Ideas of visual mathematical models.

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.

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?

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

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?

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

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