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Wajib.","2026-10-08T09:24:41.433Z",{"id":297,"subjectId":15,"levelId":55,"parentId":98,"slug":1455,"name":1456,"description":1457,"order":1458,"createdAt":1459,"updatedAt":1459},"matriks","Matriks","Matriks — Kelas 11 Lanjut.",13,"2026-10-08T09:24:41.441Z",{"id":1461,"subjectId":24,"levelId":55,"parentId":98,"slug":1462,"name":1463,"description":1464,"order":1458,"createdAt":1465,"updatedAt":1465},"cmuzbyhhz003k71r9s7s8evk1","rangkaian-pegas","Rangkaian Pegas","Rangkaian Pegas — Kelas 11.","2026-10-08T09:24:41.111Z",{"id":159,"subjectId":24,"levelId":55,"parentId":98,"slug":1467,"name":1468,"description":1469,"order":1470,"createdAt":1471,"updatedAt":1471},"fluida","Fluida","Fluida — Kelas 11.",14,"2026-10-08T09:24:41.113Z",{"id":273,"subjectId":15,"levelId":55,"parentId":98,"slug":1473,"name":1474,"description":1475,"order":1470,"createdAt":1476,"updatedAt":1476},"polinomial","Polinomial","Polinomial — Kelas 11 Lanjut.","2026-10-08T09:24:41.454Z",{"id":189,"subjectId":15,"levelId":55,"parentId":98,"slug":1478,"name":1479,"description":1480,"order":1481,"createdAt":1482,"updatedAt":1482},"fungsi-trigonometri","Fungsi Trigonometri","Fungsi Trigonometri — Kelas 11 Lanjut.",15,"2026-10-08T09:24:41.469Z",{"id":183,"subjectId":24,"levelId":55,"parentId":98,"slug":1484,"name":1485,"description":1486,"order":1481,"createdAt":1487,"updatedAt":1487},"gerak-harmonik-sederhana-ghs","Gerak Harmonik Sederhana (GHS)","Gerak Harmonik Sederhana (GHS) — Kelas 11.","2026-10-08T09:24:41.119Z",{"id":213,"subjectId":24,"levelId":55,"parentId":98,"slug":1489,"name":1490,"description":1491,"order":1492,"createdAt":1493,"updatedAt":1493},"gelombang-mekanik","Gelombang Mekanik","Gelombang Mekanik — Kelas 11.",16,"2026-10-08T09:24:41.132Z",{"id":279,"subjectId":15,"levelId":55,"parentId":98,"slug":1248,"name":1249,"description":1495,"order":1492,"createdAt":1496,"updatedAt":1496},"Vektor — Kelas 11 Lanjut.","2026-10-08T09:24:41.485Z",{"id":135,"subjectId":24,"levelId":55,"parentId":98,"slug":1498,"name":1499,"description":1500,"order":1501,"createdAt":1502,"updatedAt":1502},"gelombang-cahaya","Gelombang Cahaya","Gelombang Cahaya — Kelas 11.",17,"2026-10-08T09:24:41.150Z",{"id":219,"subjectId":15,"levelId":55,"parentId":98,"slug":1504,"name":1505,"description":1506,"order":1501,"createdAt":1507,"updatedAt":1507},"transformasi-geometri","Transformasi Geometri","Transformasi Geometri — Kelas 11 Lanjut.","2026-10-08T09:24:41.498Z",{"id":165,"subjectId":15,"levelId":55,"parentId":98,"slug":1509,"name":1510,"description":1511,"order":1512,"createdAt":1513,"updatedAt":1513},"fungsi-dan-pemodelannya","Fungsi dan Pemodelannya","Fungsi dan Pemodelannya — Kelas 11 Lanjut.",18,"2026-10-08T09:24:41.504Z",{"id":201,"subjectId":24,"levelId":55,"parentId":98,"slug":1515,"name":1516,"description":1517,"order":1512,"createdAt":1518,"updatedAt":1518},"optik","Optik","Optik — Kelas 11.","2026-10-08T09:24:41.161Z",{"id":75,"subjectId":15,"levelId":55,"parentId":98,"slug":1520,"name":83,"description":1521,"order":1522,"createdAt":1523,"updatedAt":1523},"barisan-dan-deret-kelas-12-wajib","Barisan dan Deret — Kelas 12 Wajib.",19,"2026-10-08T09:24:41.512Z",{"id":374,"subjectId":24,"levelId":55,"parentId":98,"slug":1525,"name":1526,"description":1527,"order":1522,"createdAt":1528,"updatedAt":1528},"suhu-dan-kalor","Suhu dan Kalor","Suhu dan Kalor — Kelas 11.","2026-10-08T09:24:41.169Z",{"id":105,"subjectId":15,"levelId":55,"parentId":98,"slug":1530,"name":1531,"description":1532,"order":1533,"createdAt":1534,"updatedAt":1534},"bunga","Bunga","Bunga — Kelas 12 Wajib.",20,"2026-10-08T09:24:41.518Z",{"id":171,"subjectId":24,"levelId":55,"parentId":98,"slug":1536,"name":1537,"description":1538,"order":1533,"createdAt":1539,"updatedAt":1539},"teori-kinetik-gas","Teori Kinetik Gas","Teori Kinetik Gas — Kelas 11.","2026-10-08T09:24:41.188Z",{"id":380,"subjectId":15,"levelId":55,"parentId":98,"slug":1541,"name":1542,"description":1543,"order":1544,"createdAt":1545,"updatedAt":1545},"investasi-dan-pinjaman","Investasi dan Pinjaman","Investasi dan Pinjaman — Kelas 12 Wajib.",21,"2026-10-08T09:24:41.525Z",{"id":398,"subjectId":24,"levelId":55,"parentId":98,"slug":1547,"name":1548,"description":1549,"order":1544,"createdAt":1550,"updatedAt":1550},"termodinamika","Termodinamika","Termodinamika — Kelas 11.","2026-10-08T09:24:41.202Z",{"id":326,"subjectId":15,"levelId":55,"parentId":98,"slug":1552,"name":1553,"description":1554,"order":1555,"createdAt":1556,"updatedAt":1556},"kaidah-pencacahan","Kaidah Pencacahan","Kaidah Pencacahan — Kelas 12 Wajib.",22,"2026-10-08T09:24:41.540Z",{"id":267,"subjectId":24,"levelId":55,"parentId":98,"slug":1558,"name":1559,"description":1560,"order":1555,"createdAt":1561,"updatedAt":1561},"listrik-statis","Listrik Statis","Listrik Statis — Kelas 12.","2026-10-08T09:24:41.215Z",{"id":237,"subjectId":24,"levelId":55,"parentId":98,"slug":1563,"name":1564,"description":1565,"order":1566,"createdAt":1567,"updatedAt":1567},"listrik-arus-searah","Listrik Arus Searah","Listrik Arus Searah — Kelas 12.",23,"2026-10-08T09:24:41.227Z",{"id":285,"subjectId":15,"levelId":55,"parentId":98,"slug":1569,"name":1418,"description":1570,"order":1566,"createdAt":1571,"updatedAt":1571},"peluang-kelas-12-wajib","Peluang — Kelas 12 Wajib.","2026-10-08T09:24:41.547Z",{"id":249,"subjectId":15,"levelId":55,"parentId":98,"slug":1573,"name":1574,"description":1575,"order":1576,"createdAt":1577,"updatedAt":1577},"geometri-analitik","Geometri Analitik","Geometri Analitik — Kelas 12 Lanjut.",24,"2026-10-08T09:24:41.553Z",{"id":243,"subjectId":24,"levelId":55,"parentId":98,"slug":1579,"name":1580,"description":1581,"order":1576,"createdAt":1582,"updatedAt":1582},"kemagnetan","Kemagnetan","Kemagnetan — Kelas 12.","2026-10-08T09:24:41.245Z",{"id":117,"subjectId":15,"levelId":55,"parentId":98,"slug":1584,"name":1585,"description":1586,"order":1587,"createdAt":1588,"updatedAt":1588},"limit","Limit","Limit — Kelas 12 Lanjut.",25,"2026-10-08T09:24:41.562Z",{"id":68,"subjectId":24,"levelId":55,"parentId":98,"slug":1590,"name":1591,"description":1592,"order":1587,"createdAt":1593,"updatedAt":1593},"listrik-ac-arus-bolak-balik","Listrik AC \u002F Arus Bolak Balik","Listrik AC \u002F Arus Bolak Balik — Kelas 12.","2026-10-08T09:24:41.263Z",{"id":308,"subjectId":24,"levelId":55,"parentId":98,"slug":1595,"name":1596,"description":1597,"order":1598,"createdAt":1599,"updatedAt":1599},"gelombang-elektromagnetik","Gelombang Elektromagnetik","Gelombang Elektromagnetik — Kelas 12.",26,"2026-10-08T09:24:41.273Z",{"id":123,"subjectId":15,"levelId":55,"parentId":98,"slug":1601,"name":1602,"description":1603,"order":1598,"createdAt":1604,"updatedAt":1604},"turunan-fungsi","Turunan Fungsi","Turunan Fungsi — Kelas 12 Lanjut.","2026-10-08T09:24:41.575Z",{"id":332,"subjectId":15,"levelId":55,"parentId":98,"slug":1606,"name":1607,"description":1608,"order":1609,"createdAt":1610,"updatedAt":1610},"aplikasi-turunan","Aplikasi Turunan","Aplikasi Turunan — Kelas 12 Lanjut.",27,"2026-10-08T09:24:41.587Z",{"id":362,"subjectId":24,"levelId":55,"parentId":98,"slug":1612,"name":1613,"description":1614,"order":1609,"createdAt":1615,"updatedAt":1615},"pengantar-instrumental-digital","Pengantar Instrumental Digital","Pengantar Instrumental Digital — Kelas 12.","2026-10-08T09:24:41.283Z",{"id":207,"subjectId":15,"levelId":55,"parentId":98,"slug":1617,"name":1618,"description":1619,"order":1620,"createdAt":1621,"updatedAt":1621},"integral","Integral","Integral — Kelas 12 Lanjut.",28,"2026-10-08T09:24:41.599Z",{"id":350,"subjectId":24,"levelId":55,"parentId":98,"slug":1623,"name":1624,"description":1625,"order":1620,"createdAt":1626,"updatedAt":1626},"relativitas-khusus","Relativitas Khusus","Relativitas Khusus — Kelas 12.","2026-10-08T09:24:41.291Z",{"id":356,"subjectId":24,"levelId":55,"parentId":98,"slug":1628,"name":1629,"description":1630,"order":1631,"createdAt":1632,"updatedAt":1632},"gejala-kuantum","Gejala Kuantum","Gejala Kuantum — Kelas 12.",29,"2026-10-08T09:24:41.303Z",{"id":255,"subjectId":15,"levelId":55,"parentId":98,"slug":1634,"name":1635,"description":1636,"order":1631,"createdAt":1637,"updatedAt":1637},"penerapan-integral","Penerapan Integral","Penerapan Integral — Kelas 12 Lanjut.","2026-10-08T09:24:41.607Z",{"id":147,"subjectId":15,"levelId":55,"parentId":98,"slug":1639,"name":1640,"description":1641,"order":1642,"createdAt":1643,"updatedAt":1643},"analisis-data-peluang","Analisis Data & Peluang","Analisis Data & Peluang — Kelas 12 Lanjut.",30,"2026-10-08T09:24:41.611Z",{"id":291,"subjectId":24,"levelId":55,"parentId":98,"slug":1645,"name":1646,"description":1647,"order":1642,"createdAt":1648,"updatedAt":1648},"fisika-inti-dan-radioaktivitas","Fisika Inti dan Radioaktivitas","Fisika Inti dan Radioaktivitas — Kelas 12.","2026-10-08T09:24:41.318Z",{"id":1650,"subjectId":15,"levelId":55,"parentId":98,"slug":1651,"name":1652,"description":1653,"order":1654,"createdAt":1655,"updatedAt":1655},"cmuzbyhw700gw71r9o87lq7vd","logaritma","Logaritma","Logaritma — Kelas 12 Lanjut.",31,"2026-10-08T09:24:41.623Z",{"id":1657,"subjectId":15,"levelId":55,"parentId":98,"slug":1658,"name":1659,"description":1660,"order":1661,"createdAt":1662,"updatedAt":1662},"cmuzbyhw900gy71r9d9sjh9ie","program-linier","Program Linier","Program Linier — Kelas 12 Lanjut.",32,"2026-10-08T09:24:41.625Z",{"id":1664,"subjectId":15,"levelId":55,"parentId":98,"slug":1665,"name":1666,"description":1667,"order":1668,"createdAt":1669,"updatedAt":1669},"cmuzbyhwb00h071r97764r7hr","bangun-ruang","Bangun Ruang","Bangun Ruang — Kelas 12 Lanjut.",33,"2026-10-08T09:24:41.627Z",{"id":1671,"subjectId":15,"levelId":60,"parentId":98,"slug":1672,"name":125,"description":1673,"order":1674,"createdAt":1675,"updatedAt":1675},"demo-v2-topic-matematika-kuliah-1","definisi-turunan-limit","Definisi turunan dengan limit f′(x) = lim [f(x+h) − f(x)]\u002Fh, langkah menghitungnya, gradien garis singgung, syarat diferensiabel, dan contoh soal.",100,"2026-10-14T16:01:44.645Z",{"id":1677,"subjectId":15,"levelId":55,"parentId":98,"slug":1678,"name":1679,"description":1680,"order":1674,"createdAt":1681,"updatedAt":1681},"demo-v2-topic-matematika-sma-1","fungsi-kuadrat","Fungsi Kuadrat","Fungsi kuadrat f(x) = ax² + bx + c: pengaruh a, b, c pada grafik, rumus titik puncak, sumbu simetri, diskriminan, dan contoh soal nilai maksimum.","2026-10-14T16:01:44.503Z",{"id":1683,"subjectId":33,"levelId":55,"parentId":98,"slug":1684,"name":1685,"description":1686,"order":1674,"createdAt":1687,"updatedAt":1687},"demo-v2-topic-pemrograman-sma-1","fungsi-python-def-return","Fungsi Python","Pelajari cara membuat fungsi Python dengan def, parameter, nilai default, dan return, plus perbedaan return dan print lewat contoh program yang jelas.","2026-10-14T16:01:45.616Z",{"id":1689,"subjectId":24,"levelId":49,"parentId":98,"slug":1690,"name":1691,"description":1692,"order":1674,"createdAt":1693,"updatedAt":1693},"demo-v2-topic-fisika-smp-1","glb-dan-glbb","GLB dan GLBB","Rumus GLB dan GLBB lengkap: jarak, kecepatan, percepatan, grafik posisi–waktu, perbedaan GLB dan GLBB, plus contoh soal gerak lurus dan pembahasannya.","2026-10-14T16:01:44.924Z",{"id":1695,"subjectId":24,"levelId":60,"parentId":98,"slug":1696,"name":1697,"description":1698,"order":1674,"createdAt":1699,"updatedAt":1699},"demo-v2-topic-fisika-kuliah-1","gerak-harmonik-sederhana","Gerak Harmonik Sederhana","Gerak harmonik sederhana untuk fisika dasar: persamaan x = A cos(ωt + φ), kecepatan, percepatan, periode pegas dan bandul, energi, serta contoh soal.","2026-10-14T16:01:45.223Z",{"id":1701,"subjectId":24,"levelId":55,"parentId":98,"slug":1702,"name":1703,"description":1704,"order":1674,"createdAt":1705,"updatedAt":1705},"demo-v2-topic-fisika-sma-1","hukum-newton-2","Hukum Newton 2","Hukum Newton 2: bunyi, rumus ΣF = m·a, diagram gaya, gaya gesek statis dan kinetis, serta contoh soal mencari percepatan dan massa beserta pembahasan.","2026-10-14T16:01:45.084Z",{"id":1707,"subjectId":33,"levelId":60,"parentId":98,"slug":1708,"name":1709,"description":1710,"order":1674,"createdAt":1711,"updatedAt":1711},"demo-v2-topic-pemrograman-kuliah-1","notasi-big-o-kompleksitas-waktu","Notasi Big O","Pahami notasi Big O dan kompleksitas waktu algoritma: O(1), O(log n), O(n), O(n²), cara menghitungnya dari kode Python, dan contoh soalnya.","2026-10-14T16:01:45.769Z",{"id":1713,"subjectId":33,"levelId":43,"parentId":98,"slug":1714,"name":1715,"description":1716,"order":1674,"createdAt":1717,"updatedAt":1717},"demo-v2-topic-pemrograman-sd-1","pengertian-algoritma","Pengertian Algoritma","Algoritma adalah langkah-langkah urut untuk menyelesaikan masalah. Pelajari pengertian, ciri, dan contoh algoritma sehari-hari untuk siswa SD.","2026-10-14T16:01:45.355Z",{"id":1719,"subjectId":24,"levelId":43,"parentId":98,"slug":1720,"name":1721,"description":1722,"order":1674,"createdAt":1723,"updatedAt":1723},"demo-v2-topic-fisika-sd-1","pengukuran-panjang","Pengukuran Panjang","Belajar pengukuran panjang untuk SD: satuan baku, alat ukur panjang, cara memakai penggaris, dan tangga satuan panjang km sampai mm + contoh soal.","2026-10-14T16:01:44.803Z",{"id":1725,"subjectId":15,"levelId":43,"parentId":98,"slug":1726,"name":1727,"description":1728,"order":1674,"createdAt":1729,"updatedAt":1729},"demo-v2-topic-matematika-sd-1","penjumlahan-pecahan","Penjumlahan Pecahan","Cara penjumlahan pecahan berpenyebut sama dan beda penyebut memakai KPK, pecahan senilai, dan pecahan campuran, lengkap dengan contoh soal SD.","2026-10-14T16:01:44.034Z",{"id":1731,"subjectId":15,"levelId":49,"parentId":98,"slug":1732,"name":1733,"description":1734,"order":1674,"createdAt":1735,"updatedAt":1735},"demo-v2-topic-matematika-smp-1","teorema-pythagoras","Teorema Pythagoras","Teorema Pythagoras a² + b² = c² untuk mencari sisi miring dan sisi siku-siku, tripel Pythagoras, diagonal ruang balok, dan contoh soal kelas 8.","2026-10-14T16:01:44.305Z",{"id":1737,"subjectId":33,"levelId":49,"parentId":98,"slug":1738,"name":1739,"description":1740,"order":1674,"createdAt":1741,"updatedAt":1741},"demo-v2-topic-pemrograman-smp-1","variabel-dan-tipe-data-python","Variabel dan Tipe Data Python","Belajar variabel dan tipe data Python dari nol: int, float, string, boolean, operator, print, dan input, lengkap dengan contoh program dan latihan.","2026-10-14T16:01:45.472Z",{"id":1743,"subjectId":33,"levelId":60,"parentId":98,"slug":1744,"name":1745,"description":1746,"order":1747,"createdAt":1748,"updatedAt":1748},"demo-v2-topic-pemrograman-kuliah-2","class-dan-object-python","Class dan Object Python","Pelajari class dan object Python untuk OOP: __init__, self, atribut, method, inheritance, dan invarian objek lewat contoh program dompet digital.",101,"2026-10-14T16:01:45.800Z",{"id":1750,"subjectId":15,"levelId":55,"parentId":98,"slug":1751,"name":1752,"description":1753,"order":1747,"createdAt":1754,"updatedAt":1754},"demo-v2-topic-matematika-sma-2","eksponen-dan-logaritma","Eksponen dan Logaritma","Materi eksponen dan logaritma kelas 10: sifat-sifat eksponen, definisi dan sifat logaritma, persamaan eksponen dan logaritma, serta contoh soal.","2026-10-14T16:01:44.555Z",{"id":1756,"subjectId":24,"levelId":43,"parentId":98,"slug":1757,"name":1758,"description":1759,"order":1747,"createdAt":1760,"updatedAt":1760},"demo-v2-topic-fisika-sd-2","macam-macam-gaya","Gaya dan Macam-Macamnya","Gaya adalah tarikan atau dorongan. Pelajari macam-macam gaya (otot, gravitasi, magnet, gesek, pegas), pengaruhnya pada benda, dan contoh soalnya.","2026-10-14T16:01:44.840Z",{"id":1762,"subjectId":15,"levelId":43,"parentId":98,"slug":1763,"name":1764,"description":1765,"order":1747,"createdAt":1766,"updatedAt":1766},"demo-v2-topic-matematika-sd-2","rumus-keliling-dan-luas-bangun-datar","Keliling dan Luas Bangun Datar","Rumus keliling dan luas bangun datar: persegi, persegi panjang, segitiga, jajargenjang, trapesium, dan lingkaran, dengan cara mudah dan contoh soal.","2026-10-14T16:01:44.140Z",{"id":1768,"subjectId":33,"levelId":55,"parentId":98,"slug":1769,"name":1770,"description":1771,"order":1747,"createdAt":1772,"updatedAt":1772},"demo-v2-topic-pemrograman-sma-2","list-dan-dictionary-python","List dan Dictionary Python","Pahami list dan dictionary Python: indeks, append, key-value, get, dan perulangan, plus perbedaan keduanya lewat contoh pengolahan data nilai siswa.","2026-10-14T16:01:45.659Z",{"id":1774,"subjectId":24,"levelId":49,"parentId":98,"slug":1775,"name":1776,"description":1777,"order":1747,"createdAt":1778,"updatedAt":1778},"demo-v2-topic-fisika-smp-2","rumus-massa-jenis","Massa Jenis","Rumus massa jenis ρ = m\u002FV lengkap dengan satuan kg\u002Fm³ dan g\u002Fcm³, tabel massa jenis air, besi, dan minyak, cara menghitung, serta contoh soal pembahasan.","2026-10-14T16:01:44.967Z",{"id":1780,"subjectId":33,"levelId":49,"parentId":98,"slug":1781,"name":1782,"description":1783,"order":1747,"createdAt":1784,"updatedAt":1784},"demo-v2-topic-pemrograman-smp-2","percabangan-python-if-else","Percabangan Python","Pelajari percabangan Python dengan if, elif, dan else: operator perbandingan, operator logika, dan contoh program nilai rapor lengkap dengan outputnya.","2026-10-14T16:01:45.518Z",{"id":1786,"subjectId":33,"levelId":43,"parentId":98,"slug":1787,"name":1788,"description":1789,"order":1747,"createdAt":1790,"updatedAt":1790},"demo-v2-topic-pemrograman-sd-2","percabangan-dalam-algoritma","Percabangan dalam Algoritma","Percabangan dalam algoritma memilih tindakan berdasarkan syarat jika-maka. Pelajari pengertian, contoh sehari-hari, dan simbol flowchart-nya.","2026-10-14T16:01:45.408Z",{"id":1792,"subjectId":15,"levelId":49,"parentId":98,"slug":1793,"name":1794,"description":1795,"order":1747,"createdAt":1796,"updatedAt":1796},"demo-v2-topic-matematika-smp-2","persamaan-garis-lurus","Persamaan Garis Lurus","Persamaan garis lurus y = mx + c, rumus gradien dari dua titik, garis sejajar dan tegak lurus, cara menggambar grafik, serta contoh soal kelas 8.","2026-10-14T16:01:44.363Z",{"id":1798,"subjectId":24,"levelId":60,"parentId":98,"slug":1799,"name":1800,"description":1801,"order":1747,"createdAt":1802,"updatedAt":1802},"demo-v2-topic-fisika-kuliah-2","usaha-oleh-gaya-berubah","Usaha Gaya Berubah","Usaha oleh gaya berubah dengan integral W = ∫F dx, rumus usaha W = F·s sebagai dot product, usaha pegas, dan teorema usaha–energi, plus contoh soal.","2026-10-14T16:01:45.258Z",{"id":1804,"subjectId":15,"levelId":55,"parentId":98,"slug":1805,"name":1806,"description":1807,"order":1808,"createdAt":1809,"updatedAt":1809},"demo-v2-topic-matematika-sma-3","rumus-peluang","Peluang Kejadian","Rumus peluang P(A) = n(A)\u002Fn(S), ruang sampel, peluang komplemen, frekuensi harapan, kejadian saling lepas dan saling bebas, plus contoh soal dadu dan koin.",102,"2026-10-14T16:01:44.588Z",{"id":1811,"subjectId":33,"levelId":55,"parentId":98,"slug":1812,"name":1813,"description":1814,"order":1808,"createdAt":1815,"updatedAt":1815},"demo-v2-topic-pemrograman-sma-3","pencarian-linear-dan-biner","Pencarian Linear dan Biner","Pelajari pencarian linear dan pencarian biner (binary search): cara kerja, syarat data terurut, kode Python, dan perbandingan jumlah langkahnya.","2026-10-14T16:01:45.700Z",{"id":1817,"subjectId":33,"levelId":49,"parentId":98,"slug":1818,"name":1819,"description":1820,"order":1808,"createdAt":1821,"updatedAt":1821},"demo-v2-topic-pemrograman-smp-3","perulangan-python-for-while","Perulangan Python","Pelajari perulangan Python dengan for, range(), dan while, lengkap dengan contoh program menghitung total, break, continue, dan latihan soal.","2026-10-14T16:01:45.560Z",{"id":1823,"subjectId":33,"levelId":43,"parentId":98,"slug":1824,"name":1825,"description":1826,"order":1808,"createdAt":1827,"updatedAt":1827},"demo-v2-topic-pemrograman-sd-3","perulangan-dalam-algoritma","Perulangan dalam Algoritma","Perulangan dalam algoritma mengulang langkah yang sama beberapa kali. Pelajari pengertian, contoh perulangan sehari-hari, dan cara menghitung hasilnya.","2026-10-14T16:01:45.436Z",{"id":1829,"subjectId":15,"levelId":49,"parentId":98,"slug":1830,"name":1831,"description":1832,"order":1808,"createdAt":1833,"updatedAt":1833},"demo-v2-topic-matematika-smp-3","rumus-prisma-dan-limas","Prisma dan Limas","Rumus volume prisma dan limas, luas permukaan, sifat sisi-rusuk-titik sudut, jaring-jaring, limas 3D interaktif, dan contoh soal bangun ruang sisi datar.","2026-10-14T16:01:44.400Z",{"id":1835,"subjectId":33,"levelId":60,"parentId":98,"slug":1836,"name":1837,"description":1838,"order":1808,"createdAt":1839,"updatedAt":1839},"demo-v2-topic-pemrograman-kuliah-3","unit-test-python","Unit Test Python","Pelajari unit test Python dengan modul unittest: assertEqual, assertRaises, nilai batas, dan cara menjalankan tes, lengkap dengan contoh dan versi pytest.","2026-10-14T16:01:45.832Z",{"id":1841,"subjectId":15,"levelId":60,"parentId":98,"slug":1842,"name":1843,"description":1844,"order":1808,"createdAt":1845,"updatedAt":1845},"demo-v2-topic-matematika-kuliah-3","vektor-3-dimensi-dot-product","Vektor 3D dan Dot Product","Vektor 3 dimensi: komponen, panjang vektor, vektor satuan, dot product atau perkalian titik, sudut antara dua vektor, proyeksi, dan contoh soal.","2026-10-14T16:01:44.715Z",{"id":1847,"subjectId":15,"levelId":43,"parentId":98,"slug":1848,"name":1849,"description":1850,"order":1808,"createdAt":1851,"updatedAt":1851},"demo-v2-topic-matematika-sd-3","rumus-volume-kubus","Volume dan Luas Permukaan Kubus","Rumus volume kubus V = s³ dan luas permukaan kubus L = 6s², sifat kubus, jaring-jaring, kubus 3D interaktif, dan contoh soal bertingkat.","2026-10-14T16:01:44.189Z",{"id":1853,"subjectId":15,"levelId":49,"parentId":98,"slug":1854,"name":1855,"description":1856,"order":1857,"createdAt":1858,"updatedAt":1858},"demo-v2-topic-matematika-smp-4","rumus-tabung-dan-kerucut","Tabung dan Kerucut","Rumus volume tabung dan kerucut, luas permukaan, garis pelukis, jaring-jaring berupa persegi panjang dan juring, kerucut 3D interaktif, dan contoh soal.",103,"2026-10-14T16:01:44.438Z",{"id":1860,"subjectId":33,"levelId":55,"parentId":98,"slug":1861,"name":1862,"description":1863,"order":1857,"createdAt":1864,"updatedAt":1864},"demo-v2-topic-pemrograman-sma-4","try-except-python","Try Except dan Membaca File","Pelajari try except Python untuk menangani error seperti ValueError dan FileNotFoundError, serta cara membaca dan menulis file txt dengan with open.","2026-10-14T16:01:45.731Z",{"id":1866,"subjectId":15,"levelId":43,"parentId":98,"slug":1867,"name":1868,"description":1869,"order":1857,"createdAt":1870,"updatedAt":1870},"demo-v2-topic-matematika-sd-4","rumus-volume-balok","Volume dan Luas Permukaan Balok","Rumus volume balok V = p × l × t dan luas permukaan balok L = 2(pl + pt + lt), sifat balok, jaring-jaring, balok 3D interaktif, dan contoh soal.","2026-10-14T16:01:44.239Z",[1872,1875,1880,1885],{"id":1873,"slug":25,"name":26,"createdAt":1874},"cmvogd3r1000607tdh34zf0vv","2026-10-25T23:22:15.997Z",{"id":1876,"slug":1877,"name":1878,"createdAt":1879},"cmvogctp7000507tdmugcad1g","fisika-statistik","Fisika Statistik","2026-10-25T23:22:02.971Z",{"id":1881,"slug":1882,"name":1883,"createdAt":1884},"cmvhrhrvm00027m1risodrm04","onmipa","ONMIPA","2026-10-21T06:59:26.435Z",{"id":1886,"slug":1887,"name":1887,"createdAt":1888},"cmvhrhm2s00017m1rpjm53zrv","tag","2026-10-21T06:59:18.917Z",{"id":1890,"type":1891,"slug":1892,"title":1893,"excerpt":1894,"coverUrl":98,"status":1895,"publishedAt":1896,"featured":4,"subjectId":15,"blocks":1897,"seoTitle":98,"seoDescription":98,"readingMinutes":1403,"order":21,"hiddenFromOthers":4,"createdAt":1957,"updatedAt":1958,"subject":1959,"levels":1960,"topics":1963,"tags":1966,"lang":1967,"alternates":1968,"author":1970,"resolved":1975,"related":2089,"sequence":98},"cmvxe4god001r07scxrwi3yjn","ARTICLE","hipotesis-riemann-kuasi-bilangan-prima-ai-2026","Hipotesis Riemann dan Bilangan Prima: Terobosan AI 2026","Apa itu hipotesis Riemann dan versi kuasi yang dibuktikan AI OpenAI pada 2026? Penjelasan bilangan prima, fungsi zeta, dan pita kritis dengan contoh.","PUBLISHED","2026-11-01T05:35:03.077Z",[1898,1903,1907,1911,1915,1922,1926,1930,1937,1941,1945,1949,1953],{"id":1899,"data":1900,"type":1902},"ai0b274237b7",{"markdown":1901},"Pada 6 Oktober 2026, OpenAI merilis 722 makalah pracetak matematika yang dihasilkan model AI internalnya. Salah satunya langsung jadi bahan perbincangan: bukti **hipotesis kuasi-Riemann**, yaitu versi yang lebih lemah dari hipotesis Riemann, soal terbuka paling terkenal tentang bilangan prima. Hipotesis Riemann sendiri belum terpecahkan. Yang dibuktikan adalah bahwa semua \"nol\" penting fungsi zeta Riemann pasti berada di dalam pita yang lebih sempit daripada yang selama ini diketahui. Artikel ini menjelaskan apa artinya, langkah demi langkah, mulai dari bilangan prima.","text",{"id":1904,"data":1905,"type":1902},"aib2179cd808",{"markdown":1906},"## Apa Hubungan Bilangan Prima dengan Hipotesis Riemann?\n\nBilangan prima adalah bilangan asli lebih dari 1 yang hanya habis dibagi 1 dan dirinya sendiri: 2, 3, 5, 7, 11, dan seterusnya. Semakin besar bilangannya, prima semakin jarang. Pertanyaannya: *seberapa cepat* prima menjadi jarang?\n\nJawaban kasarnya diberikan oleh **teorema bilangan prima**, yang dibuktikan secara terpisah oleh Jacques Hadamard dan Charles de la Vallée Poussin pada 1896. Jika $\\pi(x)$ menyatakan banyaknya bilangan prima yang kurang dari atau sama dengan $x$, maka\n\n$$\\pi(x) \\sim \\frac{x}{\\ln x}$$\n\nTanda $\\sim$ berarti perbandingan kedua ruas makin mendekati 1 ketika $x$ makin besar. Akibatnya, peluang sebuah bilangan acak di sekitar $x$ merupakan bilangan prima kira-kira $\\dfrac{1}{\\ln x}$.\n\nRumus ini hanya rata-rata. Banyaknya prima yang sebenarnya selalu berfluktuasi di sekitar kurva tersebut. Hipotesis Riemann adalah pernyataan tentang **seberapa besar** fluktuasi itu bisa terjadi.",{"id":1908,"data":1909,"type":1902},"ai2af3821598",{"markdown":1910},"## Contoh Perhitungan: Seberapa Akurat x\u002Fln x?\n\nMari uji rumus di atas untuk $x = 1.000$. Dengan menghitung langsung (misalnya memakai saringan Eratosthenes), ada tepat 168 bilangan prima yang tidak lebih dari 1.000, jadi $\\pi(1.000) = 168$.\n\nLangkah 1, hitung logaritma natural:\n\n$$\\ln 1.000 \\approx 6{,}9078$$\n\nLangkah 2, hitung perkiraannya:\n\n$$\\frac{1.000}{6{,}9078} \\approx 144{,}8$$\n\nLangkah 3, bandingkan: $\\dfrac{168}{144{,}8} \\approx 1{,}16$. Perkiraannya meleset sekitar 14% dari nilai sebenarnya.\n\nCek: $144{,}8 \\times 6{,}9078 \\approx 1.000{,}2$, mendekati 1.000, jadi pembagiannya benar.\n\nTabel berikut memperlihatkan bahwa perbandingannya memang mendekati 1 secara perlahan:\n\n| $x$ | $\\pi(x)$ | $x\u002F\\ln x$ | $\\pi(x) \\div (x\u002F\\ln x)$ |\n|---|---|---|---|\n| 100 | 25 | 21,7 | 1,151 |\n| 1.000 | 168 | 144,8 | 1,161 |\n| 10.000 | 1.229 | 1.085,7 | 1,132 |\n| 100.000 | 9.592 | 8.685,9 | 1,104 |\n| 1.000.000 | 78.498 | 72.382,4 | 1,085 |\n\nKamu bisa membuat tabel ini sendiri dengan program Python pendek:\n\n~~~python\nimport math\n\ndef hitung_prima(n):\n    \"\"\"Saringan Eratosthenes: kembalikan daftar penanda prima 0..n.\"\"\"\n    prima = [True] * (n + 1)\n    prima[0] = prima[1] = False\n    for i in range(2, int(n ** 0.5) + 1):\n        if prima[i]:\n            for kelipatan in range(i * i, n + 1, i):\n                prima[kelipatan] = False\n    return prima\n\nN = 1_000_000\npenanda = hitung_prima(N)\nbanyak = 0\nfor x in range(N + 1):\n    banyak += penanda[x]\n    if x in (100, 1_000, 10_000, 100_000, 1_000_000):\n        perkiraan = x \u002F math.log(x)\n        print(x, banyak, round(perkiraan, 1), round(banyak \u002F perkiraan, 3))\n~~~",{"id":1912,"data":1913,"type":1902},"aic94129419a",{"markdown":1914},"## Fungsi Zeta dan Letak Nol-Nolnya\n\nPada 1859, Bernhard Riemann menunjukkan bahwa cara bilangan prima \"menipis\" dikendalikan oleh sebuah fungsi yang kini disebut **fungsi zeta Riemann**:\n\n$$\\zeta(s) = 1 + \\frac{1}{2^s} + \\frac{1}{3^s} + \\frac{1}{4^s} + \\cdots$$\n\nInput $s$ di sini adalah bilangan kompleks, $s = \\sigma + it$, dengan $\\sigma$ bagian riil dan $t$ bagian imajiner. Deret di atas hanya konvergen bila $\\sigma > 1$, tetapi fungsinya dapat diperluas ke hampir seluruh bidang kompleks.\n\nFungsi zeta bernilai nol di $-2, -4, -6, \\dots$ Nol-nol ini disebut **nol trivial**. Nol lainnya disebut **nol nontrivial**, dan Riemann sudah tahu bahwa semuanya berada di dalam **pita kritis** $0 \\le \\sigma \\le 1$ serta tersusun simetris terhadap garis $\\sigma = \\tfrac{1}{2}$.",{"id":1916,"data":1917,"type":1921},"ai6062bbb7a5",{"title":1918,"variant":1919,"markdown":1920},"Bunyi hipotesis Riemann","info","Semua nol nontrivial fungsi zeta terletak tepat pada **garis kritis** $\\sigma = \\tfrac{1}{2}$, yaitu berbentuk $\\tfrac{1}{2} + it$.","callout",{"id":1923,"data":1924,"type":1902},"aic1bba3a31a",{"markdown":1925},"Tiga nol nontrivial pertama terletak di $\\tfrac{1}{2} \\pm 14{,}135i$, $\\tfrac{1}{2} \\pm 21{,}022i$, dan $\\tfrac{1}{2} \\pm 25{,}011i$. Secara numerik, lebih dari 10 triliun nol pertama sudah diperiksa dan semuanya berada di garis kritis. Namun, pemeriksaan sebanyak apa pun bukan bukti, karena nolnya tak berhingga banyak. Hipotesis ini diajukan sejak 1859 dan termasuk salah satu dari tujuh Masalah Hadiah Milenium dari Clay Mathematics Institute, dengan hadiah US$1 juta.\n\nMengapa letak nol penting? Makin jauh nol bisa menyimpang dari garis $\\tfrac{1}{2}$, makin besar fluktuasi $\\pi(x)$ di sekitar perkiraan rata-ratanya. Bukti teorema bilangan prima pada 1896 justru bertumpu pada fakta bahwa tidak ada nol di tepi pita, yaitu di $\\sigma = 1$.",{"id":1927,"data":1928,"type":1902},"aifdf306676f",{"markdown":1929},"## Apa yang Dibuktikan: Hipotesis Kuasi-Riemann\n\nHipotesis kuasi-Riemann tidak meminta semua nol berada tepat di $\\sigma = \\tfrac{1}{2}$. Cukup dibuktikan bahwa ada bilangan tetap $\\sigma_0 \u003C 1$ sehingga tidak ada nol dengan bagian riil lebih dari $\\sigma_0$. Karena nol tersusun simetris, otomatis tidak ada nol dengan bagian riil kurang dari $1 - \\sigma_0$. Artinya, semua nol nontrivial terkurung di pita\n\n$$1 - \\sigma_0 \\le \\sigma \\le \\sigma_0$$\n\nOpenAI merilis dua versi bukti. Versi bertanggal 30 September 2026 setebal 199 halaman menyatakan $\\sigma_0 = \\tfrac{7}{8}$ dan sudah diverifikasi dengan bahasa pemrograman pembukti Lean. Versi 5 Oktober 2026 setebal 49 halaman membuktikan hasil yang sedikit lebih lemah. Abstraknya menyatakan bahwa setiap fungsi-L Dirichlet, termasuk $\\zeta(s)$, tidak punya nol di setengah bidang $\\operatorname{Re} s > \\tfrac{11}{12}$. Menurut Quanta Magazine, para ahli lebih banyak menelaah versi 11\u002F12 karena lebih pendek, dan hanya makalah inilah yang disunting manusia sebelum dirilis.\n\n### Berapa lebar pita yang tersisa?\n\nLebar pita tempat nol masih mungkin berada adalah $\\sigma_0 - (1 - \\sigma_0) = 2\\sigma_0 - 1$.\n\nUntuk $\\sigma_0 = \\tfrac{11}{12}$:\n\n$$2 \\cdot \\frac{11}{12} - 1 = \\frac{22}{12} - \\frac{12}{12} = \\frac{10}{12} = \\frac{5}{6} \\approx 0{,}833$$\n\nUntuk $\\sigma_0 = \\tfrac{7}{8}$:\n\n$$2 \\cdot \\frac{7}{8} - 1 = \\frac{14}{8} - \\frac{8}{8} = \\frac{6}{8} = \\frac{3}{4} = 0{,}75$$\n\nCek: pita untuk 11\u002F12 berjalan dari $\\tfrac{1}{12}$ sampai $\\tfrac{11}{12}$, dan $\\tfrac{11}{12} - \\tfrac{1}{12} = \\tfrac{10}{12} = \\tfrac{5}{6}$. Hasilnya sama.\n\nSebelumnya, para matematikawan hanya bisa memastikan bahwa nol tidak berada tepat di tepi, tanpa batas tetap seperti ini. Sebagai pembanding, hipotesis Riemann penuh berarti lebar pitanya nol.\n\nCoba aset interaktif di bawah ini. Pilih preset \"1896\", lalu \"7\u002F8\", \"11\u002F12\", dan \"Hipotesis Riemann\", dan perhatikan bagaimana daerah oranye (wilayah yang terbukti bebas nol) melebar dari kedua tepi, sementara nol-nol merah tetap berada di garis tengah.",{"id":1931,"data":1932,"type":1936},"ai5d343401c5",{"height":1933,"assetId":1934,"caption":1935},520,"cmvxe10ag001n07scr4slu3xy","Geser σ₀ atau pilih preset untuk melihat seberapa sempit pita tempat nol fungsi zeta masih mungkin berada.","interactive",{"id":1938,"data":1939,"type":1902},"ai68e1c14be2",{"markdown":1940},"## Mengapa Hasil Ini Dianggap Besar?\n\nBeberapa matematikawan memberi komentar kuat. Jared Duker Lichtman dari Stanford University menyebutnya, dalam terjemahan bebas, \"pencapaian AI untuk matematika yang paling signifikan sejauh ini, dengan selisih yang jauh\". James Maynard dari University of Oxford, peraih Medali Fields, mengatakan kepada *Science* bahwa dalam teori bilangan analitik ini \"jelas hasil utama terbaik selama 100 tahun terakhir\".\n\nAda tiga alasan utama:\n\n1. **Banyak akibatnya.** Maksym Radziwiłł dari New York University menyatakan bahwa sebagian besar konsekuensi hipotesis Riemann sudah mengikuti dari versi kuasi ini.\n2. **Berlaku untuk satu keluarga fungsi.** Hasilnya mencakup fungsi-L Dirichlet, bukan hanya fungsi zeta. Menurut *Science*, ini sekaligus menyingkirkan kemungkinan \"nol Siegel\" yang telah merepotkan para ahli hampir seabad.\n3. **Tanpa konsep baru.** Bukti ini menggabungkan ide-ide lama yang sudah ada, termasuk bentuk metaplektik dan rumus yang dibuktikan Alexander Dunn dan Radziwiłł pada 2021, dengan cara yang tidak terduga.",{"id":1942,"data":1943,"type":1902},"aicfeb640917",{"markdown":1944},"## Apakah Buktinya Sudah Pasti Benar?\n\nBelum sepenuhnya. Para ahli yang menelaahnya sejauh ini umumnya sepakat bahwa hasilnya benar, tetapi Peter Sarnak dari Princeton University menyatakan belum akan menganggapnya \"sebuah teorema\" sebelum manusia memeriksa dan memahami semua detailnya. *Science* melaporkan bahwa OpenAI menarik 3 makalah dan merevisi 14 makalah lain dari kumpulan tersebut, dan dari 719 makalah yang tersisa baru 300 yang diformalkan dalam Lean.\n\nVerifikasi Lean pun bukan jaminan mutlak. Lean memastikan setiap langkah logis membuktikan pernyataan *yang ditulis di kode*, bukan otomatis pernyataan yang diklaim di makalah berbahasa Inggris. Matematikawan Olga Holtz membedakan tiga tahap: hasil yang diklaim, hasil yang diverifikasi secara independen, dan hasil yang sudah dipahami serta menjadi bagian dari budaya matematika.\n\nHipotesis Riemann penuh juga belum terlihat lebih dekat. Will Sawin dari Princeton University menduga kita mungkin akan tetap merasa sejauh sebelumnya dari bukti penuh, meski ia mengaku tidak yakin.",{"id":1946,"data":1947,"type":1902},"ai5c05bff0c2",{"markdown":1948},"## Apa Pelajarannya untuk Pelajar?\n\nKisah ini menunjukkan bahwa konsep yang kamu pelajari di sekolah, seperti bilangan prima, logaritma, deret, dan bilangan kompleks, adalah pintu masuk ke soal-soal terbesar matematika. Kalau ingin menguatkan dasarnya, pelajari dulu [eksponen dan logaritma](\u002Fmateri\u002Feksponen-dan-logaritma), lalu latih logika program lewat [perulangan Python](\u002Fmateri\u002Fperulangan-python-for-while) dan [fungsi Python](\u002Fmateri\u002Ffungsi-python-def-return) untuk membuat penghitung bilangan prima sendiri. Contoh lain matematika yang tersembunyi di teknologi sehari-hari ada di artikel [matematika di balik QRIS](\u002Fartikel\u002Fmatematika-di-balik-qris-koreksi-galat-qr-code).",{"id":1950,"data":1951,"type":1902},"ai310506a1e9",{"markdown":1952},"## Ringkasan\n\n- Teorema bilangan prima (1896) menyatakan $\\pi(x) \\sim x\u002F\\ln x$. Contohnya $\\pi(1.000) = 168$, sedangkan perkiraannya sekitar 144,8.\n- Hipotesis Riemann (1859) menyatakan semua nol nontrivial fungsi zeta berada di garis $\\operatorname{Re} s = \\tfrac{1}{2}$. Hal ini mengendalikan seberapa jauh banyaknya prima bisa menyimpang dari rata-ratanya.\n- Pada 6 Oktober 2026, OpenAI merilis bukti hipotesis kuasi-Riemann: tidak ada nol untuk $\\operatorname{Re} s > \\tfrac{11}{12}$ (versi 5 Oktober) atau $\\operatorname{Re} s > \\tfrac{7}{8}$ (versi 30 September).\n- Pita tempat nol masih mungkin berada menyempit menjadi selebar $\\tfrac{5}{6}$ (versi 11\u002F12) atau $\\tfrac{3}{4}$ (versi 7\u002F8).\n- Para ahli umumnya menilai hasilnya benar dan penting, tetapi pemeriksaan manusia masih berjalan, dan hipotesis Riemann penuh tetap belum terpecahkan.",{"id":1954,"data":1955,"type":1902},"aic973e2b445",{"markdown":1956},"## Sumber belajar\n\n- [AI edges closer to solving the Riemann hypothesis, one of math's hardest problems (Science, 13 Okt 2026)](https:\u002F\u002Fwww.science.org\u002Fcontent\u002Farticle\u002Fai-edges-closer-solving-riemann-hypothesis-one-math-s-hardest-problems)\n- [OpenAI just changed math forever. Exactly how, no one yet knows (Science, 13 Okt 2026)](https:\u002F\u002Fwww.science.org\u002Fcontent\u002Farticle\u002Fopenai-just-changed-math-forever-exactly-how-no-one-yet-knows)\n- [Riemann hypothesis - Wikipedia](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FRiemann_hypothesis)\n- [Prime number theorem - Wikipedia](https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FPrime_number_theorem)\n\nPenjelasan dan contoh disusun ulang untuk materi ini; sumber dapat dibuka untuk belajar lebih lanjut.","2026-11-01T05:29:29.197Z","2026-11-01T05:35:03.083Z",{"id":15,"slug":16,"name":17,"color":20,"icon":19},[1961,1962],{"id":55,"slug":56,"name":57},{"id":60,"slug":61,"name":62},[1964,1965],{"id":164,"slug":166,"name":167,"subjectId":15},{"id":449,"slug":450,"name":451,"subjectId":15},[],"id",[1969],{"lang":1967,"slug":1892},{"name":1971,"slug":1972,"photoUrl":1973,"profession":1974},"Risyad Raflan","risyad-raflan","https:\u002F\u002Fmyfismat.com\u002Fuploads\u002F3f3eca84-9800-4c5f-97ed-1dec08f03152.jpg","Mahasiswa Jurusan Sistem Informasi",{"assets":1976,"videos":2087,"questionSets":2088},{"cmvxe10ag001n07scr4slu3xy":1977},{"id":1934,"slug":1978,"kind":1979,"title":1980,"description":1981,"url":98,"posterUrl":98,"config":1982,"subject":2086},"pita-kritis-fungsi-zeta-riemann-dan-wilayah-bebas-nol","SCENE_2D","Pita kritis fungsi zeta Riemann dan wilayah bebas nol","Bidang kompleks dengan pita kritis 0 < Re(s) < 1, garis kritis Re(s) = 1\u002F2, dan tiga pasang nol nontrivial pertama fungsi zeta. Geser σ₀ (batas wilayah yang terbukti bebas nol) atau pilih preset 1896, 7\u002F8, 11\u002F12, dan hipotesis Riemann untuk melihat seberapa sempit pita tempat nol masih mungkin berada.",{"v":30,"alt":1983,"view":1984,"params":1992,"derived":2000,"objects":2009,"presets":2060,"sources":2078,"readouts":2079},"Bidang kompleks dengan sumbu mendatar bagian riil dan sumbu tegak bagian imajiner. Garis putus-putus di Re(s) = 0 dan Re(s) = 1 membatasi pita kritis, garis merah di Re(s) = 1\u002F2 adalah garis kritis, dan enam titik merah adalah nol nontrivial di 1\u002F2 ± 14,135i, 1\u002F2 ± 21,022i, 1\u002F2 ± 25,011i. Daerah oranye di tepi kiri dan kanan pita adalah wilayah yang terbukti bebas nol; lebarnya bertambah ketika σ₀ diperkecil.",{"x":1985,"y":1988,"axes":5,"grid":5,"xLabel":1990,"yLabel":1991,"equalScale":4},[1986,1987],-0.6,1.6,[1989,1642],-30,"bagian riil Re(s)","bagian imajiner Im(s)",[1993],{"id":1994,"max":30,"min":1995,"step":1996,"label":1997,"value":1998,"digits":1116,"control":1999},"s0",0.5,0.0001,"σ₀: tidak ada nol untuk Re(s) > σ₀",0.9167,"slider",[2001,2005],{"id":2002,"expr":2003,"label":2004},"kiri","1 - s0","batas kiri",{"id":2006,"expr":2007,"label":2008},"lebar","2*s0 - 1","lebar pita sisa",[2010,2014,2016,2021,2024,2028,2031,2034,2039,2043,2047,2050,2053,2056],{"expr":2011,"type":2012,"color":2013},"abs(x - (1 + s0)\u002F2) \u003C (1 - s0)\u002F2","region","orange",{"expr":2015,"type":2012,"color":2013},"abs(x - (1 - s0)\u002F2) \u003C (1 - s0)\u002F2",{"to":2017,"from":2018,"type":2019,"color":2020,"dashed":5},[21,30],[21,21],"line","gray",{"to":2022,"from":2023,"type":2019,"color":2020,"dashed":5},[30,30],[30,21],{"to":2025,"from":2026,"type":2019,"color":2027,"dashed":5},[1995,30],[1995,21],"red",{"to":2029,"from":2030,"type":2019,"color":2013},[1994,30],[1994,21],{"to":2032,"from":2033,"type":2019,"color":2013},[2003,30],[2003,21],{"x":1995,"y":2035,"id":2036,"type":2037,"color":2027,"label":2038},14.135,"Z1","point","1\u002F2 + 14,135i",{"x":1995,"y":2040,"id":2041,"type":2037,"color":2027,"label":2042},21.022,"Z2","1\u002F2 + 21,022i",{"x":1995,"y":2044,"id":2045,"type":2037,"color":2027,"label":2046},25.011,"Z3","1\u002F2 + 25,011i",{"x":1995,"y":2048,"id":2049,"type":2037,"color":2027},-14.135,"Z4",{"x":1995,"y":2051,"id":2052,"type":2037,"color":2027},-21.022,"Z5",{"x":1995,"y":2054,"id":2055,"type":2037,"color":2027},-25.011,"Z6",{"at":2057,"text":2059,"type":1902},[2058,1620],-0.55,"nol mungkin hanya di {kiri:4} ≤ Re(s) ≤ {s0:4}",[2061,2065,2070,2074],{"id":2062,"label":2063,"values":2064},"tepi","1896: hanya tepi pita bebas nol",{"s0":30},{"id":2066,"label":2067,"values":2068},"tujuhdelapan","Versi 30 Sep 2026: σ₀ = 7\u002F8",{"s0":2069},0.875,{"id":2071,"label":2072,"values":2073},"sebelasduabelas","Versi 5 Okt 2026: σ₀ = 11\u002F12",{"s0":1998},{"id":2075,"label":2076,"values":2077},"rh","Hipotesis Riemann: σ₀ = 1\u002F2",{"s0":1995},[],[2080,2082,2084],{"expr":1994,"label":2081,"digits":1116},"Batas kanan σ₀",{"expr":2002,"label":2083,"digits":1116},"Batas kiri 1 − σ₀ (karena simetri)",{"expr":2006,"label":2085,"digits":1116},"Lebar pita tempat nol masih mungkin (2σ₀ − 1)",{"id":15,"slug":16,"name":17,"color":20},{},{},[2090,2104,2117,2130],{"id":2091,"type":1891,"slug":2092,"title":2093,"excerpt":2094,"coverUrl":98,"status":1895,"publishedAt":2095,"featured":4,"readingMinutes":1414,"order":21,"updatedAt":2096,"subject":2097,"levels":2098,"topics":2101,"tags":2102,"author":2103},"cmvry76fb000c07s28zwl0iv1","matematika-pace-lari-rekor-maraton-sub-2-jam","Matematika di Balik Pace Lari dan Rekor Maraton Sub-2 Jam","Kenapa pace 6:00\u002Fkm sama dengan 10 km\u002Fjam? Bedah matematika dan fisika lari: rumus pace, prediksi Riegel, hambatan udara, dan kode Python-nya.","2026-10-28T10:09:04.009Z","2026-11-03T14:36:19.665Z",{"id":15,"slug":16,"name":17,"color":20,"icon":19},[2099,2100],{"id":49,"slug":50,"name":51},{"id":55,"slug":56,"name":57},[],[],{"name":1971,"slug":1972,"photoUrl":1973,"profession":1974},{"id":2105,"type":1891,"slug":2106,"title":2107,"excerpt":2108,"coverUrl":98,"status":1895,"publishedAt":2109,"featured":4,"readingMinutes":1425,"order":21,"updatedAt":2110,"subject":2111,"levels":2112,"topics":2115,"tags":2116,"author":98},"demo-v2-a-jaring-jaring-bangun-ruang","jaring-jaring-bangun-ruang","Jaring-jaring Bangun Ruang: Kubus, Balok, Prisma, Limas, Tabung","Jaring-jaring bangun ruang: 11 jaring-jaring kubus dan cara mengeceknya, jaring balok, prisma segitiga, limas, tabung, kerucut, dan kaitannya dengan luas.","2026-10-14T16:01:44.781Z","2026-10-14T16:01:44.783Z",{"id":15,"slug":16,"name":17,"color":20,"icon":19},[2113,2114],{"id":43,"slug":44,"name":45},{"id":49,"slug":50,"name":51},[],[],{"id":2118,"type":1891,"slug":2119,"title":2120,"excerpt":2121,"coverUrl":98,"status":1895,"publishedAt":2122,"featured":4,"readingMinutes":1414,"order":21,"updatedAt":2123,"subject":2124,"levels":2125,"topics":2128,"tags":2129,"author":98},"demo-v2-a-rumus-bangun-ruang","rumus-bangun-ruang","Rumus Bangun Ruang Lengkap: Volume dan Luas Permukaan + Contoh","Rumus bangun ruang lengkap: volume dan luas permukaan kubus, balok, prisma, limas, tabung, kerucut, dan bola dalam satu tabel, plus konversi liter.","2026-10-14T16:01:44.770Z","2026-10-14T16:01:44.772Z",{"id":15,"slug":16,"name":17,"color":20,"icon":19},[2126,2127],{"id":43,"slug":44,"name":45},{"id":49,"slug":50,"name":51},[],[],{"id":2131,"type":1891,"slug":2132,"title":2133,"excerpt":2134,"coverUrl":98,"status":1895,"publishedAt":2135,"featured":5,"readingMinutes":1377,"order":21,"updatedAt":2136,"subject":2137,"levels":2138,"topics":2143,"tags":2144,"author":98},"demo-v2-a-matematika","cara-belajar-matematika-dari-nol","Cara Belajar Matematika dari Nol: Urutan Materi SD–Kuliah","Cara belajar matematika dari nol: urutan materi dari pecahan, bangun ruang, aljabar, hingga kalkulus, kebiasaan belajar efektif, dan rencana 4 minggu.","2026-10-14T16:01:44.759Z","2026-10-14T16:01:44.762Z",{"id":15,"slug":16,"name":17,"color":20,"icon":19},[2139,2140,2141,2142],{"id":43,"slug":44,"name":45},{"id":49,"slug":50,"name":51},{"id":55,"slug":56,"name":57},{"id":60,"slug":61,"name":62},[],[],[2146],{"code":1967,"nativeName":2147,"isDefault":5},"Bahasa Indonesia",[]]