The form of a five-pointed star is everywhere used by the person since ancient times. We consider its form fine as unconsciously we distinguish in it ratios of golden ratio, i.e. beauty of a five-pointed star is proved mathematically. The first Euclid at ""Beginnings"" described creation of a five-pointed star. Let's join its experience.

## It is required to you

- ruler;
- pencil;
- compasses;

## Instruction

1. Creation of a five-pointed star comes down to creation of the correct pentagon with the subsequent connection of its tops with each other consistently through one. To construct the correct pentagon it is necessary to break a circle into five equal parts. Construct any circle by means of compasses. Designate its center by point O.Otmette on a circle a point of A and by means of a ruler draw OA piece. Now it is necessary to halve OA piece, for this purpose from a point And carry out an arch by OA radius before crossing it with a circle in two points of M and N. Construct MN piece. The point E in which MN crosses OA will halve OA piece. Restore OD perpendicular to the radius of OA and connect a point of D and E. Make B notch on diameter of OA of a point E radius of ED.

2. Now by means of a piece of DB mark a circle on five equal parts. Designate tops of the correct pentagon consistently by figures from 1 to 5. Connect points in the following sequence: 1 with 3, 2 with 4, 3 with 5, 4 with 1, 5 with 2. Here also the correct five-pointed star entered in the correct pentagon is ready. In such a way Euclid built a five-pointed star about 2300 years ago.

3. At the time of Euclid there were no protractors therefore it was necessary to resort to it, rather difficult way of construction. If you have a protractor, you can cope with creation of a five-pointed star quicker. Draw a circle and carry out symmetry axes through its center. Put a protractor parallel to one of axes of symmetry and measure 72 degrees from a point A crossings of other axis of symmetry with a circle. Designate the turned-out point by letter B. Put a compasses edge in a point And, and a slate pencil in B point. Received long divide a circle into five equal parts. Connect the received points the same as in the first way.