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Pengembangan Teknologi Pasca Panen Menjelang Industrialisasi Pertanian
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| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | IX-2, NOVEMBER (No. 2) |
| Halaman | : | 132-134 |
| Abstrak | : | - |
Exploring Endless Space
| Pengarang | : | David Aldous |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 54 (No. 3) |
| Halaman | : | 179-185 |
| Abstrak | : | 4X games are a genre of modern computer games, exemplified by the Civilization series, whose initial stages implicitly involve exploring an unknown graph. One exploration scheme is “move to nearest unvisited vertex” and this is in fact forced in the game Endless Space. We revisit the small body of old “worst case” results about the efficiency of this scheme, and comment on the unstudied “average case” problem. |
Balancing the Square Root of Two
| Pengarang | : | Tom Edgar |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 54 (No. 3) |
| Halaman | : | 176-178 |
| Abstrak | : | We give a physical proof, using moments of mass, that the square root of two is irrational. |
On Eulers Rotation Theorem
| Pengarang | : | Peter Gothen & António Guedes de Oliveira |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 54 (No. 3) |
| Halaman | : | 171-175 |
| Abstrak | : | It is well known that a rigid motion of the Euclidean plane can be written as the composition of at most three reflections. It is perhaps not so widely known that a rigid motion of n-dimensional Euclidean space can be written as the composition of at most n + 1 reflections. The purpose of the present article is, firstly, to present a natural proof of this result in dimension 3 by explicitly constructing a suitable sequence of reflections, and, secondly, to show how a careful analysis of this construction provides a quick and pleasant geometric path to Euler’s rotation theorem, and to the complete classification of rigid motions of space, whether orientation preserving or not. We believe that our presentation will highlight the elementary nature of the results and hope that readers, perhaps especially those more familiar with the usual linear algebra approach, will appreciate the simplicity and geometric flavor of the arguments. |
Potensi Bioteknologi Tumbuhan di Bidang Pertanian dan Industri
| Pengarang | : | E. Noerhadi |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | IX-2, NOVEMBER (No. 2) |
| Halaman | : | 125-131 |
| Abstrak | : | Abstrak tidak tersedia. |
How to Marry the Kernel and the Image
| Pengarang | : | Jean-Paul Truc |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 54 (No. 4) |
| Halaman | : | 386-387 |
| Abstrak | : | This note gives a general sufficient and necessary condition to obtain the direct sum ????=ker?????⊕Im?????, where E is a finite dimensional space over the field ???? (? or ?) and f is a linear transformation of E. |
The Largest Quadrilateral is Cyclic: A New Geometric Proof
| Pengarang | : | Jyotirmoy Sarkar |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 54 (No. 4) |
| Halaman | : | 378-384 |
| Abstrak | : | Although treated as “obvious” since antiquity, the first complete proof that “a quadrilateral with given sides achieves the maximum area when it is cyclic” is attributed to Bretschneider (1842), who proved it using trigonometry. Peter (2003) proved it using calculus. It also follows from the isoperimetric inequality, proved geometrically in [Citation5] and [Citation11]. Here we give a new Euclidean geometric proof, starting from a different maximization problem: Find the tallest vertical line segment sandwiched between two semi-circles in a plane lying on opposite sides of a horizontal line with (partially) overlapping diameters. |
Peranan Musuh Alami Dalam Pengendalian Jasad Pengganggu di Ekosistem Pertanian
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | IX-2, NOVEMBER (No. 2) |
| Halaman | : | 110-124 |
| Abstrak | : | Abstrak tidak tersedia. |
Large Independent Set vs. Large Clique
| Pengarang | : | Melissa Holly |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 54 (No. 4) |
| Halaman | : | 374-377 |
| Abstrak | : | Large cliques with cardinality |????|>⌈23?????⌉ cannot exist with large independent sets where |????|>⌈23?????⌉ in the same simple connected graph G of order ????≥2. |
Integration by Substitution: A Case Study in the Relationship Between Calculus and Analysis
| Pengarang | : | Daniel J. Velleman |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 54 (No. 4) |
| Halaman | : | 367-373 |
| Abstrak | : | Do the theorems we prove in our analysis classes justify the calculations we teach in calculus classes? In this article I use some examples of integration by substitution to show that the answer is more complicated than one might think. |