Can quadrilaterals be flatly inlayed? 10

1.Of course, the four corners of the square are 360 degrees, and it is a circumference angle.

2. Isn't a rectangle just a rectangle? A parallelogram of the same size will also work. As long as it's a quadrilateral, it's fine, because the sum of their four corners adds up to the circumferential corners.

3. Yes. 4 Such as: floor tiles, ceilings.

5.Squares can be flat inlayed. Because the four corners are all right angles, exactly one circumferential angle, 6

Rectangles, parallelograms are also OK. It is also because the sum of the four corners is a circumferential angle 7Generally, quadrilaterals are also available.

The sum of the four interior angles of any one quadrilateral is 360 degrees, 8Can you find examples of these mosaics in life?

A common example in life is the paving of floor tiles.

9.Yes, the corners of 4 squares can form a circumferential angle.

10.Similarly.

11.Similarly.

12.Floor tiles.

1.Squares can be flat inlayed. Because the four corners are all right angles, exactly one circumferential angle, 2Rectangles, parallelograms are also OK. It is also because the sum of the four corners is a circumferential angle.

3.Generally, quadrilaterals are also available. The sum of the four interior angles of any quadrilateral is 360 degrees, 4Can you find examples of these mosaics in life?

A common example in life is the paving of floor tiles.

1.Yes, the corners of 4 squares can form a circumferential angle.

2.Similarly. 3.Similarly.

3.Floor tiles.

Any congruent convex quadrilateral can be inlaid because the sum of the inner angles of the quadrilateral is 360 degrees

As long as it is congruent, it can be inlaid.

Anything that is divisible by 360 is fine.

n-2)*180/nx=360

n is the number of sides of the polygonal Qichang shape, x is the number of high keys to be laid on this polygon, if x is not the number of positive bright points, it cannot be inlaid.

regular triangles and 2 regular quadrilaterals and 1 regular hexagon.

regular quadrilaterals and 1 regular hexagon and 1 regular dodecagon.

3.Regular triangles and regular quadrilaterals and regular dodecagons.

P.S. Although regular triangles, regular quadrilaterals and regular dodecagons can be inlaid in a plane, not all vertices are composed of these three figures.

Although 2 regular pentagons and 1 regular quadrilateral can form a 360-degree sum of the inner angles at the same vertex of the same bishop, they can only form a circle, and the periphery can no longer be carried out, and there will be overlapping phenomena, so the plane mosaic cannot be carried out.

Although regular quadrilaterals and regular pentagons and regular icolaterals can form 360 degrees at the same vertex, they cannot be planarly mosaic.

Another: make a graphic inlay with a separate hand:

Any triangle, any quadrilateral, regular triangle.

Regular quadrilateral: regular hexagon.

Two regular polygon settings.

3 regular triangles and 2 squares.

2 regular triangles and 2 regular hexagons or 4 regular triangles and 1 regular hexagon, 1 regular triangle and 2 regular dodecagons.

1 regular quadrilateral and 2 regular octagons.

Pentagons can't, hexagons can.

In order to make a regular polygon be inlaid with a flat phase, the inner angle of each regular polygon must be a 360° divisor, and only the regular triangle ascending thick, square, and regular hexagon can be.

Since the inner angle of the regular pentagon is (5-2) 180° 5=108°, that is, 360° 108=3.36 (can't).

There are three types of the same shape, only regular triangles, squares and regular hexagons can be mosaic, and other regular polygons cannot be mosaic.

The first disturbance part of the first division of the plane with several types of congruent shapes without gaps and without overlapping is called these types of figures that can mosaic, cover, and pave the plane. A key ephemer point of the mosaic is that at each common vertex, the sum of the corners is 360 degrees, and the simplest mosaic is to use only one type of congruent mosaic plane.

Three are missing angles, parallelograms, and regular hexagons can be inlaid with lead (densely paved) separately.

All other polygons need to be matched with appropriate triangles or other polygons.

The principle is that the sum of all corners of the seam is only 360°, that is, the position of Huai is missing.

1. The mosaic method is: splicing one or several plane figures with the same shape and size, leaving no gaps and overlapping between each other, which is the inlay of plane figures, that is, dense paving.

2. Dense paving is to use several shapes and sizes of the same shape and size of the figure to remove hail and non-overlap to lay a plane, so that the sum of the corners at the splicing point is 360 degrees.

3. Single polygon dense paving: 6 arbitrary triangles, 4 quadrilaterals, and 3 regular hexagons can be densely paved.

4. The condition of a single regular polygon dense paving: if 360 degrees divided by a regular polygon is equal to an integer, it can be used alone for dense paving.

Summary. Hello, dear, I am happy to answer for you: how to draw the plane mosaic of the general hexagon, hello, here is the query for you:

Draw the regular hexagon in the middle, and draw the six squares on the six sides of the regular hexagon, you can get a regular dodecagon, and there are still 6 regular triangles missing.

Dear, hello, I am happy to answer for you: how to draw a hexagonal plane mosaic like a peel Dear, hello, the spring difference here for you to inquire is the circle only: the regular hexagon is drawn in the middle, six squares are drawn on the six sides of the regular hexagon, you can get the composition of the regular dodecagon, and there is still a lack of 6 regular triangles.

Plane Mosaic: Basic Concept Use several types of congruent shapes (figures that can completely coincide are called pat wax to do congruence) to cover a part of the plane without gaps and without overlapping, which is called these types of figures can mosaic (cover, pave) the plane One of the key points of inlay is: at each common vertex, the sum of the corners is 360° The simplest inlay is to use only one type of congruent inlay plane The following is a brief introduction to the plane inlay problem from three aspects

Hexagon: Hexagon, a type of polygon, refers to all the eggplant polygons with six sides and six corners. According to the regular polygon inner angle and the formula s=180°· (n-2), the sum of the inner angles of all regular hexagons is 720°, and the sum of the outer angles is 360° In nature, the molecular structure, turtle shell, and honeycomb of benzene and graphite are all in a regular hexagonal shape.

Plane mosaic 1, with the same shape, size of one or several plane figures for splicing, between each other without leaving a gap, do not overlap a piece, this is the plane figure of the dense paving, also known as the plane figure of the mosaic.

2. Lay the floor with the same regular polygon. For a given regular polygon, can it be put together into a flat shape without leaving a little gap? Obviously, the key is to analyze the characteristics of the interior corners of a regular polygon that can be used for complete ground leveling.

When the inner angles of several polygons put together around a point together form a circumference of 360°, a flat shape is formed. In fact, each inner angle of a regular n-sided is (n-2)180 n, which requires k regular n-sides to have an inner angle in one point to cover the ground, so that 360°=k(n-2)180 n, and k is a positive integer.

So n can only be 3, 4, 6Therefore, use the same regular polygon floor tiles.

Paved floor, only regular triangles.

Regular quadrilateral: regular hexagon.

The floor tiles can be used. We know that the sum of the internal angles of any quadrilateral is equal to 360°Therefore, a batch of quadrangular tiles of the exact same shape and size, but irregular, can also be used to create a floor without voids.

Can you cover the ground with any identical triangle? Please spell it out.

3. We know that we use two or more regular polygonal parquet flooring. Some identical regular polygons are able to cover the ground, while others are not. In fact, we also see quite a few flat patterns that combine two or more regular polygons with equal side lengths.

There are several cases listed in the textbook. Why do these regular polygon combinations cover the ground densely? The question is essentially a question of whether the sum of the corners of the junction can be put together to form the perimeter angles of the relevant regular polygon.

The number of sides that can be inlaid in a plane is less than 7 sides. For many years, the search for special pentagons for plane mosaics has been a dream of many mathematicians.

Let the angles add up to 360°. Speaking of which, let's go back and see why any congruent triangle or quadrilateral can be inlaid in a plane. Figure 1 is a plane mosaic of congruent arbitrary triangles, and a closer look shows that this figure is a parallelogram made up of triangles.

Translation. We call it a feature polygon. Figure 2 is the characteristic polygon of the plane mosaic of a congruent arbitrary quadrilateral.

It was found that the corresponding edges of these feature polygons were parallel. In other words, if we can properly divide the feature polygons, we can get polygons that can be inlaid planely.

As shown in Figure 3, the regular hexagon is a feature polygon that can be inlaid in a plane, and it can be divided into three equal parts as shown in Fig. As shown in Figure 4, it is a feature polygon that can be inlaid in a plane, and it can be divided into four equal parts as shown in Fig. This is San Diego.

The women of Marjorie? Rice.

Found in 1977.

If it is allowed to have a group of figures with parallel sides that can be inlaid on a plane, there are too many, and the carpenter master puts this wood together one by one into a large plank.