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How Long Can k-Gobel Sequences Remain Integers
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| Pengarang | : | Rinnosuke Matsuhira, Toshiki Matsusaka & Koki Tsuchida |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 131 (No. 9) |
| Halaman | : | 784-793 |
| Abstrak | : | Inspired by Episode 3 of the Japanese manga “Seisu-tan” by Doom Kobayashi and Shin-ichiro Seki, we investigate the k-Göbel sequence (????????,????)???? named after Fritz Göbel. Although the sequence is generally defined as rational, quite a few initial terms behave like an integer sequence. This article addresses a question raised in Seisu-tan and shows that ????????,???? is always an integer for any ????≥2 and 0≤????≤18. |
Kempner-like Harmonic Series
| Pengarang | : | Jean-Paul Allouche & Claude Morin |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 131 (No. 9) |
| Halaman | : | 775-783 |
| Abstrak | : | Inspired by a question asked on the list mathfun, we revisit Kempner-like series, i.e., harmonic sums ∑′1/???? where the integers n in the summation have “restricted” digits. First we give a short proof that lim????→∞?(∑????2?(????)=????1/????)=2 log 2, where ????2?(????) is the sum of the binary digits of the integer n. Then we give a generalization that addresses the case where ????2?(????) is replaced with ?????????(????), the sum of b-ary digits in base b: we prove that lim????→∞?∑?????????(????)=????1/????=(2 log ????)/(????−1). Finally we indicate that other generalizations could be studied: the sum of digits in base 2 could be replaced with, e.g., the function ????11?(????) of—possibly overlapping—11 in the base-2 expansion of n, for which one can obtain lim????→∞?∑????11?(????)=????1/????=4 log 2. |
Hidup Bersama Mawas di Hutan Kalimantan
| Pengarang | : | |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-6, MARET (No. 6) |
| Halaman | : | 478-480 |
| Abstrak | : | - |
Closed Geodesics on the Mylar Balloon Shape
| Pengarang | : | Siti Chamamah Soeratno |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 131 (No. 9) |
| Halaman | : | 753-774 |
| Abstrak | : | In 2006, Alexander proved a result that implied for the mylar balloon shape, if n is the number of times a closed geodesic winds around the axis of rotation and m is the number of times the geodesic oscillates about the equator, then ????/????∈(1/√2,1]. In this paper, we will provide a simpler more direct proof of Alexander’s result for the mylar balloon by using sharp estimates of certain improper integrals. The mylar balloon geodesics suggest a network of reinforcing fibers creating an isotensoid system that is lightweight, compactly foldable, and easy to deploy, making it an ideal candidate for an inflatable terrestrial or space habitat. Other applications of geodesics, including geodesic domes, aerodynamic decelerators, and the production of salami are also discussed. |
Hasil Rumusan Seminar Nasional "Langkah Pemuda di Tengah Pergolokan Dunia"
| Pengarang | : | |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-6, MARET (No. 6) |
| Halaman | : | 473-477 |
| Abstrak | : | - |
Negara Orde Baru Dalam Perspektif Kelas
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-6, MARET (No. 6) |
| Halaman | : | 466-472 |
| Abstrak | : | - |
Tri Nostalgia Nu Asas Islam, Ideologi Politik serta Strategi Konseptual dan Spiritual
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-6, MARET (No. 6) |
| Halaman | : | 461-465 |
| Abstrak | : | - |
Fukuzawa Yukichi : Guru Pencerahan Zaman Meiji Modern
| Pengarang | : | Santosa, F.X. |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-6, MARET (No. 6) |
| Halaman | : | 452-460 |
| Abstrak | : | - |
A Few Tips On Learning to Speak English For My Students At Universitas Nasional
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-6, MARET (No. 6) |
| Halaman | : | 449-451 |
| Abstrak | : | - |
Five or Ten New Proofs of the Pythagorean Theorem
| Pengarang | : | NeKiya Jackson & Calcea Johnson |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 131 (No. 9) |
| Halaman | : | 739-752 |
| Abstrak | : | We present five trigonometric proofs of the Pythagorean theorem, and our method for finding proofs (Section 5) yields at least five more. |