| 释义 |
dimensional, a.|dɪˈmɛnʃənəl|
[f. dimension n. + -al1.]
1. Of or pertaining to dimension or magnitude.
1816Keatinge Trav. (1817) I. 66 note, About the same relative situation and dimensional proportion. 1888J. T. Gulick in Linn. Soc. Jrnl. XX. 234 If structural or dimensional characters are not correlated.
2. Geom. Of or relating to (a specified number of) dimensions: see dimension 3 a.
1875Cayley in Phil. Trans. CLXV. 675 Coordinates of point in (s + 1)-dimensional space. 1880Academy 30 Oct. 314 Four-dimensional space may be built up with..ikosatetrahedroids. 1882Minchin Unipl. Kinemat. 116 The general, or three dimensional, motion of a rigid body. 1883American VII. 75 We can, I think, conceive of space as being two or even one dimensional.
3. a. Of, pertaining to, or involving dimensions of units or physical quantities.
1888Proc. Physical Soc. X. 49 Prof. S. P. Thompson considered part of the difficulties of dimensional equations arose from the fact that no distinction was made between scalar and vector quantities. 1914Physical Rev. 2nd Ser. IV. 369 The application of dimensional reasoning to mechanical problems is often useful in the interpretation of model experiments. 1964H. S. Hvistendahl Engin. Units i. 10 The reason for the apparent ambiguity of the dimensions in such cases, is that our dimensional formulae do not distinguish the relative directions of the lengths combining as some power of L in those formulae.
b. dimensional analysis, a method of mathematical analysis in which physical quantities are expressed in terms of their dimensions (i.e. length, mass, time, etc.) so that conclusions may be drawn regarding their mutual relations; it is based on the fact that quantities added to or equated with each other must have the same dimensions.
1922P. W. Bridgman Dimensional Analysis ii. 17 The purpose of dimensional analysis is to give certain information about the relations which hold between the measurable quantities associated with various phenomena. 1949O. G. Sutton Sci. of Flight iii. 68 In analysing complex physical phenomena.., mathematicians..employ a dissection process known as dimensional analysis. 1957Encycl. Brit. VI. 387/2 The principal use of dimensional analysis is to deduce from a study of the dimensions of the variables in any physical system certain necessary limitations on the form of any possible relationship between those variables. 1958J. S. Scott Dict. Civ. Engin. 105 Dimensional analysis, in the model analysis of rivers, ships, ports..and other structures involving the flow of fluids, the use of dynamic similarity to enable the experimenter to see quickly what is the relationship between different variables.
Hence dimensioˈnality, the condition of having (a particular number of) dimensions; dimensional quality.
1875Cayley in Phil. Trans. CLXV. 675 The notion of density is dependent on the dimensionality of the element of volume d ω. 1884E. A. Abbott Flatland ii. xxii. 101 A race of rebels who shall refuse to be confined to limited Dimensionality. |