A REMARKABLE FIGURE FROM THE BOOK OF LEMMAS
The Proposition 4 from the 11-th volume (called Book of Lemmas) of „Great Books of the Western World” (printed in USA in 1952) presents the properties of a remarkable curve from Antiquity. This curve was studied by Archimedes, who called it Arbelos and it looks like a shoemaker's knife. It con...
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| Format: | Article |
| Language: | English |
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SORGING
2022-11-01
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| Series: | Journal of Industrial Design and Engineering Graphics |
| Subjects: | |
| Online Access: | http://sorging.ro/jideg/index.php/jideg/article/view/271 |
| _version_ | 1827834208994721792 |
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| author | Ludmila SASS Alina DUTA Iulian POPESCU Dragos-Laurentiu POPA |
| author_facet | Ludmila SASS Alina DUTA Iulian POPESCU Dragos-Laurentiu POPA |
| author_sort | Ludmila SASS |
| collection | DOAJ |
| description |
The Proposition 4 from the 11-th volume (called Book of Lemmas) of „Great Books of the Western World” (printed in USA in 1952) presents the properties of a remarkable curve from Antiquity. This curve was studied by Archimedes, who called it Arbelos and it looks like a shoemaker's knife. It consists of 3 semicircles. The first part of the paper is dedicated to the description of an original mechanism, conceived to plot the above-mentioned curve. It is made of a rotating driving element and two dyads of RRR type. The curve plotted by the mechanism checks the equality of areas described by Archimedes. He proved (by using geometric reasonings) that the area of a circle whose diameter is equal to the height of the right triangle inscribed in the Arbelos curve’s big semicircle is equal to the Arbelos curve’s area. In the second part of the paper, the authors modified the mechanism’s parameters and obtained 3 particular cases of Arbelos curves. These particular curves, plotted with the modified mechanism, are also composed of 3 semicircles whilst exhibiting other equalities between areas. The authors used geometric reasonings to prove the equality between the area of each particular curve and the area of a circle whose diameter is equal to the leg of a right triangle inscribed in the big semicircle of the studied particular curve.
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| first_indexed | 2024-03-12T05:46:55Z |
| format | Article |
| id | doaj.art-d1c14261bc7f4fa29134318bb54d9174 |
| institution | Directory Open Access Journal |
| issn | 1843-3766 2344-4681 |
| language | English |
| last_indexed | 2024-03-12T05:46:55Z |
| publishDate | 2022-11-01 |
| publisher | SORGING |
| record_format | Article |
| series | Journal of Industrial Design and Engineering Graphics |
| spelling | doaj.art-d1c14261bc7f4fa29134318bb54d91742023-09-03T05:35:36ZengSORGINGJournal of Industrial Design and Engineering Graphics1843-37662344-46812022-11-01172A REMARKABLE FIGURE FROM THE BOOK OF LEMMASLudmila SASS0Alina DUTA1Iulian POPESCU2Dragos-Laurentiu POPA3University of CraiovaUniversity of CraiovaUniversity of CraiovaUniversity of Craiova The Proposition 4 from the 11-th volume (called Book of Lemmas) of „Great Books of the Western World” (printed in USA in 1952) presents the properties of a remarkable curve from Antiquity. This curve was studied by Archimedes, who called it Arbelos and it looks like a shoemaker's knife. It consists of 3 semicircles. The first part of the paper is dedicated to the description of an original mechanism, conceived to plot the above-mentioned curve. It is made of a rotating driving element and two dyads of RRR type. The curve plotted by the mechanism checks the equality of areas described by Archimedes. He proved (by using geometric reasonings) that the area of a circle whose diameter is equal to the height of the right triangle inscribed in the Arbelos curve’s big semicircle is equal to the Arbelos curve’s area. In the second part of the paper, the authors modified the mechanism’s parameters and obtained 3 particular cases of Arbelos curves. These particular curves, plotted with the modified mechanism, are also composed of 3 semicircles whilst exhibiting other equalities between areas. The authors used geometric reasonings to prove the equality between the area of each particular curve and the area of a circle whose diameter is equal to the leg of a right triangle inscribed in the big semicircle of the studied particular curve. http://sorging.ro/jideg/index.php/jideg/article/view/271Arbeloscurves (particular cases)areasmechanism |
| spellingShingle | Ludmila SASS Alina DUTA Iulian POPESCU Dragos-Laurentiu POPA A REMARKABLE FIGURE FROM THE BOOK OF LEMMAS Journal of Industrial Design and Engineering Graphics Arbelos curves (particular cases) areas mechanism |
| title | A REMARKABLE FIGURE FROM THE BOOK OF LEMMAS |
| title_full | A REMARKABLE FIGURE FROM THE BOOK OF LEMMAS |
| title_fullStr | A REMARKABLE FIGURE FROM THE BOOK OF LEMMAS |
| title_full_unstemmed | A REMARKABLE FIGURE FROM THE BOOK OF LEMMAS |
| title_short | A REMARKABLE FIGURE FROM THE BOOK OF LEMMAS |
| title_sort | remarkable figure from the book of lemmas |
| topic | Arbelos curves (particular cases) areas mechanism |
| url | http://sorging.ro/jideg/index.php/jideg/article/view/271 |
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