Greenwood press

144
TRANSLATIONS
The translation (slide) of a triangle by 6 right
and 2 down, 
(x, y) + (6,-2) = (x
′
, y
′
).
Coordinate system in chess.

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Coordinate notation indicates the starting square for the piece and the ending
square. The white knight can move B1-C3. This represents the translation, or
move, of the knight. Chess players keep track of games and communicate with
distant players using this coordinate system or the similar algebraic system.
When you sing “Frere Jacques” or “Row, Row, Row My Boat” with other
people, it is likely that you separate into groups. When the first group finishes the
line “Row, row, row my boat, gently down the stream,” the second group will
start singing. When it finishes the first line, the third group will start. Meanwhile,
the first two groups continue singing. Songs that are melodious when the start is
shifted by line are called rounds. The shift is a translation in time.
Shifts in musical keys are called transpositions. Shown below is a four-note
theme from a Mozart symphony in C major transposed down to G major. Each
note has been shifted six piano notes down.
Translations have been used to build patterns in painting, architecture, weav-
ing, and ceramics from ancient Greeks to medieval Celts to contemporary Acoma
Pueblo potters in New Mexico. The basic ribbon pattern is based on repeated
translations of a simple design (see the left figure below). Another design is
based on translating the basic figure, then reflecting it. This is called a glide
reflection (right figure, below). Translations, rotations, and reflections of “seed”
patterns are fundamental in designing quilt patterns.
The simple translation of a simple seed figure, as in the left illustration, is the
basis of periodic functions. A seed, such as the two nodes of the sine function
from 0° to 360° can be translated in 360° moves to create the full periodic func-
tion of the sine. (See Periodic Functions.)
online sources for further exploration
Art

Music

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