MATHEMATICAL PROPERTIES OF THE GOLDEN RATIO – A FASCINATING NUMBER
The Golden Ratio appears in many situations: in geometry, in lists with special numbers drawn up by mathematicians, in art history lectures, in rose petals arrangement or spiral shells of mollusks. This paper presents definitions and algebraic properties of Golden Section and their applications in g...
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| Format: | Article |
| Language: | English |
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SORGING
2013-11-01
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| Series: | Journal of Industrial Design and Engineering Graphics |
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| Online Access: | http://sorging.ro/jideg/index.php/jid/article/view/131 |
| _version_ | 1827849081057181696 |
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| author | DOBRE Daniel |
| author_facet | DOBRE Daniel |
| author_sort | DOBRE Daniel |
| collection | DOAJ |
| description | The Golden Ratio appears in many situations: in geometry, in lists with special numbers drawn up by mathematicians, in art history lectures, in rose petals arrangement or spiral shells of mollusks. This paper presents definitions and algebraic properties of Golden Section and their applications in geometry, in the calculation pentagon and decagon sides and area, and volume of Platonic solids. Golden Ratio occurrences are analyzed in geometric shapes as Golden Triangle, Golden Rectangle and Golden Gnomon. Different expressions involving radicals that continue indefinitely and continued fractions with Golden Section value are given and discussed. It is also revealed the connection between the Fibonacci
series and the Golden Ratio. Are presented two patterns that have symmetry of order five and that have incorporated in them the Golden Section. |
| first_indexed | 2024-03-12T09:58:18Z |
| format | Article |
| id | doaj.art-45e642d3708e46859d097623856a71e9 |
| institution | Directory Open Access Journal |
| issn | 1843-3766 2344-4681 |
| language | English |
| last_indexed | 2024-03-12T09:58:18Z |
| publishDate | 2013-11-01 |
| publisher | SORGING |
| record_format | Article |
| series | Journal of Industrial Design and Engineering Graphics |
| spelling | doaj.art-45e642d3708e46859d097623856a71e92023-09-02T11:59:15ZengSORGINGJournal of Industrial Design and Engineering Graphics1843-37662344-46812013-11-018MATHEMATICAL PROPERTIES OF THE GOLDEN RATIO – A FASCINATING NUMBERDOBRE Daniel0Ph.D., Associate professor, Department of Engineering Graphics and Industrial Design, University Politehnica of Bucharest, RomaniaThe Golden Ratio appears in many situations: in geometry, in lists with special numbers drawn up by mathematicians, in art history lectures, in rose petals arrangement or spiral shells of mollusks. This paper presents definitions and algebraic properties of Golden Section and their applications in geometry, in the calculation pentagon and decagon sides and area, and volume of Platonic solids. Golden Ratio occurrences are analyzed in geometric shapes as Golden Triangle, Golden Rectangle and Golden Gnomon. Different expressions involving radicals that continue indefinitely and continued fractions with Golden Section value are given and discussed. It is also revealed the connection between the Fibonacci series and the Golden Ratio. Are presented two patterns that have symmetry of order five and that have incorporated in them the Golden Section.http://sorging.ro/jideg/index.php/jid/article/view/131proportion, pentagram, pentagon, Golden Triangle, Golden Gnomon, Golden Ratio. |
| spellingShingle | DOBRE Daniel MATHEMATICAL PROPERTIES OF THE GOLDEN RATIO – A FASCINATING NUMBER Journal of Industrial Design and Engineering Graphics proportion, pentagram, pentagon, Golden Triangle, Golden Gnomon, Golden Ratio. |
| title | MATHEMATICAL PROPERTIES OF THE GOLDEN RATIO – A FASCINATING NUMBER |
| title_full | MATHEMATICAL PROPERTIES OF THE GOLDEN RATIO – A FASCINATING NUMBER |
| title_fullStr | MATHEMATICAL PROPERTIES OF THE GOLDEN RATIO – A FASCINATING NUMBER |
| title_full_unstemmed | MATHEMATICAL PROPERTIES OF THE GOLDEN RATIO – A FASCINATING NUMBER |
| title_short | MATHEMATICAL PROPERTIES OF THE GOLDEN RATIO – A FASCINATING NUMBER |
| title_sort | mathematical properties of the golden ratio a fascinating number |
| topic | proportion, pentagram, pentagon, Golden Triangle, Golden Gnomon, Golden Ratio. |
| url | http://sorging.ro/jideg/index.php/jid/article/view/131 |
| work_keys_str_mv | AT dobredaniel mathematicalpropertiesofthegoldenratioafascinatingnumber |