About "0"

0 can be said to be the earliest number that humans have come into contact with. Our ancestors only knew nothing and something at first, and the nothing among them is 0. So, does 0 mean nothing? I remember my teacher in elementary school once said, "Any number minus itself is equal to 0, and 0 means there is no quantity." This is obviously incorrect. We all know that 0 degrees Celsius on the thermometer represents the freezing point of water (that is, the temperature of the ice-water mixture under one standard atmospheric pressure), and 0 is the point of distinction between the solid and liquid states of water. Moreover, in Chinese characters, 0 as zero means more meanings, such as: 1) Fragmentary; small number. 2) A quantity that is not enough for a certain unit... At this point, we know that "no quantity is 0, but 0 not only means no quantity, but also means the distinction between solid and liquid water, etc."

"Any "A number divided by 0 is meaningless." This is a "conclusive conclusion" about 0 that teachers from elementary school to middle school still say. The division method at that time (in elementary school) was to divide one part into several parts and find out how many parts there are. A whole cannot be divided into 0 parts, that is, it is "meaningless". Later I learned that the 0 in a/0 can represent a variable with zero as the limit (the absolute value of a variable is always less than any small determined positive number during the change process), which should be equal to infinity (the absolute value of a variable during the change process Its absolute value is always greater than any large definite positive number). Another theorem about 0 is obtained from it: "A variable with zero as its limit is called infinitesimal." On a floor or wall paved with ceramic tiles, adjacent floor tiles or ceramic tiles fit together smoothly, leaving no gaps on the entire floor or wall.

For example, triangle. A triangle is a plane figure composed of three line segments that are not on the same straight line and are connected in sequence. Through experiments and research, we know that the sum of the interior angles of a triangle is 180 degrees and the sum of the exterior angles is 360 degrees. The ground can be covered with 6 equilateral triangles.

Looking at the regular quadrilateral again, it can be divided into 2 triangles. The sum of the interior angles is 360 degrees, the measure of an interior angle is 90 degrees, and the sum of the exterior angles is 360 degrees. The ground can be covered with 4 regular quadrilaterals.

What about the regular pentagon? It can be divided into 3 triangles, the sum of the interior angles is 540 degrees, the measure of an interior angle is 108 degrees, and the sum of the exterior angles is 360 degrees. It cannot cover the ground.

A hexagon can be divided into 4 triangles. The sum of the interior angles is 720 degrees, the measure of an interior angle is 120 degrees, and the sum of the exterior angles is 360 degrees. The ground can be covered with 3 regular quadrilaterals.

A heptagon can be divided into 5 triangles. The sum of the interior angles is 900 degrees, the measure of an interior angle is 900/7 degrees, and the sum of the exterior angles is 360 degrees. It cannot cover the ground.

From this, we conclude. An n-sided polygon can be divided into (n-2) triangles. The sum of the interior angles is (n-2)*180 degrees. The measure of an interior angle is (n-2)*180÷2 degrees. The sum of the exterior angles is 360 degrees. If (n-2)*180÷2 can be divided into 360, then it can be used to cover the ground. If not, it cannot be used to cover the ground.

Not only can we cover the ground with one kind of regular polygon, we can also cover the ground with a combination of two, three, and more shapes.

For example: equilateral triangle and square, equilateral triangle and hexagon, square and octagon, pentagon and octagon, equilateral triangle, square and hexagon...

< p>In real life, we have seen various patterns made of regular polygons. In fact, many patterns are often made of irregular basic graphics.