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We indicate that Herons formula (which relates the square of the area of a triangle to a quartic function of its edge lengths) can be interpreted as a scissors congruence in 4-dimensional space. In the process of demonstrating this, we examine a number of decompositions of hypercubes, hyper-parallelograms, and other elementary 4-dimensional solids.
A nonperturbative renormalization of the phi^4 model is considered. First we integrate out only a single pair of conjugated modes with wave vectors +/- q. Then we are looking for the RG equation which would describe the transformation of the Hamilton
The book is a unique phenomenon in Russian geometry education. It was first published in 1892; there have been more than 40 revised editions, and dozens of millions of copies (by these parameters it is trailing only Euclids Elements). Our edition i
In the present popular science paper we determine when a square can be dissected into rectangles similar to a given rectangle. The approach to the question is based on a physical interpretation using electrical networks. Only secondary school background is assumed in the paper.
This is a review of some of the interesting properties of the Riemann Zeta Function.
Dendrimers are characterized by special features that make them promising candidates for many applications. Here we focus on two such applications: dendrimers as light harvesting antennae, and dendrimers as molecular amplifiers, which may serve as no