Refers to the patchwork of different graphics without overlap and omission, and it is paved in the middle of a piece of ground without gap and overlap, that is, dense paving.
The roads on both sides of the street are often paved with bricks with geometric patterns. The shape of floor tiles is usually square and rectangular. We have also seen regular hexagonal floor tiles. Whether it is a square, rectangular or hexagonal floor tile, the middle of a floor can be paved without gaps or overlaps. This is called dense paving.
As we all know, when paving the floor, the floor should be covered, and there should be no gaps between the floor tiles. If the floor tile used is square, and each corner of it is a right angle, then four squares are put together, and the four corners of the common vertex just spell a 36-degree fillet. Every corner of a regular hexagon is 120 degrees.
When three regular hexagons are put together, the sum of the three angles on the common vertex is exactly 36O degrees. Besides squares and rectangles, regular triangles can also be densely laid on the ground. Because every internal angle of a regular triangle is 60 degrees, when six regular triangles are put together, the sum of the degrees of the six angles at the vertices of the common triangle is exactly 36 degrees.
It is precisely because the sum of several angles on the vertices of a square and a regular hexagon is exactly 36 degrees that the ground can be paved densely and beautifully.
1. Regular triangles and squares can be densely laid, with each vertex.
three
Sum of a regular triangle
2
A square.
2. Regular triangles and regular hexagons can also be densely placed, with each vertex.
2
Sum of a regular triangle
2
Regular hexagon.
3. Square and regular octagon can also be densely laid, with each vertex.
1
Square sum
2
Regular octagon.
The shape of floor tiles is often square and rectangular, and we have also seen regular hexagonal floor tiles. Whether it is a square, rectangular or hexagonal floor tile, the middle of a piece of ground can be paved without gaps or overlaps, that is, densely paved. What other shapes of graphics can be densely laid on the ground? When students think about this problem, they always experiment with the help of the pictures they draw and draw conclusions through actual observation.
This knowledge is theoretically analyzed and solved, that is, the brain sheath is 60 degrees.
Jia's Phlegm and Money is not well trained. He told Na Wei to take the lead in benzene infringement. Every corner of a regular hexagon is 120 degrees.
When three regular hexagons are put together, the sum of the three angles on the common vertex is exactly 36O degrees. Besides squares and rectangles, regular triangles can also be densely laid on the ground. Because every internal angle of a regular triangle is 60 degrees, when six regular triangles are put together, the sum of the degrees of the six angles at the vertices of the common triangle is exactly 36 degrees.
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