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## Chemical way of square root of 2 calculations

### Evgeny Ivanko and Denis Perevalov*

IMM UBr RAS
Ekaterinburg 620219 Russia

This is an abstract for a presentation given at the
Research, Applications, and Policy

The theoretical possibility for making calculations and logical computing, using self-assembling of artificial nanostructures, is studied. The main principles is illustrated on 2D solution model for calculating square root of 2.

Let's consider particles of six types (A,B,C,D,E,F) having the same sizes, with ability to create different geometrical connections with each other; the length of connections is the same. For instance, a particle of type A could connect with the two B-particles, with angle equal 90 degrees between connection; a particle of type B could connect with two particles of types A and C respectively, with angle 180 degrees between connection. Each connection type is shown on picture with colored arrow.

Let's make a solution containing particles of type A (see picture). Than we add particles of type B that can connect to A-particles and so on, following the grey arrow on the picture below.

Finally we have some closed figures – isosceles rectangular triangles and some not finished figures with free connections. Now we can add some particles, which can connect to every free connection in solution and fall out in settlings. Thus the only figures rest are closed isosceles rectangular triangles.

After cleaning our solution we can destroy all connections in solution and calculate the following ration using the chemical instruments:

```      Na + Nb + Nc + Nd
R  = __________________
Nd + Ne + Nf

where Ni Ð is the number of  i-type particles in solution.
```

We know that for sufficiently large isosceles rectangular triangle R equals √2 approximately. If the solution possesses the large number of isosceles rectangular triangles of different sizes we can suppose, that an average value of |R- √2| would tend to zero.

The numerical estimation of self-assembling possibilities of sufficiently large triangles, conditions and exactitude of approximation is studied. The practical realization of method is discussed.

Abstract in Microsoft Word® format 91,462 bytes

Denis Perevalov
IMM UBr RAS
S. Kovalevskoi 16, Ekaterinburg 620219 Russia
Phone: +79222184916
Email: denis.perevalov@mail.ru

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