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</nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> </div> <div id="contentSub"><div id="mw-content-subtitle">← <a href="/wiki/Ruang_dimensi_empat" title="Ruang dimensi empat">Ruang dimensi empat</a></div></div> <div id="mw-content-text" class="mw-body-content"><p>Anda tidak memiliki hak akses untuk menyunting halaman ini, karena alasan berikut: </p> <div class="permissions-errors"><div class="mw-permissionerror-globalblocking-blockedtext-range"><b>Your IP address is in a range that has been <a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/Global_blocks" class="extiw" title="m:Special:MyLanguage/Global blocks">blocked on all Wikimedia Foundation wikis</a>.</b> <p>The block was made by <a href="/wiki/Pengguna:Jon_Kolbert" title="Pengguna:Jon Kolbert">‪Jon Kolbert‬</a>. The reason given is <i><a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/NOP" class="extiw" title="m:Special:MyLanguage/NOP">Open proxy/Webhost</a>: See the <a href="https://meta.wikimedia.org/wiki/WM:OP/H" class="extiw" title="m:WM:OP/H">help page</a> if you are affected </i>. </p> <ul><li>Start of block: 27 Agustus 2023 15.12</li> <li>Expiry of block: 27 Agustus 2028 15.12</li></ul> <p>Your current IP address is 8.222.208.146. The blocked range is 8.222.128.0/17. </p><p>Harap sertakan semua perincian di atas dalam setiap pertanyaan yang Anda ajukan. </p> If you believe you were blocked by mistake, you can find additional information and instructions in the <a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/Stewards/Wizard" class="extiw" title="m:Special:MyLanguage/Stewards/Wizard">Stewards Block Wizard</a>.</div></div><hr /> <p>Anda dapat melihat atau menyalin sumber halaman ini. </p><textarea readonly="" accesskey="," id="wpTextbox1" cols="80" rows="25" style="" class="mw-editfont-monospace" lang="id" dir="ltr" name="wpTextbox1">{{Referensi|date=September 2020}}[[Berkas:8-cell-simple.gif|al=Animation of a transforming tesseract or 4-cube|bingkai|Animasi ini mengisyaratkan kompleksitas yang muncul ketika titik-titik pada bangun 4D dihubungkan bersama-sama untuk menciptakan ruang 4D dasar. Objek yang ditampilkan di sini adalah bangun 4D yang setara dengan [[kubus]], yang dikenal sebagai tesseract. Untuk membuat animasi ini, tesseract diputar dalam 4D, lalu diproyeksikan menjadi bangun 3D, dan akhirnya diproyeksikan ke gambar 2D.]] '''Ruang dimensi empat''' atau '''caturmatra''' ({{lang-en|four-dimensional space}}, '''4D''') adalah kelanjutan matematis dari konsep tiga dimensi atau ruang 3D. [[3 dimensi|Ruang 3D]] adalah generalisasi pengamatan paling sederhana yang mungkin, yang hanya memerlukan tiga indikator, yang disebut ''dimensi'', untuk menggambarkan ukuran-ukuran atau lokasi-lokasi berbagai benda dalam kehidupan sehari-hari. Misalnya, volume kotak persegi panjang ditentukan dengan mengukur panjang (sering diberi variabel ''x''), lebar (''y''), dan kedalaman (''z''). Lebih dari dua ribu tahun yang lalu, filsuf-filsuf Yunani mengeksplorasi secara rinci banyak implikasi dari keseragaman konsep 3D tersebut, yang berpuncak pada ''[[Elemen Euklides|Elemen]]'' ''[[Euklides]]''. Namun, hingga sesaat sebelum dimulainya era modern, jarang ada ahli matematika yang pernah menggeneralisasi konsep dimensi yang lebih dari tiga dimensi. Ide menambahkan konsep 4D dimulai oleh [[Joseph-Louis de Lagrange|Joseph-Louis Lagrange]] pada pertengahan tahun 1700-an dan memuncak dalam yang formalisasi konsep yang tepat pada tahun 1854 oleh [[Georg Friedrich Bernhard Riemann|Bernhard Riemann]]. Pada tahun 1880 Charles Howard Hinton memopulerkan wawasan ini dalam sebuah esai yang berjudul ''[[wikisource:What is the Fourth Dimension?|What is the Fourth Dimension?]]'', yang perlu diperhatikan untuk menjelaskan konsep kubus empat dimensi dengan melalui generalisasi langkah demi langkah dari sifat-sifat garis, kotak, dan batu. Bentuk yang paling sederhana dari metode Hinton adalah penggambaran dua biasa kubus dipisahkan oleh jarak "tak terlihat", dan kemudian menarik garis di antara simpul ekuivalen mereka. Bentuk ini dapat dilihat pada animasi yang menyertainya kapanpun animasi itu menunjukkan sebuah kubus yang lebih kecil di dalam sebuah kubus yang lebih besar. Delapan garis yang menghubungkan simpul-simpul dari dua kubus dalam hal ini mewakili suatu arah pada ruang 4D "tak terlihat". Dimensi ruang yang lebih tinggi, sejak itu, telah menjadi salah satu dasar untuk menyatakan matematika dan fisika modern secara formal. Bagian besar dari topik-topik ini tidak ada dalam bentuk mereka saat ini tanpa menggunakan ruang tersebut. Untuk orang yang pertama kali belajar tentang 4D dan ruang yang lebih tinggi, hal ini membantu untuk mengingat bahwa ruang 4D, hanya menambahkan satu indikator pada tiga indikator lain yang telah diketahui, dan bahwa indikator ini dapat mewakili banyak hal yang berbeda. Entri kalender, misalnya, biasanya merupakan lokasi 4D, seperti rapat pada waktu ''t'' di persimpangan dua jalan (''x'' dan ''y'') pada beberapa lantai bangunan (''z''). Dalam bentuk daftar pertemuan tersebut berlangsung di 4 lokasi (''t'',''x'',''y'',''z''). Konsep [[ruang waktu]] [[Einstein]] menggunakan konsep ruang seperti 4D, meskipun pada konsep Enstein terdapat struktur [[Ruang Minkowski|Minkowski]] yang sedikit lebih rumit dari konsep 4D [[Geometri Euklides|Euklides]]. Ketika dimensi lokasi yang diberikan seperti daftar indikator teratur seperti ''(t,x,y,z)'' mereka disebut [[Ruang vektor|vektor]] atau n-tupel. Hal ini hanya ketika lokasi tersebut dihubungkan bersama-sama dalam bentuk lebih rumit yang mana kekayaan penuh dan kompleksitas geometris dari ruang 4D dan ruang yang lebih tinggi muncul. Sebuah petunjuk bahwa kompleksitas dapat dilihat pada animasi yang menyertainya dari salah satu objek 4D yang mungkin dan paling sederhana, kubus 4D atau tesseract. {{Topik dimensi}} {{Commonscat|4D}} [[Kategori:Dimensi]] [[Kategori:Relativitas khusus]] </textarea><div class="templatesUsed"><div class="mw-templatesUsedExplanation"><p>Templat yang digunakan di halaman ini: </p></div><ul> <li><a href="/wiki/Templat:Ambox" title="Templat:Ambox">Templat:Ambox</a> (<a href="/w/index.php?title=Templat:Ambox&action=edit" title="Templat:Ambox">lihat sumber</a>) (dilindungi)</li><li><a href="/wiki/Templat:C" title="Templat:C">Templat:C</a> (<a href="/w/index.php?title=Templat:C&action=edit" title="Templat:C">sunting</a>) </li><li><a href="/wiki/Templat:Commons_category" title="Templat:Commons category">Templat:Commons category</a> (<a href="/w/index.php?title=Templat:Commons_category&action=edit" title="Templat:Commons category">lihat sumber</a>) (dilindungi)</li><li><a 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