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The square–cube law was first mentioned in Two New Sciences (1638). The square–cube law (or cube–square law) is a mathematical principle, applied in a variety of scientific fields, which describes the relationship between the volume and the surface area as a shape's size increases or decreases.
square meter (m 2) differential element of volume V enclosed by surface S: cubic meter (m 3) electric field: newton per coulomb (N⋅C −1), or equivalently, volt per meter (V⋅m −1) energy: joule (J) Young's modulus: pascal (Pa) or newton per square meter (N/m 2) eccentricity
cubic foot of atmosphere; standard cubic foot: cu ft atm; scf ≡ 1 atm × 1 ft 3 = 2.869 204 480 9344 × 10 3 J: cubic foot of natural gas: ≡ 1000 BTU IT = 1.055 055 852 62 × 10 6 J: cubic yard of atmosphere; standard cubic yard: cu yd atm; scy ≡ 1 atm × 1 yd 3 = 77.468 520 985 2288 × 10 3 J: electronvolt: eV ≡ e × 1 V ≡ 1.602 176 ...
Cube, a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex Cubic crystal system, a crystal system where the unit cell is in the shape of a cube; Cubic function, a polynomial function of degree three; Cubic equation, a polynomial equation (reducible to ax 3 + bx 2 + cx + d = 0)
Sometimes the term "unit cube" refers in specific to the set [0, 1] n of all n-tuples of numbers in the interval [0, 1]. [1] The length of the longest diagonal of a unit hypercube of n dimensions is , the square root of n and the (Euclidean) length of the vector (1,1,1,....1,1) in n-dimensional space. [2]
As this is a cube, the top and bottom surfaces are identical in shape and area, and the pressure difference between the top and bottom of the cube is directly proportional to the depth difference, and the resultant force difference is exactly equal to the weight of the fluid that would occupy the volume of the cube in its absence.
A cubic equation with real coefficients can be solved geometrically using compass, straightedge, and an angle trisector if and only if it has three real roots. [30]: Thm. 1 A cubic equation can be solved by compass-and-straightedge construction (without trisector) if and only if it has a rational root.
The IEEE symbol for the cubic foot per second is ft 3 /s. [1] The following other abbreviations are also sometimes used: ft 3 /sec; cu ft/s; cfs or CFS; cusec; second-feet; The flow or discharge of rivers, i.e., the volume of water passing a location per unit of time, is commonly expressed in units of cubic feet per second or cubic metres per second.