In plane geometry, a regular hexagon has six equal sides and six equal internal anglespolygon。The internal angles are equal, and the six sides are equal.From the sum of the external angles of the polygon equal to 360 degrees, aInternal angle180 - (360/6)=120 degrees, so each internal angle is 120 degrees.
Because it is a regular hexagon, the regular hexagon can be divided into six congruent ones in the centerEquilateral triangle, make correctionsHeight of triangle, usingPythagorean theoremThe height can be calculated as √ 3 * a/2, eachArea of triangleBoth are (√ 3 × a ²)/2/2, so the area of a regular hexagon is (3/2) × √ 3a ² (where a is the side length) (as shown in Figure 1).
Figure 1 Area formula of regular hexagon
Drawing with ruler and gauge
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Drawing with ruler and gauge[1]
Method 1: Make a circle with radius asLength unit(The radius is the side length of the regular hexagon), divide the circle, and connect theEquinox, that is, the regular hexagon sought.
Method 2:
Draw a line AB with any length.With A as the center and AB as the radius, make circle A.With B as the center and AB as the radius, make circle B and circle A intersect at point C.Connect AC, BC.triangleABC isEquilateral triangle。Take on ABTrisection pointM。Take points N and O respectively on AC and BC to make CN=AM=OB.Make MX parallel to BC and cross AC to point X.Make NY parallel to BA and intersect BC at point Y.Make OZ parallel to AC and intersect AB to point Z.
Then NYOZMX is a regular hexagon.
Method 3:
snowflake
Draw a circle and make a diameter.Draw a circle with the two ends of the diameter as the center and the radius of the circle as the radius respectively, and make four intersections. Connect the four points and the two ends of the diameter in order.Area: point O in the middle of the regular hexagon, and make any side of the regular hexagon through OverticalThen multiply the length of this side by the length of the vertical line to get the number. Divide the number by 2 and then multiply by 6.
Common Graphics
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Snow crystal
Snow crystalThe hexagonal shape of can be divided into two categories, one is sheet shape, the other is column shape.The more beautiful snowflakes that are often seen are those hexagonal symmetrical flake snow crystals.They usuallyCelsiusThe columnar snowflakes are formed between minus 5 ℃ and minus 20 ℃. The columnar snowflakes include needle shaped and hollow columnar snowflakes. The needle shaped snowflakes are formed at temperatures between minus 0 ℃ and minus 5 ℃, and the hollow columnar snowflakes are formed at temperatures below minus 20 ℃.
If you want to find out why most ice crystals are hexagonal prisms, you should first understandwaterMolecules.Water molecule is composed of twohydrogen atomAnd aOxygen atom(This is why we often call water H ₂ O)——covalent bond, glued together.
When liquid water molecules are cooled tofreezing pointWater molecules will collide with each other to form solid ice crystals, and then they will use hydrogen bonds to bond together.If molecules combine with each other, they will be more stable.Relatively speaking, the most stable arrangement is to stick six water molecules together in a hexagonal shape, which is why most ice crystals are hexagonal.
hive
hive
Honeycomb structure of bees is very exquisite, applicable and material saving.The beehive is composed of innumerable holes of the same size, all of which are regular hexagons. Each hole is surrounded by other holes. There is only a wax wall between the two holes.Surprisingly, the bottom of the hole is neither flat nor round, but pointed.The bottom is composed of three identical diamonds.Someone has measured the angle of the diamond, twoObtuse angleBoth are 109 ° and both acute angles are 70 °.What is amazing is that all honeybee honeycombs in the world are built according to this unified angle and pattern.
