"Dense paving" is a way of paving plane graphics, which refers to splicing one or more plane graphics with the same shape and size into one piece, leaving no gaps or overlapping.
The two conditions of dense shops can be explained from the following aspects:
Condition 1: consistency
The first condition of dense shop is that the graphics used must be completely coincident. This means that every figure used in the secret shop, whether in shape or size, must be the same. Only in this way can we ensure that there will be no gaps between graphics when stitching.
Condition 2: There is no gap in splicing.
In addition to the consistency of graphics, another condition of dense paving is that there can be no gaps between graphics after splicing. This requires that all kinds of graphics used in the dense shop should be closely attached without leaving gaps.
In order to better understand these two conditions, we can give an example. Suppose we use regular hexagons for dense paving. A regular hexagon is a graph that can completely overlap, so it satisfies condition one. At the same time, when we use multiple regular hexagons for dense pavement, there will be no gap between them, which satisfies the second condition. So a regular hexagon is a kind of figure that can be closely arranged.
However, if we try to use squares for dense paving, we may find that there will be gaps between them, because the four corners of the square are not completely matched. Therefore, the square does not meet the requirements of dense shops.
Dense shop is not only a decorative art, but also a mathematical concept. Understanding the two conditions of decryption can help us better appreciate and create dense patterns, and at the same time cultivate our mathematical thinking and spatial perception ability.
To sum up, the two conditions of dense paving are: the graphics used must be completely coincident (that is, congruent), and there can be no gaps between the graphics after splicing. Only graphics that meet these two conditions can be densely laid. Closing the store, the perfect combination of art and mathematics, two conditions, create unlimited possibilities.