The geometrical moiré patterns which are formed by superposing two figures of dots arranged on intersections of triangle fretworks have been investigated by using a personal computer. When a moving angle between the two figures is small, the appearing patterns have a hexagonal form. In particular, when two figures of dots arranged on intersections of regular triangle fretwork are superposed at the moving angle (θ) chosen at m
1=1, and n
1=3, 9, 15, ...... (a multiple of three in an odd-number) according to the equation, tan (θ/2)=m
1l2/n
1l1, the hexagons in the moiré patterns at each n
1 consist of all the same shape, where n
1 and m
1 are the abscissa and the ordinate of dot lines,
l1 is the dot pitch of the abscissa, and
l2 is the dot of the ordinate (double the high of triangle-dots). The appearance period of moiré patterns based on moving angle is 60° in the regular triangle-dot arrangement system, and is 180° in the equilateral triangle-dot arrangement system. Since the moiré patterns are very regularly constructed, the working technique will have a bright prospect of developing the new field of various printing patterns for cloths, papers and so forth.
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