The paper is consisted of contentually unrelated sections, where each section could be one short paper. Section 1 deals with the process of an unintentional repetition of one of the Ramanujan formulas, and the author did not know it before. The process of the unintentional repetition of the Ramanujan formula is interesting for estimating, for instance, the physical background for guessing of dimensionless physical constants. Section 2 shows an approximation which helps at memorizing the square roots of integers up to 10. Section 3 shows the specialities of the squares of integers at the last digits. Section 4 shows how the last two digits are repeated for 2 to the sequential integer powers, and how to find out this. Section 5 contains some mathematical peculiarities at calculating dates. All sections contain mnemonic methods to help us memorize and calculate. These sections belong to pedagogical and recreational mathematics, maybe even something more is here.