# Advice 1: How to divide a circle into 7 equal parts

The division of circles into equal parts is very convenient for constructing various regular polygons. The construction can be performed without a protractor, using only a compass and straightedge.
You will need
• Pencil, ruler, pair of compasses, a sheet of paper
Instruction
1
A circle can be divided into 7 equal parts using only a compass and straightedge. To do this, select the point where will be the center of your circle. Mark it as point O.
2
Draw with your compass a circle of the desired diameter with the center at point O.
3
With a ruler and pencil, draw a diameter line passing through the center of the circle. Designate as A and B the two points at which the diameter intersects the circumference.
4
From point A, draw an arc inside the circle. The radius of the arc should be equal to the radius of the circle. The arc must intersect the circle at two points.
5
Mark the points where the arc intersects the circle as C and C1.
6
With a ruler connect the points C and C1 segment.
7
The point at which the segment between points C and C1 intersects the diameter AB of the circle, mark the point D.
8
With the help of a compass put the distance between points C and D on a circle 7 times. To do this, place the tip of a compass at a random location on the circumference, for example at the point A. Mark drawing part one of the compass anywhere on the circle. Place the tip of a compass at the marked point and similarly mark the next point. Mark in this way the whole circumference.
9
Connect with a ruler and pencil all the marked points on the circle with its center at the point O.

# Advice 2: How to divide a circle

The division of a circle into equal parts is usually used to build regular polygons. In principle, it is possible to divide a circle into pieces with a protractor, but sometimes it is inconvenient and inaccurate.
Instruction
1
To divide a circle into three equal parts, spread the compass to the radius of the circle. Then set the needle of the compass on one of the axial lines and build the auxiliary circle. Three equal parts are indicated by the points of intersection of auxiliary and main circles and a point lying at the opposite end of the centerline.
2
To divide the circumference into six parts, then do the same for the other axis. Then get six points on the circle.
3
The division of the circle into four parts - trivial task. Four points on the intersection of two perpendicular axial and circumference of a circle will divide the circumference into four equal parts. To divide a circle into 8 parts, it is necessary to divide an arc corresponding to 1/4 of the circumference in half. Then breed a pair of compasses to the distance marked in red in the figure, and delay is the distance from the already obtained four points.
4
To divide a circle into five equal parts, first divide the radius on centerline in half. At this point install the needle of the compass, and stylus take before crossing perpendicular to this axis and radius of the circle. In the figure this distance is shown in red. Delay is the distance on the circumference, starting from the axis, and then shifting the compass to the resulting intersection.
Repeat all these actions mirror to break up a circle into 10 equal parts.

# Advice 3: What is the circumference of the earth

The circumference of the earth is identified based on the longest parallel is the equator. However, recent measurements of this parameter show that the common view of it is not always true.
The question, what is the value of the circumference of the planet Earth, has interested scientists for a very long time. Thus, the first measurement of this parameter was carried out in Ancient Greece.

## Measurement of the circumference

That our planet is a sphere, scientists engaged in research in the field of Geology, has been known for a long time. Therefore, the first measurement of the circumference of the earth's surface was concerned with the longest parallel of the Earth's equator. This value is believed by scientists, can be considered correct for any other way of measuring. For example, it was believed that if you measure the planet's circumference on the longest Meridian, the resulting figure will be exactly the same.

This opinion existed until the eighteenth century. However, scientists of the leading scientific institutions of the time - the French Academy - was of the opinion that this hypothesis is false, and the form that is the planet, not quite right. Therefore, according to them, the circumference of a circle the longest Meridian and the longest parallel will vary.

The proof in 1735 and 1736 was made two scientific expeditions, which proved the validity of this assumption. Later it was found and the magnitude of the difference between the two lengths - it amounted to 21.4 kilometer.

## The circumference

Currently, the circumference of the planet Earth repeatedly measured not by extrapolation the length of each segment of the earth's surface to its full value, as has been done before, and with the use of modern high-precision technology. This made it possible to establish an exact circumference for the longest Meridian and the longest parallel, and specify the value of the difference between these parameters.

So, today in the scientific community as the official values of the circumference of planet Earth at the equator, that is the longest parallel, decided to produce a figure equal to 40075,70 kilometers. While a similar parameter, measured through the longest Meridian, that is, the length of the circle passing through the earth's poles, is 40008,55 kilometers.

Thus, the difference between the lengths of the circles is 67,15 km, and the equator is the longest circle our planet. In addition, this difference means that one degree of geographical Meridian is somewhat shorter than one degree of geographic Parallels.
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