Ideas of visual mathematical models.

The formula for the area of a trapezoid can be derived from the one for the area of a rectangle.

To remember how the area of a trapezoid is found, knowing how to find the area of a triangle is enough.

What is the minimal number of parts an equilateral triangle should be cut into so that a square can be formed rearranging them?

A clear demonstration of the relationship between the prism and pyramid volumes.

A clear demonstration of the relationship between the cylinder and cone volumes.

A clear demonstration of the relationship between the cylinder and ball volumes.

Everyone remembers how to find the area of a rectangle. It turns out, that is enough to find the area of a circle.

To find the area of a circle, knowing how to find the area of a triangle is enough.

A simple to do demonstration that the number π equals “three and change”.

All the conic sections – an ellipse, a parabola and a hyperbola – can be seen on water surface.

A surface of a hyperbolic paraboloid looks like a saddle, but it can be formed by a movement of a straight line.

Сhips, packed in a cylindric tube, have a shape of a hyperbolic paraboloid, so they can pass through a narrow hole without breaking!

All the conic sections (ellipse, parabola and hyperbola) can be obtained as moiré — an additional geometric pattern that is formed by two overlaying images.

Drawing a parabola with a thread according to its geometric definition.

A XVII century tool for drawing parabola, whose functioning is based on a theorem from a modern school mathematics course.

A ball rolling down the slide in a parabolic billiard always makes it to the pocket!

A simple mechanical demonstration of the paraboloid’s optical property.

A cardboard model of a dodecahedron — one of the five regular polyhedra.

The sum of exterior angles of a convex polygon is 360°.

What’s the sum of squares of first n natural numbers?

An easy-to-make illustration of an important geometrical theorem.

“The Educated Monkey” can not only count a row (as it did in Mikhail Zoshchenko’s short story with the same title), but can multiply and add numbers!

A mirror angle is a simplest kaleidoscope that produces regular polygons.

Three triangular mirrors, some duct tape and a triangle painted in two colors, combined with the theory of reflection groups allow you to demonstrate an interesting model of a classic soccer ball to your friends.