In the study of mathematical geometry, we have learned the law that figures remain unchanged in motion. Graphic movements include translation, rotation, expansion and folding. After moving, the shape and area of the figure remain unchanged, only the position of the figure has changed.
Graphic transformation includes: cutting and filling transformation, (light changes the shape of the graphic, but the area remains the same) stretching transformation …
In the second volume of the sixth grade math book, there is a chapter about the movement of graphics.
How did this diagram 1 get to Figure 2? Figure 1 is the translated Figure 2. First, Figure A of Figure 1 moves three squares to the left, and then moves three squares down. Graph a in fig. 2 is obtained.
Figure B in figure 1 moves three squares to the right first, and then moves three squares down to get Figure B in Figure 2.
Translate Figure C in Figure 1 by three squares to the left, and then by three squares to the upward, and you will get Figure C in Figure 2.
Translate Figure D in Figure 1 by three squares to the left, and then by three squares to the upward to get Figure D in Figure 2.
If you want to find the four corners (shaded areas) in Figure 2, you can directly multiply the square area with brackets and subtract 78.5 percent of brackets (just draw the largest circle in a square, and the circle accounts for 78.5 percent of the square). This is the quickest way. If you want to find the irregular figures in the four sectors in the figure 1, you must change them into regular figures by moving them, and then find the number by the above method.
This problem can also be rotated. Firstly, the figures A, B, C and D in figure 1 are regarded as a small square with a side length of "3", and then the center of the small square is found. All four small squares are rotated clockwise 180 degrees. At this time, Figure A in Figure 1 is the same as Figure D in Figure 2.
Figure b is like figure c, figure c is like figure b, and figure d is like figure a.
If the difficulty of Figure 1 is increased, it is:
Obviously, the shaded part in this picture is the overlapping part of four semicircles with a radius of three, or it can be said that it is the overlapping part of eight circles with a radius of three. If you need this irregular number, you can convert it into:
The first problem, first add up the triangles by completion method to become a right-angled trapezoid. Take the area of the right trapezoid and subtract the area of the triangle to get the shadow area.
Cut them into three right triangles and a rectangle. As long as the area of a rectangle is equal to 10×60, the area of a right triangle on the left is equal to 20x30÷2, and the areas of two right triangles are equal, we can make a rectangle, that is, 30x20. The column synthesis formula is10× 60+20x30 ÷ 2+30x20 =1500. There are many solutions to this problem, so I won't list them one by one.
The second problem, the first solution: cut
The second solution: cutting
The third solution: cutting
The fourth solution: cutting
The fifth solution: supplement
The sixth type: cutting
There are many ways to solve this problem by truncation, but the calculated results are all the same.
This is the advantage of the movement and transformation of graphics, which can solve many problems in one problem and turn a complex graphic into a learned one through geometric changes.