Pyramid (redirected from pyramidical)

pyramid, structure

pyramid. The true pyramid exists only in Egypt, though the term has also been applied to similar structures in other countries. Egyptian pyramids are square in plan and their triangular sides, which directly face the points of the compass, slope upwards at approximately a 50° angle from the ground and meet at an apex. The prototype for the pyramid are the mastabas of the Old Kingdom (2680–2565 B.C.), which are rectangular in plan and have only two sloping sides. After these came the step-pyramid at Sakkara, built c.2620 B.C., which soon evolved into the straight-sided true pyramid. This monumental structure was developed around the IV dynasty and continued to be the favored form for royal burial through the VI dynasty.

Each monarch built his own pyramid in which his mummified body might be preserved for eternity away from human view and sacrilege. As a result of the lack of sophisticated machinery, the construction of each pyramid took many years and required measureless amounts of building materials and labor. Entrance into a pyramid is through an opening in the northern wall. A small passage, traversing lesser chambers, leads to the sepulchral room deep beneath the surface. Stone blocks forming a gable divert the weight of the great masonry masses over these chambers. Though the pyramids were usually built of rough stone blocks laid up in horizontal courses, many were constructed of mud bricks with a stone casing.

The three pyramids of Giza near Cairo, all of the IV dynasty, are the largest and finest of their kind. The Great Pyramid of Khufu or Cheops (begun c.2680 B.C.) was designated one of the Seven Wonders of the World and is the largest pyramid ever built. A solid mass of limestone blocks covering 13 acres (5.3 hectares), it was originally 756 ft (230 m) along each side of its base and 482 ft (147 m) high. It has several passages, two large chambers in addition to one beneath the ground level, and two small air chambers for ventilation.

Although not true pyramids, pyramidical structures were also built by the Mesopotamians and by the Maya of Mexico and Central America. Mesopotamian ziggurat was square in plan and built up in receding terraces. Mayan pyramids, built in steep, receding blocks, also were topped by ritual chambers, and in some cases, possessed an interior crypt. Stepped funeral pyramids dating from the 4th cent. B.C. were discovered in the 1990s in the Altai region of Siberia. The Romans built small pyramidical tombs of which the most famous was the Pyramid of Cestius (62 B.C.–12 B.C.) in Rome. Built of concrete faced with marble, it has an interior tomb vault and is 116 ft (35 m) high. Many modern architects have admired pyramids for their pure geometry. In the reconstruction of the Louvre in Paris, architect I. M. Pei added a pyramidal entrance pavilion (1987–89).

Bibliography

See I. E. S. Edwards, The Pyramids of Egypt (rev. ed. 1961); P. Tompkins, Secrets of the Great Pyramid (1971); K. Mendelssohn, The Riddle of the Pyramids (1974).

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pyramid, in geometry

pyramid, in geometry, solid figure bounded by a polygon (the base, or directrix) and the surface generated by a moving line (the generator) passing through a fixed point (vertex) and continually intersecting the perimeter of the polygon. The surface, or lateral faces, of the pyramid are triangles having as a common vertex the vertex of the pyramid; in a regular pyramid the base is a regular polygon and the lateral faces are congruent triangles. The altitude of a pyramid is the perpendicular distance from the vertex to the base. The volume of a pyramid is equal to one third the product of the altitude and the area of the base. The frustum is the portion of a pyramid between the base and a plane parallel to the base cutting the pyramid into two parts.

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pyramid

Ancient monumental structure constructed of or faced with stone or brick and having a rectangular base and four sloping triangular sides meeting at an apex. Pyramids have been built at various times and places; the best-known are those of Egypt and of Central and South America. The pyramids of ancient Egypt were royal tombs. Each contained an inner sepulchral chamber that housed the deceased (usually mummified) ruler, members of his entourage, and artifacts. The rest of the pyramid complex consisted of a large enclosure, an adjacent mortuary temple, and a causeway leading down to a pavilion. About 80 royal pyramids survive in Egypt, the greatest being those at Giza. American pyramids include the pyramids of the Sun and Moon at Teotihuacán, the Castillo at Chichén Itzá, and various Inca and Chimú structures in Andean settlements. These pyramids were generally built of earth and faced with stone; they are typically stepped pyramids and are topped by a platform or temple structure used for rituals, including human sacrifice.

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pyramid

1. a huge masonry construction that has a square base and, as in the case of the ancient Egyptian royal tombs, four sloping triangular sides

2. Maths a solid having a polygonal base and triangular sides that meet in a common vertex

3. Crystallog a crystal form in which three planes intersect all three axes of the crystal

4. Anatomy any pointed or cone-shaped bodily structure or part

5. a game similar to billiards with fifteen coloured balls

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pyramid [′pir·ə‚mid]

(crystallography)

An open crystal having three, four, six, eight, or twelve nonparallel faces that meet at a point.

(mathematics)

A polyhedron with one face a polygon and all other faces triangles with a common vertex.

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pyramid

A massive funerary structure of stone or brick with a square base and four sloping triangular sides meeting at the apex; used mainly in ancient Egypt. In Central America stepped pyramids formed the bases of temples; in India some temples had the shape of truncated pyramids.

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Pyramid 

a polyhedron with one face a polygon and the other faces triangles with a common vertex. The polygon, which may also be a triangle, is called the base, the remaining faces are called lateral faces, and the common vertex is called the vertex of the pyramid. Examples of pyramids are illustrated in Figure 1.

Figure 1

Pyramids are classified as triangular, quadrangular, and so on according to the number of their lateral faces. The line segment drawn perpendicularly from the vertex of the pyramid to the plane of the base is called the altitude of the pyramid, as is the length of the segment. The volume of a pyramid is given by the formula

where B is the area of the base and h is the altitude. A pyramid is said to be regular (see Figure l,b) if its base is a regular polygon and its altitude passes through the center of the base. The lateral faces of a regular pyramid are congruent isosceles triangles. The altitude of each of these triangles is called a regular pyramid’s slant height, or apothem (the projection of the slant height on the plane of the base is the apothem of the base). If a pyramid is cut into two parts by a plane parallel to its base, there result a pyramid similar to the original pyramid and a truncated pyramid.

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Pyramid 

a massive architectural structure with a square base and sloping sides meeting at an apex. Pyramids, which may be stepped or regular, are characteristic of ancient times. Pyramids were the tombs of the Egyptian pharaohs of the Old and Middle Kingdoms (from roughly 2800 to 1700 B.C.). The structures symbolized the superhuman greatness of the ruler. The largest Egyptian pyramid, that of Cheops at Gizeh, is 146.6 m high and was constructed in the 28th century B.C. In Central and South America, pyramidal structures, which often served as foundations for temples and were associated with cosmologic cults, were erected in the first millennium B.C. In ancient Roman and later in European art, the pyramidal motif was often used in memorial structures.

REFERENCES

Lauer, J. P. Zagadki egipetskikh piramid. Moscow, 1966. (Translated from French.)
Kink, Kh. A. Kak stroilis’ egipetskie piramidy. Moscow, 1967.
Mikhailovskii, K. Piramidy i maslaby. Warsaw, 1973.