Advice 1: How can an equilateral octagons

In our time, an enormous widespread ancient Chinese art of Feng Shui, which considers man and his surrounding world as an integrated whole. Feng Shui tries to harmonize all spheres of human activity, using this magic figure - regular octagon Bagua. Let's try to draw it.
How can an equilateral octagons
You will need
  • - notebook sheet in a cage;
  • - the range;
  • pencil or pen;
  • a pair of compasses.
Instruction
1
Take the notebook sheet in a cage, in the center of the sheet, draw horizontal and vertical lines at an angle of 90 degrees to each other (we call them conditional axis). On a notebook sheet of vertical and horizontal lines that form the cells, just drawn at an angle of 90 degrees. So it is very convenient to draw the axis in the cells.
2
Next, draw a circle of arbitrary radius, whose center is the point of intersection of the coordinate axes. Get the circle divided into four parts. Now every quarter of a circle, divide in half. To do this, from the center of the circle (the point of intersection of the axes of coordinates), draw the rays. They should be located at an angle of 45 degrees relative to any adjacent axes.
3
The angle of 45 degrees is easy to build and without a protractor. This will depart from the center of the circle is equal to the number of cells both horizontally and vertically. Neatly on squares draw lines parallel to the axes. We obtain a square. Now connect the point of intersection of the coordinate axes, with the opposite vertex of the square. The resulting diagonal extend to the intersection with the circle. Repeat this operation with other parts of the circle.
4
In the end you'll have a circle that is intersected by eight rays. Connect the intersection points of rays and circle together. Regular octagon ready.
An octagon with a compass
5
If you have no compass – no problem. The algorithm of construction of the octagon will change slightly. To do this, after the creation of the conditional axes, draw the rays, separating in half, obtained four areas of the coordinate system, using the above in step 3 recommendations. From the point of intersection of the axes with a ruler mark on each of the resulting eight beams lines the same length. Connect in a circle the ends of the lines with a ruler - get a regular octagon.
The octagon on the line

Advice 2: How to draw a circle without a compass

Well, when there is a standard set for drawing – ruler, pencil, compass, protractor, various triangles, by which you can draw on paper any geometric shape. However, if there is nothing suitable, and in this case it is possible to get out of the situation is enough to apply simple techniques that will help to implement the plan drawing.
How to draw a circle without a compass
You will need
  • paper;
  • pencil;
  • the thread or rope;
  • items round shape;
  • - a needle, a nail, a peg.
Instruction
1
The easiest way to get a circle of any diameter is to use items circle theLOI form, which is usually enough. For the circleand the average diameter of suitable kitchen utensils – assorted plates, cups, discs, glasses and even pots. If you have a swivel chair, it is possible to use and its just enough to turn and circle on the paper. If the diameter required is less, as the basis of use of glasses, coins of various denominations, bottles.
2
If the shape of the right big size, here, not even a compass, and therefore it is necessary to make an improvised device. This makes it possible to draw a circle of any diameter, for example, for flower beds. Take a pointed peg and tie him to the rope. Insert the peg in the center of the alleged circle. If the figure on the pavement, we need the help of another person, which will hold the peg in the center. Measure the rope or a strong thread (you can on the wire) to the desired length (the radius). Tie in that place a new peg or a piece of chalk. Now holding it in her hand and slightly pulling the rope go round, leaving on the ground or pavement mark.
3
The same can be done on paper. To do this, take a needle, attach it to the thread and keep this fixture in the center of the circleand with one hand. Measure a length of thread, tie to the second end of a pencil or pen and lead in the round. Get the required geometric shape.
4
We can proceed a little differently. Take a sheet of paper and fold it along the length a few times to get a semblance of a line. Apply marks, which correspond to the radius of the circle. Take another sheet of paper and fold in half, then in half. Repeat this one more time. When you perform these steps, please note that the rolled paper in the form of a cone, that is, the type of fold paper for cutting snowflakes.
5
A long narrow cone put in front of him and make a mark. To do this, start an impromptu line align with the sharp part of the folded paper. This will be the center of the future figure. Measure with a ruler the radius of the circleand first one side of the cone, and then the other. Now perform the same action throughout the segment, which resembles a piece of cake. Obtained the points that mark as close as possible to each other, connect. Get a line in the form of an arc. Cut along the outline and unfold the paper, which will take the form of a circle. Prepared samples can circle on a clean sheet.
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