Sofia dropped her purse on the desk in her cube without removing her sunglasses.
That amount, if melted, would form a cube fifty-five feet on each side.
She popped one water cube but replaced the sugary cube with some hesitation.
This points to the conclusion that substitution has been effected in one of the cube faces.
She pushed herself up, reaching into a pocket for a food and water cube. Gabriel took her arm and pulled her to her feet. She nearly choked on the cubes and swallowed them whole, struggling to keep up with the death-dealer as he darted into the forest.
The power required to circulate the air through a mine increases as the cube of the velocity of the air current.
Projecting from the upper platform at the centre of the chord of the semicircular area is a cube of rock, ii ft.
When a z and the invariants B and C all vanish, either A or j must vanish; in the former case j is a perfect cube, its Hessian vanishing, and further f contains j as a factor; in the latter case, if p x, ax be the linear factors of i, f can be expressed as (pa) 5 f =cip2+c2ay; if both A and j vanish i also vanishes identically, and so also does f.
The curve also permits the solution of the problems of duplicating a cube and trisecting an angle.
It became known as the "Delian problem" or the "problem of the duplication of the cube," and ranks in historical importance with the problems of "trisecting an angle" and "squaring the circle."
For this purpose four vertical mirrors are arranged round the vertical sides of a cube which is rapidly revolved about a vertical axis.
End of the temple is the fountain Glauce cut out of a cube of rock, apparently left standing when the material for the temple was quarried around it.
Yet it appears to be only an approximate relation, and therefore probably accidental, as the volume by the examples is too large to agree to the cube of the length or to the weight, differing 1/20, or sometimes even as 1/12.
The crystals are feebly doubly refracting, and in polarized light exhibit a banded structure parallel to the cube faces.
He has only one symbol (written somewhat like a final sigma) for an unknown quantity, which he calls apc0µ6s (defined as "an undefined number of units"); the symbol may be a contraction of the initial letters ap, as A Y, K Y, D Y O, &c., are for the powers of the unknown (Suvaµcs, square; icu(30s, cube; Svva,uo& va i ccs, fourth power, &c.).
In general his object is to reduce the final equation to a simple one by making such an assumption for the side of the square or cube to which the expression in x is to be equal as will make the necessary number of coefficients vanish.
He evolved an ingenious solution of the duplication of the cube, which shows considerable knowledge of the generation of cylinders and cones.
Zeit., 1905, 29, p. 30), assumed the six carbon atoms to occupy six of the corners of a cube, each carbon atom being linked to a hydrogen atom and by single bonds to two neighbouring carbon atoms, the remaining valencies being directed to the unoccupied corners of the cube, three to each, where they are supposed to satisfy each other.
If we denote the critical volume, pressure and temperature by Vk, Pk and Tk, then it may be shown, either by considering the characteristic equation as a perfect cube in v or by using the relations that dp/dv=o, d 2 p/dv 2 =o at the critical point, that Vk = 3b, Pk= a/27b2, T ic = 8a/27b.
Among the contents of this book we simply mention a trigonometrical chapter, in which the words sinus versus arcus occur, the approximate extraction of cube roots shown more at large than in the Liber abaci, and a very curious problem, which nobody would search for in a geometrical work, viz.
Van 't Hoff's formula is equivalent to taking the frequency of dissociation as proportional to the square of the concentration of the molecules, and the frequency of recombination as proportional to the cube of the concentration of the ions.
The discriminant of f is equal to the discriminant of 0, and is therefore (0, 0') 2 = R; if it vanishes both f and 0 have two roots equal, 0 is a rational factor of f and Q is a perfect cube; the cube root being equal, to a numerical factor pres, to the square root of A.
(22) It will be seen that, whereas the couple varies inversely as the cube of the distance, the force varies inversely as the fourth power.
When P is the neutral point, H is equal and opposite to R; therefore M = Hd 3, or the moment is numerically equal to the cube of the distance from the neutral point to a pole, multiplied by the M.
In the preface to this work, which is dedicated to one Dionysius, Diophantus explains his notation, naming the square, cube and fourth powers, dynamis, cubus, dynamodinimus, and so on, according to the sum in the indices.
Others occur in the Metrica where also a method of finding such approximate square, and even approximate cube, roots is shown.
Apart from modifications in the details of sugar refining which have come into use in late years, it should be mentioned that loaf sugar made in conical moulds, and sugars made otherwise, to resemble loaf sugar, have practically disappeared from the trade, having been replaced by cube sugar, which is found to be more economical as subject to less waste by grocers and housekeepers, and also less troublesome to buy and sell.
Although bismuth is readily obtained in fine crystals by artificial means, yet natural crystals are rare and usually indistinct: they belong to the rhombohedral system and a cube-like rhombohedron with interfacial angles of 92° 20' is the predominating form.
There is a perfect cleavage perpendicular to the trigonal axis of the crystals: the fact that only two (opposite) corners of the cube-like crystals can be truncated by cleavage at once distinguishes them from true cubes.
(If the molecules of air at normal temperature and pressure were arranged in cubical order, the edge of each cube would be about 2.9 X I o - ' cms.; the average diameter of a molecule in air is 2.8X Io - 8 cms.) Further and very important evidence as to the nature of the gaseous state of matter is provided by the experiments of Joule and Kelvin.