Make a drawing of a quadrangular prism. Development of a straight prism

A prism is a three-dimensional figure, a polyhedron, of which there are many types: positive and irregular, straight and oblique. According to the figure lying at the base, the prism can be from triangular to polygonal. It’s easier for everyone to make a straight prism, but an inclined one requires a little more work.

You will need

• – compass;
• - ruler;
• - pencil;
• - scissors;
• - glue;
• – paper or cardboard.

Instructions

1. Draw the bases of the prism, in this case they will be 2 hexagons. To draw a regular hexagon, use a compass. Draw a circle with it, and using the same radius, divide the circle into six parts (for a regular hexagon, the sides are equal to the radius of the circumscribed circle). The resulting figure resembles a honeycomb cell. Draw an irregular hexagon at random, but with the help of a ruler.

2. Now start designing the “pattern”. The walls of the prism are parallelograms, and you need to draw them. In the straight model, the parallelogram would be a light rectangle. And its width will invariably be equal to the side of the hexagon lying at the base of the prism. With the correct figure at the base, all faces of the prism will be equal to each other. If it is incorrect, the entire side of the hexagon will correspond to only one parallelogram (one side face), suitable in size. At the same time, keep an eye on the sequence of edge sizes.

3. On a horizontal straight line, stepwise lay out 6 segments equal to the side of the base of the hexagon. From the obtained points, draw perpendicular lines of the required height. Connect the ends of the perpendiculars with a 2nd horizontal line. You now have 6 rectangles joined together.

4. Attach 2 previously constructed hexagons to the bottom and top sides of one of the rectangles. To any base if it is positive, and to the corresponding length if the hexagon is irregular. Outline the silhouette with a solid line and the fold lines inside the figure with a dotted line. You have obtained a development of the surface of a straight prism.

5. To create an inclined prism, leave the base the same. Draw a parallelogram side, which will be one of the faces. There should be six such faces, as you remember. In order to now draw the development of an inclined prism, it is necessary to arrange six parallelograms in the following order: three in ascending order, so that their oblique sides form one line, then three in descending order with the same condition. The steepness of the resulting line is directly proportional to the degree of inclination of the prism.

6. To the five rectangles in the development, draw small trapezoidal overlaps on the short sides to glue the figure, as well as on one free long side. Cut out the blank for the prism along with the overlaps and glue the model together.

A prism is a device that separates typical light into individual colors: scarlet, orange, yellow, green, blue, indigo, violet. It is a translucent object, with a flat surface that refracts light waves depending on their wavelengths and, as a result, allows light to be seen in different colors. Do prism easy enough on your own.

You will need

• Two sheets of paper
• Foil
• Cup
• CD
• Coffee table
• Flashlight
• Pin

Instructions

1. A prism can be made from a simple glass. Fill the glass a little more than half full with water. Place the glass on the edge of the coffee table so that about half of the bottom of the glass hangs in the air. At the same time, make sure that the glass is stable on the table.

2. Place two sheets of paper, one after another, next to the coffee table. Turn on the flashlight and shine rays of light through the glass so that it falls on the paper.

3. Adjust the position of the flashlight and paper until you see a rainbow on the sheets - this is how your beam of light is decomposed into spectra.

Video on the topic

The basic skill of an artist in academic drawing is the knowledge to depict on a plane the simplest volumetric geometric shapes - a cube, prism, cylinder, cone, pyramid and sphere. Having mastered this skill, you can build more complex, combined volumetric forms of architectural and other objects. A prism is a polyhedron whose two faces (bases) have identical shapes and are parallel to each other. The lateral faces of the prism are parallelograms. Depending on the number of side faces, prisms can be 3-, tetrahedral, etc.

You will need

• – drawing paper;
• – primitive pencils;
• – easel;
• – a prism or an object shaped like a prism (a wooden block, a box, a box, a part of a children’s construction set, etc.), preferably white.

Instructions

1. Erect prism allowed by inscribing it either in a parallelepiped or in a cylinder. The main difficulty when drawing a prism is the positive construction of the shape of the 2 faces of its base. When drawing a prism lying on one of the side faces, an additional difficulty appears in observing the laws of perspective, because in such an arrangement the perspective reduction of the side faces becomes noticeable.

2. When drawing a vertical prism, start by marking its central axis - a vertical line drawn in the middle of the sheet. On the axis line, mark the center of the top (visible) edge of the base and draw a horizontal line through this point. Determine the ratio of the height and width of the prism using the sighting method: look at nature, covering one eye, and, holding a pencil in an outstretched hand on the tier of the eyes, mark with your finger on the pencil the width of the prism visible from your point of view and mentally lay this distance along the line of the height of the prism a certain number times (as many times as possible).

3. Measuring the segments with a pencil closer to the drawing, mark the width and height of the prism with dots on the 2 previously drawn lines, observing the resulting ratio. Draw an ellipse around the center of the top edge. Try to accurately convey its imaginary form, looking at nature. Draw approximately the same ellipse (but less flattened) in the plane of the lower edge of the base of the prism. Combine the resulting ellipses with two vertical lines.

4. Now on the upper ellipse it is necessary to mark the segments of intersection of the side faces and its bases. Looking at nature, mark the points - the vertices of the polygon - lying at the base of the prism, as you see them, and unite them step by step. From these points, draw lines down to the intersection with the lower ellipse. Combine the resulting intersection points as well. During subsequent drawing, the edges visible from the selected point of view are erased or shaded, therefore, draw all auxiliary construction lines without pressure.

5. Lying on her side prism draw with the help of an auxiliary parallelepiped. Focusing on nature, draw a parallelepiped, observing the principles of perspective - the lines of the lateral edges, when mentally extended to the horizon line, which is invariably located on the tier of the viewer’s eyes, converge at one point. Consequently, the (noticeable) edge far from us will be slightly smaller than the front one. When determining the aspect ratio of a parallelepiped, use the “arm's length” (or sight) method.

6. On the front and back square faces, mark the vertices of the polygons lying at the base of the prism and construct them. Combine these points in pairs on 2 faces - draw the side edges of the prism. Remove unnecessary lines. Highlight the lines of edges and corners of the prism that are closest to you in bolder colors, and indicate the distant ones with light lines.

7. Looking at nature, determine the angle of incidence of light, the clearest, most shaded edges and, with the help of shading of varying intensity, convey these light relationships in the drawing. Draw a shadow falling from the object. Emphasize the contact line between the prism and the table with the darkest line. Please note that the light reflected from the table surface (reflex) falls on the most shaded face of the prism from below and slightly illuminates it. When applying shading to this face, take this result into account and apply a less saturated tone in the place of the reflex.

Video on the topic

A prism is a polyhedron formed by any final number of faces, two of which - the bases - must certainly be parallel. Any straight line drawn perpendicular to the bases contains a segment connecting them, called the height of the prism. If all the side faces are adjacent to both bases at an angle of 90°, the prism is called straight .

You will need

• Prism drawing, pencil, ruler.

Instructions

1. IN straight prism Every lateral edge is, by definition, perpendicular to the base. And the distance between the parallel planes of the side faces is identical at every point, including at those points where the side edge adjoins them. From these two circumstances it follows that the length of the edge of each lateral face straight the prism is equal to the height of this volumetric figure. This means that if you have a drawing that depicts such a polyhedron, it already contains segments (edges of the lateral faces), all of which can be designated as the height of the prism. If this is not prohibited by the conditions of the task, simply designate every lateral edge as a height, and the problem will be solved.

2. If you want to draw a height in the drawing that does not coincide with the side edges, draw a segment parallel to any of these edges connecting the bases. It is not always possible to do this “by eye”; therefore, build two auxiliary diagonals on the side faces - combine a pair of any angles on the top and a corresponding pair on the bottom base. After this, measure any comfortable distance on the upper diagonal and put a point - this will be the intersection of the height with the upper base. On the lower diagonal, measure exactly the same distance and place a second point - the intersection of the height with the lower base. Connect these points with a segment, and construct the height straight the prism will be completed.

3. A prism can be depicted taking into account perspective, that is, the lengths of identical edges of the figure can have different lengths in the drawing, the side faces can adjoin the bases at different and not strictly right angles, etc. In this case, in order to correctly maintain the proportions, proceed in the same way as described in the previous step, but place the points on the upper and lower diagonals correctly in their middles.

In detail - how to fold a sheet of paper and cut out a beautiful snowflake.

You will need

• A sheet of paper, I have an ordinary A4 sheet, it’s better to take huge napkins
• Scissors

Instructions

1. Fold the sheet in half crosswise

2. Now double it, just to find the middle

3. We wrap the edges of the paper folded in half, one by one - you can see it as in the photo

4. We make sure that the leaf bends evenly and the ends reach the folds.

5. Now we fold the resulting envelope in half. It is necessary to practice in order to ensure that the outer edge of the sheet reaches exactly to the fold.

6. While you don’t have the skill, it’s better to draw the approximate silhouette of a snowflake in advance.

7. Carefully cut out according to the silhouette.

8. We carefully unwrap it.

Note!
Remember that it is impossible to make a through cut; the snowflake will fall apart.

Helpful advice
The thinner the paper, the easier it is to cut out the snowflake. You can also make snowflakes from foil.

Note!
When developing an inclined prism, do not draw its edges at too great an angle; on the contrary, the model will be unstable.

A prism is a geometric body, a polyhedron, the bases of which are equal polygons, and the side faces are parallelograms. To the uninitiated, this may sound somewhat intimidating. And when your child needs to bring a prism that you made at home to your geometry lesson, you are at a loss, not knowing how to help your beloved child. In fact, everything is not so difficult and, using our tips on how to make a prism, you will adequately cope with this problem.

How to make a prism out of paper

Let’s immediately agree that we will make a straight prism, that is, a prism whose side ribs will be perpendicular to the bases. Do it inclined prism made from paper is very problematic (such layouts are usually made from wire).

We already know that at the bases of the prism there are two identical polygons. Therefore, we will begin our work with them. The simplest of polygons is a triangle. This means that we will first make the prism triangular.

How to make a triangular prism

We will need thick white paper for drawing, a pencil, a protractor, a compass, a ruler, scissors and glue.

We draw a triangle, we can use any triangle, but to make our prism especially beautiful, we will make an equilateral triangle. In geometry, such a prism is called “regular”. We choose at our discretion the size of the side of the triangle, say 10 cm. We put this segment on paper with a ruler and use a protractor to measure an angle of 60 ∗ from one end of our segment.

We draw an inclined line. Using a ruler, mark it 10 cm from the end of the segment. Thus, we have found the third vertex of the triangle. We connect this point with the ends of the initial segment and the equilateral triangle is ready. It can be cut out. We make the second triangle in the same way, or carefully trace the contours of the first one on paper. Well, we already have two reasons.

Making the side edges. We decide what height the prism will have. Let's say 20 cm. We draw a rectangle, the size of one side of which is the height of the prism (in our case - 20 cm), and the second side is equal to the size of the base side multiplied by the number of these sides (for us: 10 cm x 3 = 30 cm) .

On the long sides we make marks every 10 cm. We connect the opposite marks with straight lines. Then you will need to carefully bend the paper along them. These are the side edges of our prism. We mark narrow allowances for gluing along two long and one short sides of the rectangle (strips 1 cm wide are enough). We cut out the rectangle along with the allowances, carefully bend them along the markings. Bend the ribs.

Let's start assembly. Glue the rectangle along the side edge into a triangular pipe. Glue base triangles onto the folded allowances at the top and bottom. The prism is ready.

It’s probably not worth going into the details of the question of how to make a prism from cardboard. The entire assembly algorithm remains the same, just replace the paper with thin cardboard. By changing the number of sides of the base polygons, you can now make a pentagonal and hexagonal prism yourself.

Given:
The intersection of a pyramid and a prism
Necessary:
Construct a development of a straight prism and show on it the line of intersection of the prism with the pyramid.

Constructing a development of a straight prism is much easier than constructing a development of a pyramid.

Constructing a prism scan

The construction of a development of a straight prism is facilitated by the fact that all dimensions for development are taken from diagrams and we do not need to find the natural values ​​of the edges of the prism. Since a straight prism is given, the lateral edges of the prism are projected onto the frontal plane of projections in full size. The edges of the bases of a straight prism are parallel to the horizontal projection plane and are also projected onto it in full size.

Algorithm for constructing a prism scan

• We draw a horizontal line.
• From an arbitrary point G of this line we lay off segments GU, UE, EK, KG equal to the lengths of the sides of the base of the prism.
• From points G, U, ..., perpendiculars are restored and values ​​equal to the height of the prism are laid on them. The resulting points are connected by a straight line. Rectangle GG1G1G is a development of the lateral surface of the prism. To indicate the faces of the prism on the development, perpendiculars are drawn from points U, E, K.
• To obtain a complete development of the surface of the prism, polygons of its bases are attached to the development of the surface.

To construct on the development the line of intersection of the prism with the pyramid of closed broken lines 1, 2, 3 and 4, 5, 6, 7, 8, we use vertical straight lines.

More details in the video tutorial on descriptive geometry in AutoCAD

This image is a "regular" street photo. Overpasses lead the eye to the image... through a prism

The key element of any photography is how you use light. In this article you will learn how to split it. Using a prism in photography gives new possibilities and is another way to use the refraction of light.

What does a prism do with light?

Because a prism is a glass object, light is refracted as it passes through it, creating several effects that you can use in photography.

There are two ways to use a prism.

• Rainbow Projection - A prism, and specifically its triangular shape, acts by splitting light and revealing different wavelengths to form a rainbow. And now you can take a picture of it.
• Light Redirection - Light can change direction dramatically when passing through a prism. This means that when you look through it, you will be able to see the painting at a 90 degree angle to you. This factor makes it possible to create double exposure.

The image clearly shows the rainbow light from the prism, as well as the remnants of light emitted from different angles

Using a Crystal Prism to Create a Rainbow

A great way to use a prism is to create a rainbow. The larger the prism, the larger the resulting rainbow. Another way to increase its size is to increase the distance between the prism and the surface on which you are projecting the rainbow. The difference between these options is that as the aforementioned distance increases, the rainbow light becomes more diffuse and less intense.

You can use a prism to create your own rainbow

Also pay attention to how high the sun is in the sky. The angle of sunlight hitting the prism affects the angle of the rainbow projected. It is easier to project a rainbow onto the earth at noon. To project a rainbow more horizontally, you need to photograph when the sun is lower in the sky, that is, after sunrise or before sunset.

Rainbow, as a photo detail

Rainbow light is very colorful and when projected onto a surface it can create an interesting effect. Look for a surface that is a neutral color (such as gray or white). Pay attention to surfaces with a pleasant texture.

Twist the prism until you can see the rainbow being projected onto the surface you are photographing. You can, of course, take a photo while holding the prism and camera. But it's good if you have a friend who will help. Since this is a detailed photo, it is better to use a macro lens, but you can find equally interesting compositions using other lenses.

Rainbow in portrait photography

Without a doubt, one of the most popular forms of prism photography is projecting a rainbow onto the subject's face. The rainbow won't end up being big, and again, it would be nice to have another person hold the prism while you take the photo.

Three images in one frame

You can shoot through glass those objects that appear inside the prism. Lift the prism and rotate it. You will see images inside. However, they will not be the same as those that are right in front of you. Depending on how you rotate the glass prism, you may see one or two images. These are the ones you can work with to create with a single press of the shutter button.

Lens selection

For prism photography - wide-angle and macro lenses.

• A wide-angle lens allows you to add a background image to your photo. However, the edge of the prism becomes more visible in the frame. It's not easy to blur an image using the aperture available on most wide-angle lenses.
• Macro lens. Most prism photography is done using it, as this lens allows you to focus close to the prism and avoid having your hand caught in the frame. The transition from background to image in a prism is also more difficult to detect.

The image was taken with a macro lens and a prism, and it ends up looking like an optical illusion.

Aperture for prism photography

Which one you use for these types of photos largely depends on what you plan to do with the background and how sharp you want the prism image to be.

An open aperture of f/2.8 or larger will certainly work for blurring the background. Most photographs need to achieve the feeling of multiple exposure. This means that an aperture of around f/8 is the right balance between background and detail and avoids the prism line being too sharp when transitioning into the background.

Background image

Due to the small width of the prism, even with a macro lens, the background takes up most of the frame. So what works as a background for this type of photography?

• Leading lines - a background that draws attention to the images inside the prism - are used effectively. It could be a tunnel or a road that goes off to infinity.
• The textured background is more of a blank canvas for prism images. It could be a brick wall or leaves and flowers.
• Symmetry. Since the prism splits your image down the middle, using symmetry on both sides of that split is a pretty effective strategy.

Using background symmetry can work well in prism photography

Image in glass

Now the hard part is getting a good image inside the prism. The images in it may be positioned at a 90 degree angle to where you are looking, or perhaps at a 60 degree angle to the edge and in front of where the photographer is standing. Incorporating this into the background composition is a challenging aspect of prism photography.

• Composition - You already have a good composition for your background. Now we need to save it while adding a point of interest that would look good through the prism. Just use trial and error. Change the angle of the prism or rotate it; You can also try moving forward and backward.
• Adding a model. An easier way to add interest to a prism image is to make it a portrait photograph. The advantage is that you can simply ask the model to stand in the desired position from which the refracted light passes through the prism.

Adding a model to the composition of this image made the cherry blossom photo much more interesting.

Use fractals

Fractals are another element that uses refraction in photography. They produce prismatic effects, but are not themselves triangular in shape. You can take photos through them without having to worry about making sure the images are at a 90-degree angle to you. Fractals are often used to create creative portrait photographs with soft edges or other abstract shots.

Time to go and share the light!

If you want to try something new in photography, you will definitely enjoy it. It's a little difficult to photograph with, but that's what makes it really fun. Now is the time to pick up a crystal prism and go experimenting!

It is necessary to construct developments of faceted bodies and mark the intersection of the prism and the pyramid on the development.

To solve this problem in descriptive geometry you need to know:

— information about developments of surfaces, methods of their construction and, in particular, construction of developments of faceted bodies;

— one-to-one properties between a surface and its development and methods of transferring points belonging to the surface to the development;

— methods for determining the natural values ​​of geometric images (lines, planes, etc.).

Procedure for solving the Problem

It's called a sweep a flat figure that is obtained by cutting and bending the surface until it is completely aligned with the plane. All surface developments ( blanks, patterns) are constructed only from natural quantities.

1. Since the developments are constructed from natural quantities, we proceed to their determination, for which we use tracing paper (graph paper or other paper) of A3 format to transfer task No. 3 with all the points and lines of intersection of the polyhedra.

2. To determine the natural values ​​of the edges and base of the pyramid, we use right triangle method. Of course, others are possible, but in my opinion, this method is more understandable for students. Its essence is that “on the constructed right angle, the projection value of the straight line segment is plotted on one side, and on the other, the difference in coordinates of the ends of this segment, taken from the conjugate projection plane. Then the hypotenuse of the resulting right angle gives the natural value of the given line segment.”.

Fig.4.1

Fig.4.2

Fig.4.3

3. So, in the free space of the drawing (Fig.4.1.a) we build a right angle.

Along the horizontal line of this angle we plot the projection value of the edge of the pyramid D.A. taken from the horizontal projection plane - lDA. Along the vertical line of the right angle we plot the difference in the coordinates of the points D’ AndA’ , taken from the frontal plane of projections (along the axis z down) - . By connecting the resulting points with the hypotenuse, we obtain the actual size of the edge of the pyramid | D.A.| .

In this way we determine the natural values ​​of the other edges of the pyramid D.B. And DC, as well as the base of the pyramid AB, BC, AS (Fig.4.2), for which we construct a second right angle. Note that determining the natural size of an edge DC is carried out in cases where it is given projectionally in the original drawing. This is easily determined if we remember the rule: “ if a straight line on any projection plane is parallel to the coordinate axis, then on the conjugate plane it is projected in natural size.”

In particular, in the example of our problem, the frontal projection of the edge D’ C’ parallel to the axis X, therefore, in the horizontal plane DC immediately expressed in actual size | DC| (Fig. 4.1).

Fig.4.4

4. Having determined the natural values ​​of the edges and base of the pyramid, we proceed to constructing the development ( Fig.4.4). To do this, take an arbitrary point on a sheet of paper closer to the left side of the frame D believing that this is the top of the pyramid. We carry out from the point D an arbitrary straight line and plot the natural size of the edge on it | D.A.| , getting a point A. Then from the point A, using a compass to measure the actual size of the base of the pyramid R=|AB| and placing the leg of the compass at the point A we make an arc notch. Next, take the actual size of the edge of the pyramid onto the compass solution R=| D.B.| and, placing the leg of the compass at the point D we make a second arc notch. At the intersection of arcs we get a point IN, connecting it with points A and D we get the edge of the pyramid DAB. Similarly, we attach to the edge D.B. edge DBC, and to the edge DC- edge DCA.

To one of the sides of the base, for example INC, we attach the base of the pyramid also using the method of geometric serifs, taking the dimensions of the sides on the compass solution ABAndAWITH and making arc serifs from points BAndC getting the point A(Fig.4.4).

5. Constructing a sweep the prism is simplified by the fact that in the original drawing in the horizontal plane of projections the base, and in the frontal plane - with a height of 85 mm, it set immediately in natural size

To construct a scan, we mentally cut the prism along some edge, for example along E Having fixed it on the plane, we will unfold the other faces of the prism until they are completely aligned with the plane. It is quite obvious that we will get a rectangle whose length is the sum of the lengths of the sides of the base, and the height is the height of the prism - 85mm.

So, to construct a prism scan we do:

- on the same format where the pyramid is constructed, draw a horizontal straight line on the right side and from an arbitrary point on it, for example E, sequentially lay out the segments of the base of the prism E.K., KG, G.U., UE, taken from the horizontal plane of projections;

- from dots E, K, G, U, E we restore the perpendiculars on which we plot the height of the prism taken from the frontal plane of the projections (85mm);

— connecting the obtained points with a straight line, we obtain a development of the lateral surface of the prism and to one of the sides of the base, for example, G.U. we attach the upper and lower bases using the geometric serif method, as we did when building the base of the pyramid.

Fig.4.5

6. To construct an intersection line on a development, we use the rule that “any point on the surface corresponds to a point on the development.” Take, for example, the face of a prism G.U., where the line of intersection with the points lies 1-2-3 ; . Let's put the bases on the development G.U. points 1,2,3 by distances taken from the horizontal projection plane. Let us restore perpendiculars from these points and plot the heights of the points on them 1’ , 2’, 3’ , taken from the frontal plane of projection – z 1 , z 2 Andz 3 . Thus, we got points on the scan 1, 2, 3, connecting which we get the first branch of the intersection line.

All other points are transferred similarly. The constructed points are connected, obtaining the second branch of the intersection line. Highlight the desired line in red. Let us add that in case of incomplete intersection of faceted bodies, there will be one closed branch of the intersection line on the development of the prism.

7. The construction (transfer) of the intersection line on the pyramid development is carried out in the same way, but taking into account the following:

— since scans are built from natural values, it is necessary to transfer the position of the points 1-8 the lines of intersection of projections on the lines of edges of natural dimensions of the pyramid. To do this, take, for example, the points 2 and 5 in the frontal projection of the rib D.A. Let's transfer them to the projection value of this edge of the right angle (Fig. 4.1) along communication lines parallel to the axis X, we obtain the required segments | D2| and |D5| ribs D.A. in natural quantities, which we put aside (transfer) to the development of the pyramid;

— all other points of the intersection line are transferred in the same way, including points 6 and 8, lying on the generators Dm And Dn why at a right angle (Fig.4.3) the natural values ​​of these generators are determined, and then the points are transferred to them 6 and 8;

- on the second right angle, where the natural values ​​of the base of the pyramid are determined, the points are transferred mAndn intersections of generatrices with the base, which are subsequently transferred to the development.

Thus, the points obtained on natural values 1-8 and transferred to the development, we connect sequentially with straight lines and finally obtain the line of intersection of the pyramid on its development.