Seventeen square calligraphy works can be arranged in the following three ways with the least amount of lace.
(1) First, make a rectangle in three rows and five columns, or three columns and five rows, and arrange two works adjacent to each other.
(2) First, make a square according to 4 rows and 4 columns, and arrange a work adjacent to it.
(3) First, make a rectangle by three rows and six columns, or six columns and three rows, in which one work needs to be arranged less.
The circumference of the three arrangements is 36 decimeters, and the number of colored stripes used is the least.
In practical application, the corresponding arrangement mode can be selected according to the calculation results and aesthetic principles.
Analysis:
17 is a prime number. You can use adjacent composite numbers 15, 16 or 18 to find the factor, and then add and subtract to get 17, and get the arrangement of the works. According to the perimeter formula of the rectangle, the corresponding perimeter is obtained, and the perimeter = (length+width) * 2.
（1）3*5＋2＝17； First, make a rectangle in three rows and five columns, or three columns and five rows, and arrange two works nearby. The convex figure needs to be added with the length of the protruding side.
The length of the rectangle is 5 * 2 = 1, the width is 3 * 2 = 6, the circumference is 32, and the total circumference is 36 when the two adjacent sides are added;
（2）4*4＋1＝17； First, make a square according to four rows and four columns, and arrange one work adjacent to it.
the circumference of the square is 8 * 4 = 32, plus the two sides of the adjacent one, the total circumference is 36;
（3）2*8＋1＝17； First, put together a rectangle in two rows and eight columns, or eight columns and two rows, and arrange a work adjacent to it.
The length of the rectangle is 8 * 2 = 16, the width is 2 * 2 = 4, and the circumference is 4. Together with the two sides adjacent to one frame, the total circumference is 44.
（4）2*9－1＝17； First, make a rectangle by two rows and nine columns, or nine columns and two rows, in which one work needs to be arranged less. However, the concave figure formed by one less work is equal to the circumference of the rectangle.
The rectangle is 9 * 2 = 18 in length, 2 * 2 = 4 in width and 44 in circumference;
（5）3*6－1＝17； First, make a rectangle by three rows and six columns, or six columns and three rows, in which one work needs to be arranged less. However, the concave figure formed by one less work is equal to the circumference of the rectangle.
The rectangle is 6 * 2 = 12 in length, 3 * 2 = 6 in width and 36 in circumference;
to sum up, the arrangement in three ways (1), (2) and (5) has a circumference of 36 decimeters, with the least number of colored stripes used. According to the calculation, the corresponding arrangement mode can be selected according to the aesthetic principle.
Extended data:
Arrange 17 works, because 17 is a prime number, you can use adjacent composite numbers 15, 16 or 18 to find the factor, and then add or subtract 1 or 2 to get 17. Using the obtained factor as the length and width of the rectangle, the perimeter is calculated according to the rectangle perimeter formula. Among them, the convex figure needs to be added with the protruding side length; The circumference of the concave figure is the same as that of the rectangle. The following five situations can be obtained:
(1) 3 * 5+2 = 17;
First, make a rectangle in three rows and five columns, or three rows and five rows, and arrange two works adjacent to each other. Total circumference 36;
（2）4*4＋1＝17；
First, make a square according to 4 rows and 4 columns, and arrange one work next to it. Total circumference 36;
（3）2*8＋1＝17；
First, make a rectangle by two rows and eight columns, or eight columns and two rows, and arrange one work adjacent to it. Total circumference 44;
（4）2*9－1＝17；
First, make a rectangle by two rows and nine columns, or nine columns and two rows, in which one work needs to be arranged less. The circumference is 44;
（5）3*6－1＝17；
First, make a rectangle by three rows and six columns, or six columns and three rows, in which one work needs to be arranged less. The circumference is 36;
compare the perimeters of five cases, among which (1), (2) and (5) have perimeters of 36 decimeters, and the required colored stripes are the least.
it can be found that when the length and width of a rectangle are close, its circumference is relatively small.
In practical application, the corresponding arrangement mode can be selected according to the calculation results and aesthetic principles, so that the arrangement is relatively beautiful.