You will need

- A sheet of paper, pencil, ruler, compass, eraser.

Instruction

1

The simple

**spiral**in the drawing can be obtained by moving the centers of the semicircle from one center of the spiral to another. The part is simple to construct and has equal step increase of the radius of the coils. To build label on a sheet of paper or the drawing the center of the spiral O.2

Through the center of the spiral, draw a horizontal straight line. Its length on each side from the centre must be greater than or equal to the maximum radius of the spiral.

3

Note on the direct point at a distance from the center O, which is equal to the minimum radius of the spiral. This is the second center of the spiral, which needed for its construction. Denote it as O1.

4

From the center O of the spiral guide compass arc, which is a half circle. Arc starts from the circle center O1, and the ends through 180 degrees, the company built a horizontal straight line. The radius of the arc equal to the minimum radius of the spiral.

5

Set the compass size, equal to two minimum radii of the spiral, and set his leg with the sharp tip of the second center of the spiral - O1. Draw a arc that starts at the point which ended the first arc, and the ends, reaching the horizontal line on the opposite side of the center of the spiral O.

6

Similarly do the third and subsequent necessary steps of building a spiral. The radius of the semicircle to the third step should be equal to the minimum radius of the spiral loop, multiplied by 3. The radius of the arc for the next steps is equal to the number of construction steps, which multiplied by the minimum radius of the spiral loop.

# Advice 2: How to build a spiral of Archimedes

**The spiral**

**of Archimedes**build to convey the trajectory of a point which moves uniformly gradual radius a rotating uniformly round. The trajectory of a point can make a clearer drawing of some mechanisms or the movement of objects on the diagram.

You will need

- - a sheet of paper;
- - gon;
- pencil;
- a pair of compasses;
- - pattern;
- - eraser;
- calculator.

Instruction

1

Mark on the drawing point which is the center of the spiral

**of Archimedes**. Mark the centre of the letter O.2

Build from the center of the spiral, the circle whose radius is equal to the pitch of the helix. The pitch of the spiral

**of Archimedes**equal to the distance travelled by the point on the surface of the circle for one complete revolution.3

In descriptive geometry, the spiral

**of Archimedes**relates to a radial curve. It is constructed using curves connecting the points on the circle. To get construction points, divide the circle into several equal parts with straight lines. For example, 8.4

Number for the convenience of straight lines, dividing the circumference in the direction of rotation of the circle.

5

Divide the radius of the constructed circle to the number to which the divided circle using straight lines. With the help of a compass or ruler, divide the last in the numbering straight on the value of the marks. You only need to divide the interval between the center of the circle O and the point of intersection of a straight circle.

6

Number the marks, starting with the closest to the center of the circle. You can use numbers or letters in alphabetical order.

7

Using the compass, draw an arc of a circle center O. Arc starts from a straight line, which separated the marks and is conducted to a straight line under the number 1. Label the point where the arc is connected to the line 1 of figure 1. Similarly, construct the following arc from the marked straight line to straight at number 2. Designate a point of connection with figure 2, and then mark that point on all straight separates the circle.

8

Using the patterns, connect the center circle with the first point. Then connect the first point with the second and so connect all the marked points. You will get the first turn of the spiral

**of Archimedes**. Try to connect the dots as evenly as possible. To get the spiral**of Archimedes,**higher accuracy, divide the circle into a greater number of equal parts and construct the corresponding number of arcs.