You will need
- a compass, ruler, pencil.
The methods of constructing a regular hexagon based on the following well-known statements. About any regular polygon can be circumscribed by a circle. Side of a regular hexagon equals the radius of its circumcircle.
Method the first. To construct a regular hexagon given one side a, you must use a compass to draw a circle with center at point O and a radius R equal to the a side. From the center of the circle at the point On the guide beam to any point lying on the circle. At the intersection of a circle and beam you get some point A. With a compass from point A with a radius R equal to the side and make circles notch and get the point V. From the points In the solution of the compass equal to the radius R=a, do the following notch and get the point C. Doing likewise on the circumference of successive notches of radius R is equal to a specified party and you will receive a total of six points - A, B, C, D, E, F, which will be the vertices of the hexagon. Connecting them with a ruler, get a regular hexagon with sides equal to.
The second way. Through some point And guide the cut KB so that KA=AB=a. In the interval BK, is equal to 2A as diameter construct a semicircle with center at a and radius equal to. This semi-circle divide into six equal parts. Get points C, D, E, F, G. the Center And connect the rays with all the points except the last two points K and G. From the point with radius AB draw a arc, making a notch on the ray AC. Get the point L. From point L to the same radius draw a arc, making a notch on the beam AD. Get the point M. in the Same way carry out the arc and make the notches for the other points. The points B, L, M, N, F, A sequentially connect the straight lines. Get ABLMNF – regular hexagon with sides equal to.