International Journal of Mathematics Trends and Technology
Volume 70 | Issue 1 | Year 2024 | Article Id. IJMTT-V70I1P103 | DOI : https://doi.org/10.14445/22315373/IJMTT-V70I1P103
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 29 Nov 2023 | 02 Jan 2024 | 16 Jan 2024 | 31 Jan 2024 |
There are three classical problems remaining from ancient Greek mathematics which are extremely influential
in the development of Geometry. They are Trisecting An Angle, Squaring The Circle, and Doubling The Cube problems.
The Squaring The Circle problem is solved accurately and is published in the International Journal Of Mathematics
Trends And Technology (Volume 69, June 2023). Upstream from this method of exact “Squaring The Circle”, one can
deduce, conversely/inversely, to get a new Mathematical challenge "CIRCLING THE SQUARE" with a straightedge & a
compass in Euclidean Geometry. This study idea came from the exact solution “Squaring The Circle by Straightedge &
compass in Euclidean Geometry”, published by IJMTT in June 2023 at https://ijmttjournal.org/Volume-69/Issue-6/IJMTTV69I6P506.pdf for this ancient Greek Geometry problem. In this research, the ANALYSIS method is adopted to prove the
process of solving this new challenge problem, which has not existed in the Mathematics field till today. The process is an
inverse/converse solution solving the ancient Greek Geometry challenge problem of “Squaring The Circle”, using a
straightedge & a compass. I hereby commit that this is my own personal research project.
Circling the square, Circulating square, Circle mature of square, Make square circled, Find circle area same
as square, Make a square rounded.
[1] Steve Nadis, An Ancient Geometry Problem Falls to New Mathematical Techniques, Geometry, Quanta Magazine, 2022. [Online].
Available: https://www.quantamagazine.org/an-ancient-geometry-problem-falls-to-new-mathematical-techniques-20220208/
[2] T. Albertini, “Squaring the Circle by Ibn al-Haytham. Philosophical or Mathematical Solution?,” Journal for the History of Arabic
Science, vol. 9, no. 1-2, pp. 5-21, 1991.
[Google Scholar] [Publisher Link]
[3] Rolf Wallisser, On Lambert's Proof of the Irrationality of π, De Gruyter, 2000.
[CrossRef] [Google Scholar] [Publisher Link]
[4] Tran Dinh Son, "Exact Angle Trisection with Straightedge and Compass by Secondary Geometry," International Journal of
Mathematics Trends and Technology, vol. 69, no. 5, pp. 9-24, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[5] L. Wantzel, “Research on Ways to Recognize Whether a Geometry Problem can be Solved with a Ruler and Compass,” Journal of
Pure and Applied Mathematics, vol. 2, pp. 366–372, 1837.
[Google Scholar] [Publisher Link]
[6] Tran Dinh Son, "Exact Squaring the Circle with Straightedge and Compass by Secondary Geometry," International Journal of
Mathematics Trends and Technology, vol. 69, no. 6, pp. 39-47, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[7] Tran Dinh Son, "Exact Doubling the Cube with Straightedge and Compass by Euclidean Geometry," International Journal of
Mathematics Trends and Technology, vol. 69, no. 8, pp. 45-54, 2023.
[CrossRef] [Publisher Link]
[8] David H. Bailey et al., “The Quest for Pi,” The Mathematical Intelligencer, vol. 19, pp. 50-57, 1997.
[CrossRef] [Google Scholar] [Publisher Link]
[9] Lam Lay Yong, and Ang Tian Se, “Circle Measurements in Ancient China,” Historia Mathematica, vol. 13, no. 4, pp. 325–340,
1986.
[CrossRef] [Google Scholar] [Publisher Link]
[10] Henk J. M. Bos, “The Legitimation of Geometrical Procedures before 1590,” Redefining Geometrical Exactness, pp. 23–36, 2001.
[CrossRef] [Google Scholar] [Publisher Link]
[11] James Gregory, “Vera Cirkovic and Hyperbolæ Quadratura,” Gottfried Wilhelm Leibniz Bibliothek, 1667.
[Google Scholar]
[12] Davide Crippa, “James Gregory and the Impossibility of Squaring the Central Conic Sections,” The Impossibility of Squaring the
Circle in the 17th Century, pp. 35–91, 2019.
[CrossRef] [Google Scholar] [Publisher Link]
[13] M. Laczkovich, “On Lambert's Proof of the Irrationality of π,” The American Mathematical Monthly, vol. 104, no. 5, pp. 439–443,
1997.
[CrossRef] [Google Scholar] [Publisher Link]
[14] F. Lindemann, “Über die Zahl π,” Mathematische Annalen, vol. 20, pp. 213–225, 1882.
[CrossRef] [Google Scholar] [Publisher Link]
[15] Rudolf Fritsch, “The Transcendence of π has been known for about a Century, but Who was the man who Discovered It?,” Results
in Mathematics, vol. 7, no. 2, pp. 164–183, 1984.
[CrossRef] [Google Scholar] [Publisher Link]
[16] William C. Jagy, “Squaring Circles in the Hyperbolic Plane,” The Mathematical Intelligencer, vol. 17, no. 2, pp. 31–36, 1995.
[CrossRef] [Google Scholar] [Publisher Link]
[17] Wiesław Witold, “Squaring the Circle in XVI–XVIII Centuries,” Mathematics Throughout the Ages, vol. 17, pp. 7–20, 2000.
[Google Scholar] [Publisher Link]
[18] Fukś Henryk, “Adam Adamandy Kochański's Approximations of π: Reconstruction of the Algorithm,” The Mathematical
Intelligencer, vol. 34, pp. 40–45, 2012.
[CrossRef] [Google Scholar] [Publisher Link]
[19] Hobson, Ernest William, Squaring the Circle: A History of the Problem, Cambridge University Press, 1913.
[Google Scholar] [Publisher Link]
[20] Robert A Dixon, Mathographics, Dover Publications, 1991.
[Google Scholar] [Publisher Link]
[21] Frédéric Beatrix, “Squaring the Circle like a Medieval Master Mason,” Parabola, UNSW School of Mathematics and Statistics, vol.
58, no. 2, 2022.
[Google Scholar] [Publisher Link]
[22] Alexander Bird, “Squaring the Circle: Hobbes on Philosophy and Geometry,” Journal of the History of Ideas, vol. 57, no. 2, pp.
217–231, 1996.
[CrossRef] [Google Scholar] [Publisher Link]
[23] Meruprastaar, Circling the Square Baudhayana’s method of Constructing a Circle Equal in area to a Square Circling the Square in
Hindi, Mathematics, 2021. [Online]. Available: https://meruprastaar.com/circling-the-square-baudhayanas-method-of-constructing-a-circle-equal-in-area-to-a-square-baudhayana-method-of-constructing-a-circle-equal-in-area-to-a-square-
%E0%A4%B5%E0%A4%B0%E0%A5%8D%E0%A4%97/
[24] Oliver Knill, “Introduction to Geometry and Geometric Analysis,” General Relativity, vol. 64, no. 1, 1995.
[Google Scholar] [Publisher Link]
[25] Lukasz Grabowski, András Máthé, and Oleg Pikhurko, “Measurable Circle Squaring,” Annals of Mathematics, vol. 185, no. 2, pp.
671–710, 2017.
[CrossRef] [Google Scholar] [Publisher Link]
[26] Ronald B. Herzman, and Gary W. Towsley, “Squaring the Circle: Paradiso 33 and the poetics of geometry,” Traditio, vol. 49, pp.
95–125, 1994.
[CrossRef] [Google Scholar] [Publisher Link]
[27] Daniel E. Otero, “The Quadrature of the Circle and Hippocrates' Lunes – The Quadrature of Curved Figures,” Mathematical
Association of America, 2010.
[Publisher Link]
Tran Dinh Son, "Circling the Square with Straightedge and Compass in Euclidean Geometry," International Journal of Mathematics Trends and Technology (IJMTT), vol. 70, no. 1, pp. 16-26, 2024. Crossref, https://doi.org/10.14445/22315373/IJMTT-V70I1P103
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