Displaying similar documents to “O sumowaniu liczb waryacyj”

Teoretyczne podstawy dzielenia z resztą liczb naturalnych wraz z uwagami o dzieleniu z resztą liczb całkowitych, wymiernych i rzeczywistych

Antoni Chronowski (2019)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In this article, I analyze the theoretical foundations of the division with remainder in the arithmetic of natural numbers. As a result of this analysis I justify that the notation a:b=c r s, where a, b, c, s are natural numbers and r denotes, is correct at school mathematics level and does not lead to a contrediction suggested by the author of the article (Semadeni, 1978). As a generalization of the division with remainder of natural numbers, I consider the division with remainder of...

O cechach podzielności liczb i odkrywaniu twierdzeń

Jan Górowski, Adam Łomnicki (2006)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The paper contains some theorems (with proofs) from numbers divisibility theory, and suggestions how to use them in the process of teacher training, which provide good opportunities for developing students’ creative attitude in the process of discovering new facts in elementary mathematics.

O nieskończonych ciągach liczb parami względnie pierwszych raz jeszcze

Jan Górowski, Adam Łomnicki (2012)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In the paper the authors, using general formulas, determine and describe a class of infinite sequences of natural numbers, pairs of which are relatively prime. This result was obtained using the theory of Lucas sequences and recurrent equations of the second degree.

Wokół liczb i szeregów harmonicznych

Damian Wiśniewski (2015)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The harmonic series is one of the most celebrated infinite series ofmathematics. From a pedagogical point of view, the harmonic series providesa wealth of opportunities. Applications such as Gabriel’s wedding cake andEuler’s proof of the divergence of prime numbers can lead to some verynice discussions. The main idea of this article is to survey some of unusual,insightful and inspiring divergence proofs. First of all, this article is addressedat first-year calculus students. ...

Różne reprezentacje liczb rzeczywistych

Barbara Pieronkiewicz (2017)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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This article is devoted to the different representations of real numbers. In particular, the following types are distinguished and discussed: (1)representations based on theorems referring to the axiomatic characterization of the field of real numbers, (2) genetic representations – related to the construction of real numbers, (3) visual representations – mainly related to the geometrical way of presenting numbers. The paper addresses different representations of real numbers from a higher...

Przegląd Literatury. Bibliografia

(1902)

Wiadomości Matematyczne

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R. Merecki. Klimatologia ziem polskich (E. Romer). str. 112-118 F. Chłapowski. Życie i prace księdza Józefa Rogalińskiego (S. Dickstein). str. 118-119 W. Urbański. O postępach w astronomii i fizyce (S. Dickstein). str. 119-120 K. Czajkowski. O mnogości liczb prostych (T. Łopuszański). str. 120 A. Jaglarz. Heron z Aleksandryi i jego problemat o powierzchni trójkąta (T. Łopuszański). str. 121 K. Piestrak. Geneza twierdzeń...

Miscellanea

(1902)

Wiadomości Matematyczne

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B. Niewęgłowski, S. Dickstein. Z elementarnej teoryi liczb - Sur la théorie élémentaire des nombres. str. 252-257 B. Niewęgłowski. Pewne zagadnienie o hyperboli - Un problème sur l'hyperbole. str. 257-258 S. Dickstein. G. Vacca, Z rękopisów T. Harriota - Sur les manuscrits de T. Harriot. str. 259-260 S. Dickstein. Tablica krzywych panalgebraicznych według prof. G. Loria - G. Loria. Table des courbes panalgébriques. str. 261-266 ...