”Mathematical etudes” develop Russian traditions in popularization of mathematics. Contents of the site is originally published in Russian. Translations into other languages will appear in time.
What is the net of a polyhedron? – May you ask. It is simply a sheet of cardboard whose folding gives the polyhedron. This is true, but there’s more. The concept of the net of a polyhedron contains something more than just a sheet of cardboard.
Since James Watt invented the steam engine there was a problem of transforming rotary motion of one hinge into the perfect straight-line motion of another. This problem was unsolved for long time. And only beautiful mathematics helped finally to solve it.
In reading this text or in downloading a film you may have used the solution of the balls contact number problem in 8-dimensional space. Are you surprised? This movie tells about applications of this well-known mathematical problem.
How N equal charges will arrange on a sphere trying to minimize the potential energy of the system? The problem was posed by Thomson at the turn of the XIXth and XXth centuries, but still has been solved in a few special cases.
The escalator of the metropolitan railway... How many things are hidden behind these words for a curious observer. How to estimate the depth of a subway station, which is accessed via an escalator? It happens that even to answer this question the knowledge of mathematics can be very useful!
The area of a square equals to the square of it’s side length. It’s easy to compute the area of a figure that is built of several squares. And what is the area of a figure bounded by an arbitrary curve?