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.
Advice 2: How to draw a hexagon
Image of geometric shapes are used to create many games, collages, illustrations. Using the tools of photoshop, you can draw any three-dimensional shape, including, and hexagon.
You will need
- Adobe Photoshop
Open a new document. On the toolbar, select the Polygon Tool. On the property bar, set sides=6 and any color to suit your taste. Hold down the Shift key, draw a hexagon. Hover over a shape, click the right mouse button and click Rasterize Layer.
Double-copy this layer (Ctrl+J) so you've got three of the hexagon. Stand on a new layer. Hold down Ctrl, click the icon with the image of a new figure to get selection. On the Toolbox, set the foreground color a darker shade. Using the Paint Bucket tool fill the hexagon. Again, go to new layer and fill the shape with a suitable shade. Thus, your hexagons are painted in different shades of one color.
Using the Move tool to position the hexagons as shown in the figure. In this case, consider where in your picture will be located light source. There, where the light needs to be brighter face. The dark face in the shadows.
For layers with the hexagons, which represent the side faces, set the Opacity=50%. On the toolbar, choose the Eraser Tool. Set hardness=100% and begin carefully erasing the excess image. In order to remove the unwanted color is near the edge, you should do the following: reduce the diameter of the gum, in order not to capture extra. Move the cursor one end of edges of the hexagonand click the left mouse button. Then move the cursor to the other end, press the Shift key and again click the left key. You get a flat empty strip. Repeat this procedure as many times as it takes to remove the unwanted background around the figure.
For layers with side return Opacity=100%.
When selecting colors for faces consider the location of the light source to your image
Advice 3: How to draw a hexagon
At the time, drawing a regular hexagon was described by the ancient Greek Euclid. To date, however, there are other ways of constructing this geometric shape. The main principle to follow when drawing the figures of some well-known rules.
You will need
- - a sheet of paper;
- a pair of compasses;
- - the range.
Note that the main rules for sketching a hexagon are the following statement: around any polygon of the correct form is possible to describe a circle, and that side of the hexagon correct form is equal to the radius of the circle described around it.
To construct a regular hexagon, provided a given side take a compass and draw a circle. The center of the circle is point O and radius R will be equal to the a side. Guide a ray from the point O to any point that lies on the circle. You get the point And that is where intersects the circle and the line.
Take a compass and making a centre in the point A, draw a tick on the circle. The radius will be equal to side A. At the intersection of the point B. Then, making a center point In, again mark the notch with the same radius. Name the point of the section S. in This way, making consistently ticks you end up with only six points. They will be the future of the vertices of the hexagon. Connect them with a line, and you have a regular hexagon given one side.
There is another way of building this shape. Mark the point A and through it, draw the cut KB. In this case KA=AB=a (i.e. the side of the hexagon). Further on the segment BK, which is equal to 2A, construct a semicircle. Its center must be at point A and let the radius equals the side of the hexagon.
A semicircle, divide into 6 parts. They should be equal. What are the points which turned out C, D, E, F, G. the center point And the rays connect each point except the last two, K and G. draw a arc of radius AB from a point In and make a notch on the segment AC. Put a point L. this point again carry out the arc with the same radius, we get a notch on the segment AD. Similarly, let's move on. Plotting points connect the lines sequentially, taking advantage of the ruler. In the end, you get a regular hexagon.