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Analyticam demonstrationem, propos. 47. primi elementorum Euclidis consensu amplissimae facultatis philosophicae in incluta lipsiensi adornatam,Christ, Andreas Stephanus, Thorinus, Andreas, January 1900 (has links)
Diss.--Leipzig (Andreas Thorinus, respondent). / At head of title: Q.D.B.V. Day of the month in title supplied in manuscript.
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Analyticam demonstrationem, propos. 47. primi elementorum Euclidis consensu amplissimae facultatis philosophicae in incluta lipsiensi adornatam,Christ, Andreas Stephanus, Thorinus, Andreas, January 1900 (has links)
Diss.--Leipzig (Andreas Thorinus, respondent). / At head of title: Q.D.B.V. Day of the month in title supplied in manuscript.
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Should the Pythagorean Theorem Actually be Called the 'Pythagorean' TheoremMoledina, Amreen 05 December 2013 (has links)
This paper investigates whether it is reasonable to bestow credit to one person or group for the famed theorem that relates to the side lengths of any right-angled triangle, a theorem routinely referred to as the “Pythagorean Theorem”. The author investigates the first-documented occurrences of the theorem, along with its first proofs. In addition, proofs that stem from different branches of mathematics and science are analyzed in an effort to display that credit for the development of the theorem should be shared amongst its many contributors rather than crediting the whole of the theorem to one man and his supporters.
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Pythagorean theorem extensionsLau, Christina, 1987- 02 February 2012 (has links)
This report expresses some of the recent research surrounding the Pythagorean Theorem and Pythagorean triples. Topics discussed include applications of the Pythagorean Theorem relating to recursion methods, acute and obtuse triangles, Pythagorean triangles in squares, as well as Pythagorean boxes. A short discussion on the depth of the Pythagorean Theorem taught in secondary schools is also included. / text
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Should the Pythagorean Theorem Actually be Called the 'Pythagorean' TheoremMoledina, Amreen 05 December 2013 (has links)
This paper investigates whether it is reasonable to bestow credit to one person or group for the famed theorem that relates to the side lengths of any right-angled triangle, a theorem routinely referred to as the “Pythagorean Theorem”. The author investigates the first-documented occurrences of the theorem, along with its first proofs. In addition, proofs that stem from different branches of mathematics and science are analyzed in an effort to display that credit for the development of the theorem should be shared amongst its many contributors rather than crediting the whole of the theorem to one man and his supporters.
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Das pythagoreische system in seinen grundgedanken. ...Sobczyk, Peter. January 1878 (has links)
Insug.-diss.-Leipzig. / Lebenslauf.
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Die metaphysischen grundlehren der älteren Pythagoreer. ...Heinze, Albert, January 1871 (has links)
Inaug.-diss.--Leipzig.
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A study of the doctrine of metempsychosis in Greece from Pythagoras to Plato /Long, Herbert Strainge. January 1948 (has links)
Thesis--Princeton University. / Includes bibliographical references.
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A Study of Grade Eight Students¡¦ Concepts on Pythagorean Theorem and Problem-Solving Process in Two Problem RepresentationsCHIU, HSIN-HUI 30 June 2008 (has links)
The aim of this study is to analyze students¡¦ mathematics concepts in solving
Pythagorean Theorem problems presented in two different representations (word
problems and word problems with diagrams). The investigators employed the
mathematics competence indicators in Grade 1-9 Integrated Curriculum in developing
such problems. In analyzing data, the investigator used Schoenfeld¡¦s method in
depicting their problem-solving processes, with attention to students¡¦ sequence and
difference in time consumption. Four eight grade students with good competence in
mathematics and expressions from a secondary school were selected as research
subjects. Problems related to Pythagorean Theorem were divided into three types:
Shape, Area, and Number. Data were collected using thinking aloud method and
semi-structured interview, and triangulation was further applied in protocol analysis.
The research results revealed 3 findings: (1) For the ¡§Shape¡¨ type problems,
students¡¦ problem-solving concepts varied with different problem representation. For
the ¡§Area¡¨ and ¡§Number¡¨ types of problems (without diagram), students were
required to use their geometric concept when processing word problems. Students¡¨
use of problem-solving concepts would not significantly vary with problem
representation types. However, students¡¦ use of problem-solving methods would
affect the types and priorities of concepts used. Generally, the types of mathematics
concepts could be made up by the frequency of concepts used, and more types of
problem-solving concepts would be used for word problems representation than for
word problems with diagrams representation. (2) In terms of the time consumed in the
first three problem-solving stages of Schoenfeld, the time required to solve word
problems was 1.6 times of that required to solve word problems with diagrams. In
terms of the total time consumed, the time required to solve word problems was 1.25
times of that required to solve word problems with diagrams. In the problem-solving
stages, students needed to explore the problem first when dealing with word problems
before they could go on to solve the problem, and such repetition was more frequent
when they dealt with word problems. (3) For both type of problem representations,
there is a higher number of correctly-answered problems. This finding indicated that
a higher frequency of problem-solving concepts and less repetition in the
problem-solving stage were required; and vice versa.
As to the sequence of Pythagorean Theorem concepts to be taught, the
investigator suggest teachers to start with the concept of area filling in the ¡§Shape¡¨
type of problems to derive Pythagorean Theorem, and further apply the formula to
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solving ¡§Number¡¨ problems. After students have acquired basic competency in
¡§Shape¡¨ and ¡§Number¡¨ Pythagorean Theorem problems, teachers could explain and
introduce this theorem from the perspective of ¡§Area¡¨. Finally, in problem posing,
teachers were also advised to apply various contexts; covering all kinds of
representations of problems that enhance students¡¦ utilization of mathematics
concepts; and to cater for various needs of students.
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The arithmetical philosophy of Nicomachus of GerasaJohnson, George, January 1916 (has links)
Thesis (Ph. D.)--University of Pennsylvania, 1911. / "The Introductionis arithmeticae libri duo ... is the basis of the present essay"--P. 1. Includes bibliographical references (p. 1).
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