[计] 幻方, 魔方, 纵横图

[ noun ]
a square matrix of n rows and columns; the first n^2 integers are arranged in the cells of the matrix in such a way that the sum of any row or column or diagonal is the same
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Magic \Mag"ic\, Magical \Mag"ic*al\, a. [L. magicus, Gr. ?, fr.
?: cf. F. magique. See {Magi}.]
1. Pertaining to the hidden wisdom supposed to be possessed
by the Magi; relating to the occult powers of nature, and
the producing of effects by their agency.

2. Performed by, or proceeding from, occult and superhuman
agencies; done by, or seemingly done by, enchantment or
sorcery; as, a magical spell. Hence: Seemingly requiring
more than human power; imposing or startling in
performance; producing effects which seem supernatural or
very extraordinary; having extraordinary properties; as, a
magic lantern; a magic square or circle.

The painter's magic skill. --Cowper.

Note: Although with certain words magic is used more than
magical, -- as, magic circle, magic square, magic wand,
-- we may in general say magic or magical; as, a magic
or magical effect; a magic or magical influence, etc.
But when the adjective is predicative, magical, and not
magic, is used; as, the effect was magical.

{Magic circle}, a series of concentric circles containing the
numbers 12 to 75 in eight radii, and having somewhat
similar properties to the magic square.

{Magic humming bird} (Zo["o]l.), a Mexican humming bird
({Iache magica}), having white downy thing tufts.

{Magic lantern}. See {Lantern}.

{Magic square}, numbers so disposed in parallel and equal
rows in the form of a square, that each row, taken
vertically, horizontally, or diagonally, shall give the
same sum, the same product, or an harmonical series,
according as the numbers taken are in arithmetical,
geometrical, or harmonical progression.

{Magic wand}, a wand used by a magician in performing feats
of magic.


Square \Square\ (skw[^a]r), n. [OF. esquarre, esquierre, F.
['e]querre a carpenter's square (cf. It. squadra), fr.
(assumed) LL. exquadrare to make square; L. ex + quadrus a
square, fr. quattuor four. See {Four}, and cf. {Quadrant},
{Squad}, {Squire} a square.]
1. (Geom.)
(a) The corner, or angle, of a figure. [Obs.]
(b) A parallelogram having four equal sides and four right
angles.

2. Hence, anything which is square, or nearly so; as:
(a) A square piece or fragment.

He bolted his food down his capacious throat in
squares of three inches. --Sir W.
Scott.
(b) A pane of glass.
(c) (Print.) A certain number of lines, forming a portion
of a column, nearly square; -- used chiefly in
reckoning the prices of advertisements in newspapers.
(d) (Carp.) One hundred superficial feet.

3. An area of four sides, generally with houses on each side;
sometimes, a solid block of houses; also, an open place or
area for public use, as at the meeting or intersection of
two or more streets.

The statue of Alexander VII. stands in the large
square of the town. --Addison.

4. (Mech. & Joinery) An instrument having at least one right
angle and two or more straight edges, used to lay out or
test square work. It is of several forms, as the T square,
the carpenter's square, the try-square., etc.

5. Hence, a pattern or rule. [Obs.]

6. (Arith. & Alg.) The product of a number or quantity
multiplied by itself; thus, 64 is the square of 8, for 8
[times] 8 = 64; the square of a + b is a^{2} + 2ab +
b^{2}.

7. Exact proportion; justness of workmanship and conduct;
regularity; rule. [Obs.]

They of Galatia [were] much more out of square.
--Hooker.

I have not kept my square. --Shak.

8. (Mil.) A body of troops formed in a square, esp. one
formed to resist a charge of cavalry; a squadron. ``The
brave squares of war.'' --Shak.

9. Fig.: The relation of harmony, or exact agreement;
equality; level.

We live not on the square with such as these.
--Dryden.

10. (Astrol.) The position of planets distant ninety degrees
from each other; a quadrate. [Obs.]

11. The act of squaring, or quarreling; a quarrel. [R.]

12. The front of a woman's dress over the bosom, usually
worked or embroidered. [Obs.] --Shak.

{fair and square} in a fair, straightforward, and honest
manner; justly; as, he beat me fair and square.

{Geometrical square}. See {Quadrat}, n., 2.

{Hollow square} (Mil.), a formation of troops in the shape of
a square, each side consisting of four or five ranks, and
the colors, officers, horses, etc., occupying the middle.


{Least square}, {Magic square}, etc. See under {Least},
{Magic}, etc.

{On the square}, or {Upon the square},
(a) in an open, fair manner; honestly, or upon honor;
justly. [Obs or Colloq.]
(b) at right angles.

{On the square with}, or {Upon the square with}, upon
equality with; even with. --Nares.

{To be all squares}, to be all settled. [Colloq.] --Dickens.

{To be at square}, to be in a state of quarreling. [Obs.]
--Nares.

{To break no squares}, to give no offense; to make no
difference. [Obs.]

{To break squares}, to depart from an accustomed order.
[Obs.]

{To see how the squares go}, to see how the game proceeds; --
a phrase taken from the game of chess, the chessboard
being formed with squares. [Obs.] --L'Estrange.