0.00 $
 0 item(s)

Nets solids of revolution. How to make pdf template

solids of revolutionWhat happens if a flat geometric shape, such as a rectangle, begins to rotate rapidly relative to one of its sides?
We create a new geometric solid in space by rotation.

The sides of a rotating rectangle form the side surfaces of the cylinder.
get rotation cylinder
The official definition for such geometric solids is as follows:

The solids of revolution are volume solids that arise when a flat geometric figure bounded by a curve rotates around an axis lying in the same plane. Here it is important that a flat geometric figure can be a completely arbitrary shape.

For example, a curve that, when rotated, forms a vase or a light bulb. Such tools for creating bodies of revolution are very popular with those who work in 3D-design programs. solids created by rotation curves But from a mathematical point of view, the following geometric solids of revolution are of primary interest to us:


cylinder rotation
The cylinder is formed by a rectangle rotating around one of the sides.
rotation cone
The cone is formed by a rectangular triangle rotating around one of the sides.
truncated cone rotation
A truncated cone is part of the cone located between its base and the cutting plane parallel to the base. It is formed by rotating a rectangular trapezoid around its side, perpendicular to the trapezoid bases.
ball rotation
The ball is formed by a semicircle rotating around the diameter of the cut.
During the rotation of the figures' contours, a surface of revolution arises (for example, a sphere formed by a circle). During the rotation of filled contours, bodies appear (like a ball formed by a circle).
rotation ellipse
An ellipsoid is a surface in three-dimensional space, obtained by deforming a sphere along three mutually perpendicular axes.
torus rotation
The torus is formed by a circle rotating around a straight line that does not intersect it.
The usual sense of the torus is a "bagel".
paraboloid rotation
A paraboloid is a surface formed due to a rotation around the axis of a curve formed by a parabola graph. Hence the name paraboloid.
hyperboloid rotation
A hyperboloid is a surface formed due to rotation around the axis of a curve formed by a hyperbola graph. Accordingly, the name is a hyperboloid.

How to make a cylinder of paper?
How to make a cone of paper?
How to make a paraboloid of paper?
How to make a paper hyperboloid?
How to make a paper torus?

To compare the resulting models' sizes, we tried to assemble them on the same surface together with prisms from the Magic Edges #16 issue.

solids of revolution prisms
It turned into a whole mathematical city of paper that fits on the table!


Polyhedra made of ribbon

The article in “Science and Life” tells about an interesting way of making polyhedra....

Symphony of metal

Metal processing is a very complex process. But some masters can cut out polyhedrons from metal...

Polyhedra at a science festival

The festival of fascinating science was held in Moscow on April 24 and 25, 2015, at the physics...

A Note on Archimedes - Ancient Greek Scientist

ARCHIMEDES (287 - 212 BC) - Ancient Greek mathematician, physicist, and mechanic. Archimedes is...

Practical apply

When we demonstrate polyhedra assembled from the Magic Edges set, people often ask the same question...

Star of the Game of Thrones

  The popular television series "Game of Thrones" is interesting not only by the complex plot, the...