Pyramid - sweep. Development of the pyramid for gluing. Paper reamers

2024 Author: Sierra Becker | [email protected]. Last modified: 2024-02-26 03:46

Rectangle, square, triangle, trapezium and others - geometric shapes from the section of exact science. The pyramid is a polyhedron. The base of this figure is a polygon, and the side faces are triangles with a common vertex, or trapezoid. For a complete presentation and study of any geometric object, mock-ups are made. Use the most diverse material from which the pyramid is made. The surface of a polyhedral figure, developed on a plane, is called its development. The method of converting flat objects into volumetric polyhedra and certain knowledge from geometry will help to create a layout. It is not easy to make reamers from paper or cardboard. You will need the ability to make drawings according to given dimensions.

Materials and fixtures

Modeling and execution of multifaceted three-dimensional geometric shapes is an interesting and exciting process. From paper, you can make a large number of various layouts. For work you will need:

• paper orcardboard;
• scissors;
• pencil;
• ruler;
• compass;
• eraser;
• glue.

Define parameters

First of all, let's define what the pyramid will be. The development of this figure is the basis for the manufacture of a three-dimensional figure. Doing the job will require extreme precision. If the drawing is incorrect, it will be impossible to assemble a geometric figure. Suppose you need to make a layout of a regular triangular pyramid.

Any geometric body has certain properties. This figure has a regular polygon base, and its vertex is projected into its center. An equilateral triangle is chosen as the base. This condition determines the name. The side edges of the pyramid are triangles, the number of which depends on the polyhedron chosen for the base. In this case, there will be three. It is also important to know the dimensions of all the constituent parts of which the pyramid will be composed. Paper sweeps are performed in accordance with all data of a geometric figure. The parameters of the future model are negotiated in advance. The choice of material used depends on these data.

How is a regular pyramid unfolded?

The basis of the model is a sheet of paper or cardboard. Work begins with a pyramid drawing. The figure is shown expanded. A flat image on paper corresponds to pre-selected dimensions and parameters. A regular pyramid has a regular polygon as its base, and its height passes through its center. Let's start with a simple model. In this caseis a triangular pyramid. Determine the dimensions of the selected shape.

To build a net of a pyramid, the base of which is a regular triangle, in the center of the sheet, using a ruler and a pencil, draw the base of the given dimensions. Next, to each of its sides, we draw the side faces of the pyramid - triangles. Now let's move on to building them. The dimensions of the sides of the triangles of the lateral surface are measured with a compass. We put the leg of the compass at the top of the drawn base and make a notch. We repeat the action, moving to the next point of the triangle. The intersection resulting from such actions will determine the vertices of the side faces of the pyramid. We connect them to the base. We get a drawing of a pyramid. For gluing the three-dimensional figure, valves are provided on the sides of the side faces. Finishing small trapezoids.

Build layout

Cut out the completed pattern along the contour with scissors. Gently bend the scan along all lines. We fill the trapezoid valves inside the figure so that its faces close. Lubricate them with glue. After thirty minutes, the glue will dry. Volumetric figure is ready.

Sweep of a quadrangular pyramid

First, let's imagine what a geometric figure looks like, the layout of which we will make. The base of the chosen pyramid is a quadrilateral. Lateral ribs - triangles. For work, we use the same materials and fixtures as in the previous version. The drawing is done on paper with a pencil. In the center of the sheet we draw a quadrangle with the selectedparameters.

Divide each side of the base in half. We draw a perpendicular, which will be the height of the triangular face. With a compass solution equal to the length of the side face of the pyramid, we make notches on the perpendiculars, setting its leg to the top of the base. We connect both corners of one side of the base with the resulting point on the perpendicular. As a result, we get a square in the center of the drawing, on the faces of which triangles are drawn. To fix the model on the side faces, draw auxiliary valves. For reliable fastening, a centimeter-wide strip is enough. The pyramid is ready for assembly.

Final stage of layout execution

Cut out the resulting pattern of the figure along the contour. Bend the paper along the drawn lines. The volumetric figure is collected by gluing. Lubricate the provided valves with glue and fix the resulting model.

3D layouts of complex shapes

After completing a simple polyhedron model, you can move on to more complex geometric shapes. The development of a truncated pyramid is much more difficult to perform. Its bases are similar polyhedra. The side faces are trapezoids. The sequence of work will be the same as that in which a simple pyramid was made. The sweep will be more cumbersome. To complete the drawing, use a pencil, a compass and a ruler.

Building a drawing

The truncated pyramid is unfolded in several stages. Side facea truncated pyramid is a trapezoid, and the bases are similar polyhedra. Let's say they are squares. On a sheet of paper, we draw a trapezoid with the given dimensions. We extend the sides of the resulting figure to the intersection. The result is an isosceles triangle. We measure its side with a compass. On a separate sheet of paper we build a circle, the radius of which will be the measured distance.

The next step is to build the side edges that the truncated pyramid has. The sweep is performed inside the drawn circle. The lower base of the trapezoid is measured with a compass. On the circle we mark five points that connect the lines with its center. We get four isosceles triangles. With a compass we measure the side of the trapezoid drawn on a separate sheet. This distance is set aside on each side of the drawn triangles. We connect the obtained points. The side faces of the trapezoid are ready. It remains only to draw the upper and lower bases of the pyramid. In this case, these are similar polyhedra - squares. Draw squares to the upper and lower bases of the first trapezoid. The drawing shows all the parts that the pyramid has. The sweep is almost ready. It remains only to finish the connecting valves on the sides of the smaller square and one of the faces of the trapezoid.

End simulation

Before gluing the three-dimensional figure, the drawing along the contour is cut out with scissors. Next, the scan is carefully bent along the drawn lines. Mounting valves are filled inside the model. Lubricate them with glue andpressed to the edges of the pyramid. Let the model dry.

Making different models of polyhedrons

Performing three-dimensional models of geometric shapes is an exciting experience. To master it thoroughly, you should start by performing the simplest scans. Gradually moving from simple crafts to more complex models, you can start creating the most intricate designs.