Relevant bibliographies by topics / Pythagorean Triangle

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Pythagorean Triangle'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Pythagorean Triangle"

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Shanthi, J., та M. A. Gopalan. "Formulation of Special Pythagorean Triangles through Integer Solutions of the Hyperbola 𝑦𝟐 = (𝑘𝟐 + 𝟐𝑘)𝑥𝟐 + 𝟏". Indian Journal Of Science And Technology 17, № 41 (2024): 4307–12. http://dx.doi.org/10.17485/ijst/v17i41.3132.

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Objectives: The objective of this research paper is to formulate Pythagorean triangles, each of which satisfies the relation: Hypotenuse = (𝑘 + 1) times the leg with even values added with unity, through employing the integer solutions to the Hyperbola 𝑦2 = (𝑘2 + 2𝑘)𝑥2 + 1. Methods: The sides of the Pythagorean triangle satisfying the requirement are obtained by suitably choosing its generators consisting of the integer solutions to the considered hyperbola. Findings : There are plenty of Pythagorean triangles satisfying the given characterization for each value of k > 0 in the binary quadr
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A., Dinesh Kumar, and Vasuki M. "A STUDY ON PYTHAGOREAN TRIPLES." International Journal of Interdisciplinary Research in Arts and Humanities 1, no. 1 (2016): 14–21. https://doi.org/10.5281/zenodo.155337.

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The Pythagorean numbers play a significant role in the theory of higher arithmetic as they come in the majority of indeterminate problem. For the discovery of the law of the three squares (Pythagorean equation), really, one should be indebted to the Pythagorean who were the first Greeks with great intellectual perception. One may notice to his surprise that the Egyptians, the Chinese, the Babylonians and the Indians knew some knowledge of the property of right angled Pythagorean triangles or Pythagorean numbers .Since there is a 1−1 correspondence between Pythagorean numbers and Pythagorean tr
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J, Shanthi, та A. Gopalan M. "Formulation of Special Pythagorean Triangles through Integer Solutions of the Hyperbola 𝑦𝟐 = (𝑘𝟐 + 𝟐𝑘)𝑥𝟐 + 𝟏". Indian Journal of Science and Technology 17, № 41 (2024): 4307–12. https://doi.org/10.17485/IJST/v17i41.3132.

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Abstract <strong>Objectives:</strong>&nbsp;The objective of this research paper is to formulate Pythagorean triangles, each of which satisfies the relation: Hypotenuse = (𝑘 + 1) times the leg with even values added with unity, through employing the integer solutions to the Hyperbola 𝑦2 = (𝑘2 + 2𝑘)𝑥2 + 1.&nbsp;<strong>Methods:</strong>&nbsp;The sides of the Pythagorean triangle satisfying the requirement are obtained by suitably choosing its generators consisting of the integer solutions to the considered hyperbola.&nbsp;<strong>Findings :</strong>&nbsp;There are plenty of Pythagorean triangles
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Hikmatovich, Ibragimov Husniddin. "Connection Between A Right Triangle And An Equal Side Triangle." American Journal of Interdisciplinary Innovations and Research 02, no. 11 (2020): 105–14. http://dx.doi.org/10.37547/tajiir/volume02issue11-20.

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There is some evidence that a right triangle and an equilateral triangle are related. Information about Pythagorean numbers is given. The geometric meaning of the relationship between right triangles and equilateral triangles is shown. The geometric meaning of the relationship between an equilateral triangle and an equilateral triangle is shown.
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Deguma, Jabin J., Reylan G. Capuno, Melona C. Deguma, Ramil P. Manguilimotan, Raymond C. Espina, and Gengen G. Padillo. "An Analogical Investigation of the Pythagorean Triangle: From a Mathematical Figure to an Ethical Praxis." Academic Journal of Interdisciplinary Studies 10, no. 1 (2021): 373. http://dx.doi.org/10.36941/ajis-2021-0031.

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This paper exposes an alternative and juxtaposed interdisciplinary view of the Pythagorean Triangle, from a mathematical point of view to ethical applicability. Pythagorean Theorem is understood as a mathematical principle (a2+b2=c2), where the sum of the square of the shorter legs, a and b, is equal to the square of the most extended leg, the hypotenuse, c, resulted in the equation of the right triangle (Pythagorean Triangle). As an antediluvian mathematical figure, the Pythagorean Triangle's beauty and intricacy still amazed and provoked present-day thoughts. It is indubitable that the Theor
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Rajput, Chetansing. "Metallic Ratios in Primitive Pythagorean Triples : Metallic Means embedded in Pythagorean Triangles and other Right Triangles." JOURNAL OF ADVANCES IN MATHEMATICS 20 (July 15, 2021): 312–44. http://dx.doi.org/10.24297/jam.v20i.9088.

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The Primitive Pythagorean Triples are found to be the purest expressions of various Metallic Ratios. Each Metallic Mean is epitomized by one particular Pythagorean Triangle. Also, the Right Angled Triangles are found to be more “Metallic” than the Pentagons, Octagons or any other (n2+4)gons. The Primitive Pythagorean Triples, not the regular polygons, are the prototypical forms of all Metallic Means.
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Nurafni, Nurafni, Asih Miatun, and Hikmatul Khusna. "PROFIL PEMAHAMAN KONSEP TEOREMA PYTHAGORAS SISWA BERDASARKAN PERBEDAAN GAYA KOGNITIF FIELD INDEPENDENT DAN FIELD." KALAMATIKA Jurnal Pendidikan Matematika 3, no. 2 (2018): 175–92. http://dx.doi.org/10.22236/kalamatika.vol3no2.2018pp175-192.

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This research is a descriptive qualitative approach which aims to describe profile of understanding of pythagoras theorem concept of students based on the difference of field independent and dependent cognitive style. The subjects of this study are 9th grade students of junior secondary school. Subject determination is done using GEFT instrument and mathematics teacher’s consultation, then continued by giving concept comprehension test on Pythagorean theorem material and interview. Checking the validity of data is done by time’s triangulation. The results showed that student: 1) states the mea
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Dr., R. Sivaraman. "TRIANGLE OF TRIANGULAR NUMBERS." TRIANGLE OF TRIANGULAR NUMBERS 9, no. 10 (2021): 2390–94. https://doi.org/10.47191/ijmcr/v9i10.01.

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Among several interesting number triangles that exist in mathematics, Pascal&rsquo;s triangle is one of the best triangle possessing rich mathematical properties. In this paper, I will introduce a number triangle containing triangular numbers arranged in particular fashion. Using this number triangle, I had proved five interesting theorems which help us to generate Pythagorean triples as well as establish bijection between whole numbers and set of all integers.
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Laudano, Francesco. "PYTHAGOREAN-LIKE FORMULAS FOR ANY TRIANGLE." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 10, no. 12 (2022): 3050–51. http://dx.doi.org/10.47191/ijmcr/v10i12.07.

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S., Mallika. "PYTHAGOREAN TRIANGLE WITH 2A/P+H-LEG AS A NARCISSTIC NUMBER OF ORDERS 3, 4 AND 5." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 6, no. 3 (2019): 1–4. https://doi.org/10.5281/zenodo.2582935.

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Dissertations / Theses on the topic "Pythagorean Triangle"

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Wigren, Thomas. "The Cauchy-Schwarz inequality : Proofs and applications in various spaces." Thesis, Karlstads universitet, Avdelningen för matematik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-38196.

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We give some background information about the Cauchy-Schwarz inequality including its history. We then continue by providing a number of proofs for the inequality in its classical form using various proof techniques, including proofs without words. Next we build up the theory of inner product spaces from metric and normed spaces and show applications of the Cauchy-Schwarz inequality in each content, including the triangle inequality, Minkowski's inequality and Hölder's inequality. In the final part we present a few problems with solutions, some proved by the author and some by others.
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Jesus, Manoel Bernardes. "Triângulo: formas, medidas e aplicações." Universidade Federal de Goiás, 2016. http://repositorio.bc.ufg.br/tede/handle/tede/5639.

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Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-06-02T18:51:04Z No. of bitstreams: 2 Dissertação - Manoel Bernardes de Jesus- 2016.pdf: 8498646 bytes, checksum: df9ec5bab5a7bc205f3b14b7ac2d5b70 (MD5) license_rdf: 19874 bytes, checksum: 38cb62ef53e6f513db2fb7e337df6485 (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-06-03T12:08:15Z (GMT) No. of bitstreams: 2 Dissertação - Manoel Bernardes de Jesus- 2016.pdf: 8498646 bytes, checksum: df9ec5bab5a7bc205f3b14b7ac2d5b70 (MD5) license_rdf: 19874 bytes, checksum: 38cb62ef53e6f513db2fb7e337df64
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Leite, Adriane de Oliveira. "Material complementar para o professor da rede SESI-SP de ensino : semelhança e software GeoGebra." Universidade Federal de São Carlos, 2015. https://repositorio.ufscar.br/handle/ufscar/7578.

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Submitted by Daniele Amaral (daniee_ni@hotmail.com) on 2016-09-21T19:25:25Z No. of bitstreams: 1 DissAOL.pdf: 6820225 bytes, checksum: 00793d2a933ccdc18ce28c12bf53f7ac (MD5)<br>Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2016-09-28T19:38:02Z (GMT) No. of bitstreams: 1 DissAOL.pdf: 6820225 bytes, checksum: 00793d2a933ccdc18ce28c12bf53f7ac (MD5)<br>Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2016-09-28T19:38:13Z (GMT) No. of bitstreams: 1 DissAOL.pdf: 6820225 bytes, checksum: 00793d2a933ccdc18ce28c12bf53f7ac (MD5)<br>Made available in DSp
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Lau, Christina 1987. "Pythagorean theorem extensions." Thesis, 2011. http://hdl.handle.net/2152/ETD-UT-2011-08-3839.

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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.<br>text
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Books on the topic "Pythagorean Triangle"

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Sierpiński, Wacław. Pythagorean triangles. Dover Publications, 2003.

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Oliver, George. Pythagorean Triangle: Or The Science of Numbers. Kessinger Publishing, 1997.

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The Pythagorean Triangle; or, the Science of Numbers. Wylie Press, 2010.

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Oliver, George. Ancient Superstitions Attached to the Ennead or Triple Triangle in the Pythagorean Triangle or the Science of Numbers. Kessinger Publishing, 2005.

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Oliver, George. The Pythagorean Triangle Explained With A Dissertation On The Peculiarities Of Masonic Number. Kessinger Publishing, LLC, 2006.

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Oliver, George. The Duad or Line Exemplified in the Pythagorean Triangle or the Science of Numbers. Kessinger Publishing, 2005.

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Oliver, George. Remarkable Properties of the Heptad in the Pythagorean Triangle or the Science of Numbers. Kessinger Publishing, 2005.

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Oliver, George. Illustration of the Triad or Superfice in the Pythagorean Triangle or the Science of Numbers. Kessinger Publishing, 2005.

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Oliver, George. The Perfect Nature of the Decad or Circle in the Pythagorean Triangle or the Science of Numbers. Kessinger Publishing, 2005.

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Oliver, George. Geometrical Application of the Pentad or Pyramid Representing Water in the Pythagorean Triangle or the Science of Numbers. Kessinger Publishing, 2005.

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Book chapters on the topic "Pythagorean Triangle"

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Takloo-Bighash, Ramin. "What numbers are the edges of a right triangle?" In A Pythagorean Introduction to Number Theory. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02604-2_5.

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Anglin, W. S., and J. Lambek. "Pythagorean Triangles and Fermat’s Last Theorem." In The Heritage of Thales. Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-0803-7_50.

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Takloo-Bighash, Ramin. "What integers are areas of right triangles?" In A Pythagorean Introduction to Number Theory. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02604-2_4.

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Enfield, Jacob. "Distance | Right Triangles, Pythagorean Theorem, and the Distance Formula." In Mathematics of Game Development. CRC Press, 2024. http://dx.doi.org/10.1201/9781032701431-5.

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Pickover, Clifford A. "Everything You Wanted to Know about Triangles but Were Afraid to Ask." In Wonders of Numbers. Oxford University PressNew York, NY, 2001. http://dx.doi.org/10.1093/oso/9780195133424.003.0099.

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Abstract Pythagorean triangles with integral sides have been the subject of a huge amount of mathematical inquiry. For example, Albert Beiler, author of Recreations in the Theory of Numbers, has been interested in Pythagorean triangles with large consecutive leg values. These triangles are as rare as diamonds for small legs. Triangle 3-4-5 is the first of these exotic gems. The next such one is 21-20-29. The tenth such triangle is quite large: 27304197-27304196-38613965.
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Dunajski, Maciej. "1. What is geometry?" In Geometry: A Very Short Introduction. Oxford University Press, 2022. http://dx.doi.org/10.1093/actrade/9780199683680.003.0001.

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‘What is geometry?’ mentions the Greek philosopher Pythagoras of Samos and his followers, the Pythagoreans, who spent their time unveiling the relationship between numbers and geometric forms. They were credited for what is now known as the Pythagorean theorem, wherein for any right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. Geometry stands out from most other branches of mathematics, as the proof of a theorem can be given in pictorial terms. The Pythagorean theorem is valid in Euclidean geometry and relies on concepts that play a ce
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Pickover, Clifford A. "Quincunx." In Wonders of Numbers. Oxford University PressNew York, NY, 2001. http://dx.doi.org/10.1093/oso/9780195133424.003.0015.

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Abstract Five is Dr. Googol’s favorite number, and 5-fold symmetry is his favorite symmetry. Would you care for a barrage of mathematical trivia befitting only the most ardent mathophiles? ® Not only is 5 the hypotenuse of the smallest Pythagorean triangle, but it is also the smallest automorphic number. Let me explain. A Pythagorean triangle is a right-angled triangle with integral sides. For example, the smallest Pythagorean triangle has side lengths 3, 4, and 5. An automorphic number n, when multiplied by itself, leads to a product whose rightmost digits are n. Not counting the trivial case
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Van Brummelen, Glen. "The Modern Approach: Right-Angled Triangles." In Heavenly Mathematics. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691175997.003.0005.

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This chapter discusses the modern approach to solving right-angled triangles. After a brief background on John Napier's trigonometric work, in which he referred mostly to right-angled spherical triangles, the chapter describes the theorems for right triangles. It then considers an oblique triangle split into two right triangles and the ten fundamental identities of a right-angled spherical triangle, how the locality principle can be applied to derive the Pythagorean Theorem, and how to find a ship's direction of travel using the theorem. It also looks at Napier's work on logarithms which was d
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Lapp, Douglas A., Tibor Marcinek, and Sarah E. Lapp. "Active Learning and the Pythagorean Theorem Through Dynamic Geometry and Robotic Optimization." In Advances in Educational Technologies and Instructional Design. IGI Global, 2022. http://dx.doi.org/10.4018/978-1-6684-5920-1.ch005.

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This chapter examines the use of technology within an active learning environment. The case follows Kaitlyn, a first-year high school teacher, through a series of 3 lessons designed to develop the Pythagorean Theorem by way of an applied real-world problem involving a robotic rover. Technology is used to motivate students to want to make sense of the mathematics involved and discover patterns that they will later justify. Throughout the lessons, the students employ concepts from previous classes and integrate several mathematical ideas, including: the triangle inequality, function notation and
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Nicolaides, Demetris. "Numbers and Shapes." In In Search of a Theory of Everything. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780190098353.003.0006.

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Pythagoras initiated the mathematical analysis of nature, a cornerstone practice in modern physics. “Things are numbers” is the most significant Pythagorean doctrine. It signifies that the phenomena of nature are describable by equations and numbers. Therefore, nature is quantifiable and potentially knowable through the scientific method. The Pythagoreans quantified pleasing sounds of music, right-angled triangles, even the motion of the heavenly bodies. The “Copernican revolution” (heliocentricity) is traced back to Pythagorean cosmology. But, finally, Einstein’s relativity clarifies a popula
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Conference papers on the topic "Pythagorean Triangle"

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Magnaghi-Delfino, Paola, Giampiero Mele, and Tullia Norando. "Il pentagono come strumento per il disegno delle fortezze." In FORTMED2020 - Defensive Architecture of the Mediterranean. Universitat Politàcnica de València, 2020. http://dx.doi.org/10.4995/fortmed2020.2020.11324.

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The pentagon as a tool for fortresses’ drawingStarting from the fifteenth century, the diagram of many fortresses has a pentagonal shape. Among the best known fortresses, in Italy we find the Fortezza da Basso of Florence, the Cittadella of Parma, the Cittadella of Turin, Castel Sant’Angelo in Rome. The aim of this article is to analyze the reasons that link form and geometry to the planning of the design and the layout of pentagonal fortresses. The pentagon is a polygon tied to the golden section and to the Fibonacci sequence and it is possible to construct it starting from the golden triangl
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Kumar, Vineet. "On the dynamic behaviour of pythagorean triangle employed in power space on account of bilateral swing for given hypotenuse arm." In 2018 2nd International Conference on Inventive Systems and Control (ICISC). IEEE, 2018. http://dx.doi.org/10.1109/icisc.2018.8399005.

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Latinčić, Dragan. "Experiments with Rhythm Using the Method of Harmonic Spectrum Projection." In Iskošeni ugao Dragutina Gostuškog. Muzikološki institut SANU Beograd, 2024. https://doi.org/10.46793/dgost23.129l.

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In his capital work The Time of Art. The Contribution to the Foundation of a General Science of Forms, Dragutin Gostuški also points to the perspective of musical art, seen through significant changes in the theory of rhythm and the theory of proportions. Gostuški is a follower of the Pythagorean teachings on music, which he accepted creatively, as he looked for beauty and harmony in formulas, mathematical expressions, and laws of physics. This is mostly manifested in his discussions and postulates on rhythm. Using numerous and valuable examples, Gostuški points to an extraordinary synthetic p
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Darbari, Mita, and Prashans Darbari. "Eight extraordinary pythagorean triangles." In INTELLIGENT BIOTECHNOLOGIES OF NATURAL AND SYNTHETIC BIOLOGICALLY ACTIVE SUBSTANCES: XIV Narochanskie Readings. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0179381.

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Darbari, Mita, and Prashans Darbari. "Connection between primitive Pythagorean triangles and Mersenne primes." In FOURTH INTERNATIONAL CONFERENCE ON ADVANCES IN PHYSICAL SCIENCES AND MATERIALS: ICAPSM 2023. AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0216176.

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