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).

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.

food pyramid or Food Guide Pyramid, diagram used in nutrition education that fits food groups into a triangle and notes that, for a healthful diet, those at the base should be eaten more frequently than those at the top. At the base of the pyramid are breads, cereals, rice, and pasta, with a recommendation that 6 to 11 servings be eaten daily. On the next levels up are the vegetable (3 to 5 servings) and fruit (2 to 4 servings) groups, followed by the dairy group (2 to 3 servings) and a group including meats, eggs, nuts, and dry beans (2 to 3 servings). Fats, oils and sweets are at the apex, with a recommendation that they be eaten sparingly.

The Food Guide Pyramid was adopted by the U.S. Agriculture Department in 1992 as a replacement for the "four food groups" scheme that had been used to teach children about nutrition since the 1950s. The four food groups (the milk group, the meat group, the bread and cereals group, and the vegetable and fruit group) had put a greater emphasis on the consumption of meat and dairy products. The adoption of the food pyramid design was delayed by debate between nutritionists (who felt that it was an effective teaching tool that demonstrated current thinking about the benefits of a low-fat, high-complex carbohydrate diet) and the meat and dairy industries (which felt that the positioning of their products among the foods to be consumed less frequently implied that those foods were unhealthful).

Pyramid Lake, 188 sq mi (487 sq km), W Nev. The lake, a remnant of ancient Lake Lahontan, receives the Truckee River. Visited (1844) by U.S. explorer John Frémont, the lake was named for its large pyramidal rocks. It is located in the Pyramid Lake (Native American) reservation. In the lake is Anaho Island, a national wildlife refuge.

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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