0.00 $

0 item(s)

What 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 official definition for such geometric bodies is as follows:

The solids of revolution are volume bodies that arise when a flat geometric figure bounded by a curve rotates around an axis lying in the same plane.

And 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.

But from a mathematical point of view, the following geometric bodies of revolution are primarily of interest to us:

The cylinder is formed by a rectangle rotating around one of the sides.

The cone is formed by a rectangular triangle rotating around one of the legs.

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 bases of the trapezoid.

It is formed by rotating a rectangular trapezoid around its side, perpendicular to the bases of the trapezoid.

The ball is formed by a semicircle rotating around the diameter of the cut.

During the rotation of the contours of the figures, a surface of revolution arises (for example, a sphere formed by a circle), while during the rotation of filled contours, bodies appear (like a ball formed by a circle).

During the rotation of the contours of the figures, a surface of revolution arises (for example, a sphere formed by a circle), while during the rotation of filled contours, bodies appear (like a ball formed by a circle).

Ellipsoid is a surface in three-dimensional space, obtained by deforming a sphere along three mutually perpendicular axes.

The torus is formed by a circle rotating around a straight line that does not intersect it.

In the usual sense of the torus - it is a "bagel".

In the usual sense of the torus - it is a "bagel".

A paraboloid is a surface that is formed as a result of a rotation around the axis of a curve formed by a graph of a parabola. Hence the name parabol-oid.

A hyperboloid is a surface that is formed as a result of rotation around the axis of a curve formed by a graph of a hyperbola. Accordingly, the name is hyperb-o-loid.

**How to make a cylinder of paper?**

**How to make a paraboloid of paper?**

**How to make a paper hyperboloid?**

In order to compare the sizes of the resulting models of rotation bodies, we tried to assemble them on the same surface together with prisms from the Magic Edges #16 issue.

It turned out a whole mathematical city of paper that fits on the table!

It is not often possible to encounter polyhedra outside of math textbooks. Even though such...

In the second half of the 19th century, a new way of teaching was born in the US schools - the...

(challenging task called “the star”) It consists of 6 symmetrical small bars of complex shapes...

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

The plot of the fantastic blockbuster "The Fifth Element", is built on the legend that there are...

This is a new, very unusual way to create a star octahedron model. The polyhedron itself was...

In issue 25 of the Magic Edges, we turned our attention to the fact that by cutting a cube with a...