space. It simply means the overlapping area of two or more objects or geometries. Intersection is one of the basic concepts of geometry. An intersection can have various geometric shapes, but a point is the most common in a plane geometry. Incidence geometry defines an intersection (usually, of flats) as an object of lower dimension that is incident to each of the original objects. In this approach an intersection can be sometimes undefined, such as for paral ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Altitude (triangle)
In geometry, an altitude of a triangle is a line segment through a given Vertex (geometry), vertex (called ''apex (geometry), apex'') and perpendicular to a line (geometry), line containing the side or edge (geometry), edge opposite the apex. This (finite) edge and (infinite) line extension are called, respectively, the ''base (geometry), base'' and ''extended side, extended base'' of the altitude. The point (geometry), point at the intersection of the extended base and the altitude is called the ''foot'' of the altitude. The length of the altitude, often simply called "the altitude" or "height", symbol , is the distance between the foot and the apex. The process of drawing the altitude from a vertex to the foot is known as ''dropping the altitude'' at that vertex. It is a special case of orthogonal projection. Altitudes can be used in the computation of the area of a triangle: one-half of the product of an altitude's length and its base's length (symbol ) equals the triangle's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Obtuse Angle
In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight lines at a point. Formally, an angle is a figure lying in a plane formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the '' vertex'' of the angle. More generally angles are also formed wherever two lines, rays or line segments come together, such as at the corners of triangles and other polygons. An angle can be considered as the region of the plane bounded by the sides. Angles can also be formed by the intersection of two planes or by two intersecting curves, in which case the rays lying tangent to each curve at the point of intersection define the angle. The term ''angle'' is also used for the size, magnitude or quantity of these types of geometric figures and in this context an angle consists of a number and unit of measurement. Angular measure or measure of angle are sometimes used to distinguish between the measurement an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Obtuse Triangle
An acute triangle (or acute-angled triangle) is a triangle with three ''acute angles'' (less than 90°). An obtuse triangle (or obtuse-angled triangle) is a triangle with one '' obtuse angle'' (greater than 90°) and two acute angles. Since a triangle's angles must sum to 180° in Euclidean geometry, no Euclidean triangle can have more than one obtuse angle. Acute and obtuse triangles are the two different types of oblique triangles—triangles that are not right triangles because they do not have any right angles (90°). Properties In all triangles, the centroid—the intersection of the medians, each of which connects a vertex with the midpoint of the opposite side—and the incenter—the center of the circle that is internally tangent to all three sides—are in the interior of the triangle. However, while the orthocenter and the circumcenter are in an acute triangle's interior, they are exterior to an obtuse triangle. The orthocenter is the intersection po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
