You will need

- pencil;
- - square or ruler;
- a pair of compasses;
- - protractor.

Instruction

1

The construction of the ellipse in the isometric begins with the definition of the position of its minor and major axes which intersect in the center. Therefore, first determine the position of the center of the circle on the right plane isometric projection. Mark the center of the circle point O.

2

Draw the minor axis of the oval. The minor axis is parallel to the missing in-plane axis isometric projection and passes through the center of the circle O. for Example, in the plane ZY minor axis parallel to the axis X.

3

With the straightedge or ruler with protractor build large axis of the oval. Is it perpendicular to the minor axis of the ellipse and intersects it in the center of the circle O.

4

Guide through the circumcenter O, the two lines parallel to the axes of the plane in which the projection is based.

5

With a compass mark on the small axis of the oval, and on the lines parallel to the axes of the projection at two points opposite from the center of the sides. The distance to each point on all lines is delayed from the center O equal the radius of the projected circle. All you should have 6 points.

6

Label on the small axis of the oval points A and B. Point A is closer to the origin plane than point B. the origin of the plane corresponds to the point of intersection of the axes isometric projection drawing.

7

Label the marked points on the lines parallel to the axes of the projection points C, D, E and F. the Points C and D must appear on the same line. Point C is closer to the origin of the axis of projection, which is parallel to the selected line. Similar rules are valid for the points E and F, which should be located on the second line.

8

Connect the points A and D, as well as point BC line segments, must intersect the large axis of the oval. If the resulting segments do not intersect the great axis, label the point E as point C, and point C as point E. Similarly, change the designation of the point F on D, and points D And F. connect the resulting points A and D, B and C segments.

9

Mark the points where line segments AD and BC intersect the large oval axis as G and H.

10

Set the compass radius equal to the length of the segment CG, and draw the arc between points C and F. the arc Center must be located at the point G. in a Similar way, draw the arc between points D and E.

11

From point A, draw an arc of radius equal to the length of the segment AD between points F and D. in a Similar way, draw the second arc between points C and E. the Construction of the ellipse in the first plane ready.

12

Repeat similarly the construction of the ovals for the rest of the planes isometric projection.

# Advice 2: How to draw in isometric

Construction of isometric projection of the part allows to obtain the most detailed view on the spatial characteristics of the object image. Isometric cutaway of the part in addition to appearance shows the internal structure of the subject.

You will need

- - a set of drawing pencils;
- - the range;
- - triangles;
- - protractor;
- a pair of compasses;
- eraser.

Instruction

1

The drawing in the

**isometric view**select a location depicted part or device, which will be visible all the time.2

After you select the location, decide what type of

**isometry**you will perform. There are two types of**isometry**: isometric rectangular and horizontal oblique isometric (or military perspective).3

*Draw axis thin lines so that the image is located in the center of the sheet. In a rectangular*

**isometric**angles between the axes are one hundred and twenty degrees. In a horizontal oblique

**isometric**angles between the X and Y axes are ninety degrees. And between X and Z; Y and Z one hundred and thirty-five degrees.

4

Begin performing isometric with the upper surface of the depicted items. From the corners of horizontal surfaces swipe down the vertical line and mark on these lines the corresponding linear dimensions from the detail drawing. In

**the isometric**linear dimensions on all three axes remain a multiple of the unit. Sequentially connect the points obtained on the vertical lines. The external contour of the part ready. Follow the images available on the faces of holes, grooves, etc.5

Remember that when drawing objects in

**isometric view**the appearance of curvilinear elements will be distorted. A circle in**isometric view**is depicted as an ellipse. The distance between the points of the ellipse on the axes**of isometries**is equal to the diameter of the circle, and the axes of the ellipse do not coincide with the axes of the**isometric view**.6

If the item has a hidden cavity or a complex internal structure, complete the isometric projection with the cutout of the part. The neckline can be simple or stepped depending on the complexity of the part.

7

All steps must be performed using the drawing tools — ruler, pencil, compass and protractor. Use multiple pencils of different hardness. Solid — thin lines, hard-soft — dotted and dash-dotted lines, soft — for main lines. Don't forget to draw and fill in the title block and frame in accordance with GOST. Design

**isometric**can be performed in specialized software such as Compass, AutoCAD.# Advice 3: How to draw an ellipse in isometric

**The ellipse**is an isometric projection of a circle. Oval build points and get on the patterns or curved lines. The easiest way to draw an ellipse in

**isometric**, inscribing a figure in a rhombus, otherwise isometric projection of a square.

You will need

- - the range;
- - gon;
- pencil;
- paper for sketching.

Instruction

1

Consider how to draw an ellipse in

**isometric view**, lying in a horizontal plane. Construct a perpendicular to the axis X and Y. the intersection of the mark O.2

From point O mark on the axes the segments is equal to the radius of the circle. Marked points indicate the numbers 1, 2, 3, 4. Through these points parallel to the guide axes of the straight.

3

From point O mark on the axes the segments is equal to the radius of the circle. Marked points indicate the numbers 1, 2, 3, 4. Through these points parallel to the guide axes of the straight.

4

Draw a arc from the vertex of obtuse angle of the connecting point 1 and 4. Similarly, connect the dots 2 and 3, having an arc from vertex D. Connect the points 1,2 and 3,4 of the centers of the small arcs. Thus constructed the ellipse in

**the isometric**inscribed in a rhombus.5

The second way to draw an ellipse in

**isometric**is to circle map distortion. Draw X and Y axis, from point O, draw two auxiliary circle. The diameter of the inner circle equals the minor axis of the ellipse, the major axis.6

In one quarter build auxiliary rays emanating from the center of the ellipse. The number of rays is arbitrary and the more, the more accurate the drawing. In our case it will be enough three auxiliary beams.

7

Will receive additional points of the ellipse. From the point of intersection of the beam with the smaller circle draw a horizontal line parallel to the X axis towards the outer circumference. From the top of the point lying at the intersection of the beam and of a large circle, drop a perpendicular.

8

The resulting point label figure 2. Repeat the operation for finding 3 and 4 points of the ellipse. Point 1 is located at the intersection of the Y-axis and the small circle, point 5 on the X-axis in place of the passage of the outer circumference.

9

Guide curve through these 5 points of the ellipse. At points 1 and 5 curve are strictly proportional to the axes. Spend a similar construction of an ellipse in

**isometric**on the remaining ¾ of the drawing.# Advice 4: How to build isometric projection

All objects of reality exist in three-dimensional space. In the drawings they have to portray in a two dimensional coordinate system, and it does not give the viewer an adequate understanding of how the object looks in reality. Therefore, technical drawing, apply the projection, allowing to transfer the amount. One of them is called isometric.

You will need

- paper;
- - drawing utensils.

Instruction

1

Construction of isometric projections start with the arrangement of the axles. One of them is always vertical, and in the drawings it is usually designated as the Z axis, the Initial point is denoted as O. we Continue the axis OZ down.

2

The remaining two axes can be defined in two ways, depending on what drawing tools you have. If you have a protractor, set aside from the axis OZ in both sides of the angles equal to 120º. Swipe X and y axes.

3

If you have only a compass, draw a circle of arbitrary radius with center at point O. let's Continue the axis OZ until its second intersection with the circle and a dot, for example, 1. Spread the legs of the compasses at a distance equal to the radius. Draw a arc with center at point 1. Mark the point of intersection with the circle. They also indicate the directions of the axes X and Y. the left side of the Z-axis moves the X axis to the right - Y.

4

*Construct an isometric*

**projection**of a plane figure. The coefficients of distortion in isometric along all axes are accepted 1. To construct a square of side a, put it away from point O of the axes X and Y and make the serifs. Swipe through the resulting points straight lines parallel to both these axes. Square in this projection looks like a parallelogram with angles of 120º and 60º.

5

*To build the triangle, it is necessary to continue the X-axis so that a new part of the beam is located between the axes Z m Y. Divide the side triangle in half and mark the resulting dimension from the point On the X-axis in both directions. On the Y-axis put the height of the triangle. Connect the ends of the segment located on the X-axis, with the resulting point on the y-axis.*

6

*In a similar way is constructed in an isometric projection and a trapezoid. On the X-axis in one and the other side of the point About set aside half of the base of this geometric figure, and the Y - axis height. Using the tick marks on the Y-axis guide line parallel to the X-axis, and mark on it in both directions half of the second founding. Connect the resulting points with ticks on the x-axis.*

7

*A circle in isometric view looks like an ellipse. It can be constructed as the coefficient of distortion, and without. In the first case, the large diameter is equal to the diameter of the circle, and the small amount of 0.58 from him. When you build without accounting for this factor axis of the ellipse will be equal to, respectively, 1.22 and 0.71 diameter of the original circle.*

8

Flat figures can be located in space both horizontally and vertically. As a basis we can take any axis, principles of construction remain the same as in the first case.

Useful advice

Dimensional object of complex shape, analyze and mentally divide it into more simple, is better every way to present a close to form geometric shapes. It may be necessary to postpone the dimensions are not on the axes, and parallel to them lines. The distance between these lines depend on the shape of the part. For example, one of the axes to postpone the distance from the edge to a recess or protrusion and draw a line parallel to the other two axes. Isometric projection of a fragment in this case is based not on the main grid, and additional.

# Advice 5: 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.

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.

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.

## 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.