Bangun ruang Platonik
Dalam ruang tiga dimensi, bangun ruang Platonik (bahasa Inggris: Platonic solid) adalah sebuah polihedron beraturan yang bersifat cembung dalam ruang Euklides dimensi tiga. Polihedron beraturan berarti bahwa sebuah bangunan mempunyai muka yang kongruen (yang artinya bentuk dan juga ukurannya identik atau sama), berupa poligon beraturan (yang artinya semua sudut dan semua sisinya kongruen), dan jumlah muka yang sama bertemu di masing-masing titik sudut. Lima bangun ruang yang memenuhi kriteria tersebut adalah:
| Tetrahedron | Kubus | Oktahedron | Dodekahedron | Ikosahedron |
| Empat muka | Enam muka | Delapan muka | Duabelas muka | Duapuluh muka |
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|
|
|
|
Selama bertahun-tahun, para ahli geometri telah mempelajari bangun ruang Platonik.[1] Bangun ruang tersebut dinamai dari Plato, seorang filsuf asal Yunani kuno, yang menghipotesis dalam salah satu dialognya di Timaeus, yang mengatakan bahwa elemen klasik terbuat dari bangun ruang beraturan.[2]
Referensi
sunting- ^ Gardner (1987): Martin Gardner wrote a popular account of the five solids in his December 1958 Mathematical Games column in Scientific American.
- ^ Zeyl, Donald (2019). "Plato's Timaeus". The Stanford Encyclopedia of Philosophy.
Sumber
sunting- Atiyah, Michael; Sutcliffe, Paul (2003). "Polyhedra in Physics, Chemistry and Geometry". Milan J. Math. 71: 33–58. arXiv:math-ph/0303071
. doi:10.1007/s00032-003-0014-1.
- Boyer, Carl; Merzbach, Uta (1989). A History of Mathematics (edisi ke-2nd). Wiley. ISBN 0-471-54397-7.
- Coxeter, H. S. M. (1973). Regular Polytopes (edisi ke-3rd). New York: Dover Publications. ISBN 0-486-61480-8.
- Euclid (1956). Heath, Thomas L., ed. The Thirteen Books of Euclid's Elements, Books 10–13 (edisi ke-2nd unabr.). New York: Dover Publications. ISBN 0-486-60090-4.
- Gardner, Martin(1987). The 2nd Scientific American Book of Mathematical Puzzles & Diversions, University of Chicago Press, Chapter 1: The Five Platonic Solids, ISBN 0226282538
- Haeckel, Ernst, E. (1904). Kunstformen der Natur. Available as Haeckel, E. (1998); Art forms in nature Diarsipkan 2009-06-27 di Wayback Machine., Prestel USA. ISBN 3-7913-1990-6.
- Hecht, Laurence; Stevens, Charles B. (Fall 2004). "New Explorations with The Moon Model" (PDF). 21st Century Science and Technology. hlm. 58.
- Kepler. Johannes Strena seu de nive sexangula (On the Six-Cornered Snowflake), 1611 paper by Kepler which discussed the reason for the six-angled shape of the snow crystals and the forms and symmetries in nature. Talks about platonic solids.
- Kleinert, Hagen and Maki, K. (1981). "Lattice Textures in Cholesteric Liquid Crystals" (PDF). Fortschritte der Physik. 29 (5): 219–259. Bibcode:1981ForPh..29..219K. doi:10.1002/prop.19810290503
- Lloyd, David Robert (2012). "How old are the Platonic Solids?". BSHM Bulletin: Journal of the British Society for the History of Mathematics. 27 (3): 131–140. doi:10.1080/17498430.2012.670845.
- Pugh, Anthony (1976). Polyhedra: A visual approach. California: University of California Press Berkeley. ISBN 0-520-03056-7.
- Weyl, Hermann (1952). Symmetry. Princeton, NJ: Princeton University Press. ISBN 0-691-02374-3.
- Wildberg, Christian (1988). John Philoponus' Criticism of Aristotle's Theory of Aether. Walter de Gruyter. pp. 11–12. ISBN 9783110104462
Pranala luar
suntingWikimedia Commons memiliki media mengenai Platonic solids.
- Platonic solids at Encyclopaedia of Mathematics
- Weisstein, Eric W. "Platonic solid". MathWorld.
- Weisstein, Eric W. "Isohedron". MathWorld.
- Book XIII of Euclid's Elements.
- Interactive 3D Polyhedra in Java
- Solid Body Viewer[pranala nonaktif permanen] is an interactive 3D polyhedron viewer which allows you to save the model in svg, stl or obj format.
- Interactive Folding/Unfolding Platonic Solids Diarsipkan 2007-02-09 di Wayback Machine. in Java
- Paper models of the Platonic solids created using nets generated by Stella software
- Platonic Solids Diarsipkan 2018-12-15 di Wayback Machine. Free paper models(nets)
- Grime, James; Steckles, Katie. "Platonic Solids". Numberphile. Brady Haran. Diarsipkan dari versi asli tanggal 2018-10-23. Diakses tanggal 2019-04-08.
- Teaching Math with Art student-created models
- Teaching Math with Art teacher instructions for making models
- Frames of Platonic Solids images of algebraic surfaces
- Platonic Solids with some formula derivations
- How to make four platonic solids from a cube