If the faces be all equal equilateral triangles the solid is termed the "regular" tetrahedron.
A third reflecting plate is sometimes employed, the cross-section of the three forming an equilateral triangle.
Ladenburg (Ber., 2, p. 140) devised his prism formula (IV), the six carbon atoms being placed at the six corners of a right equilateral triangular prism, with its plane projections (V, VI).
In shape roughly resembling an equilateral triangle, with base uppermost, Bosnia and Herzegovina cover an area of 19,696 sq.
The French army was thus disposed almost in an equilateral triangle with sides of about 570 m., with 95,000 men at the apex at Moscow opposed to 120,000, 30,000 about Brest opposite ioo,000, and 17,000 about Drissa confronted by 40,000, whilst in the centre of the base at Smolensk lay Victor's corps, about 30,000.
Division of the nucleolus by elongation, construction, and equilateral division of the nucleus.
Inside an equilateral triangle, for instance, of height h, - 2Ra/3y/h, (8) where a, 13, y are the perpendiculars on the sides of the triangle.
The following method, depending on the constancy of the sum of the perpendiculars from any point on to the sides of an equilateral triangle, can be adopted: - Let ABC (fig.
8) be an equilateral triangle, the angular points corresponding to the three pure metals A, B, C. C Then the composition of any alloy can be FIG.
The isothermals are approximately equilateral hyperbolas (pv= constant), with the axes of p and v for asymptotes, for a gas or unsaturated vapour, but coincide with the isopiestics for a saturated vapour in presence of its liquid.
In crystallography the icosahedron is a possible form, but it has not been observed; it is closely simulated by a combination of the octahedron and pentagonal dodecahedron, which has twenty triangular faces, but only eight are equilateral, the remaining twelve being isosceles (see Crystallography).
These problems were also attacked by the Arabian mathematicians; Tobit ben Korra (836-901) is credited with a solution, while Abul Gud solved it by means of a parabola and an equilateral hyperbola.
Warren type in which the bracing bars form equilateral triangles, the Whipple Murphy in which the struts are vertical and the ties inclined, and the lattice in which both struts and ties are inclined at equal angles, usually 45° with the horizontal.
Dimyarian, with orbicular and almost equilateral shell; adherent; hinge without teeth Sand ligament internal.
Unicardiidae.-Shell sub-orbicular, nearly equilateral, with concentric striae.
The regular octahedron has for its faces equilateral triangles; it is the reciprocal of the cube.
Octahedra having triangular faces other than equilateral occur as crystal forms. See Polyhedron and Crystallography.
Incidentally Pappus describes the thirteen other polyhedra bounded by equilateral and equiangular but not similar polygons, discovered by Archimedes, and finds, by a method recalling that of Archimedes, the surface and volume of a sphere.
32 was first proved in a general way by the Pythagoreans; but, on the other hand, we learn from Geminus that the ancient geometers observed the equality to two right angles in each kind of triangle - in the equilateral first, then in the isosceles, and lastly in the scalene (Apoll.
The theorem, then, seems to have been arrived at by induction, and may have been suggested by the contemplation of floors or walls covered with tiles of the form of equilateral triangles, or squares, or hexagons.
P the octahedron faces; the latter are particularly well defined and have the form =% of equilateral triangles (fig.
Nicaragua forms an irregular equilateral triangle with its base stretching for 280 m.