By Yarmukhamedov Sh.

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**Additional resources for A Carleman Function and the Cauchy Problem for the Laplace Equation**

**Sample text**

It serves as a justification for the next chapter, where I turn to some examples from the history of physics and the natural sciences. 1 Fantasy units of measurement L’eau, qui valait au début du siège deux késitah le bât, se vendait maintenant un shekel d’argent ; les provisions de viande et de blé s’épuisaient aussi ; on avait peur de la faim ; quelques-uns même parlaient des bouches inutiles, ce qui effrayait tout le monde. Gustave Flaubert, Salammbô As a boy I was a voracious reader with, unsurprisingly, a strong bent towards all kinds of fantasy, adventure and exoticism.

A bit later we shall turn wonderful applications of the scaling principles to physical laws. We start with the basic observation: area of geometric figure changes as squares of its characteristic linear measurement. For example, if we increase a side of a square by factor of two, its area increases by factor of four. This observation allows us to prove Pythagoras’ Theorem: If a and b are sides and c the hypothenuse of a right-angled triangle, then a2 + b2 = c2 . Indeed, consider all triangles similar to the given triangle with sides a and b and the hypotenuse c; the corresponding sides a′ , b′ and the hypothenuse c′ are obtained from a, b, c by stretching with the same coefficient.

A lasting effect of early linguistic experiences is emphasized by Tim Swift6 : By the way, related to the issue of language, I was taught to read and write (in a Yorkshire primary school in the mid 1960s) using an ‘experimental language’ called ITA (Initial Teaching Alphabet); I don’t know if this hindered or accelerated my development of communication skills, but I do remember that I seemed to be the only person in the class who, when we finally arrived at standard English when I was six or seven, had to translate everything back to ITA before I was happy with its meaning.