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| Pengarang | : | WLODZIMIERZ REDZIOCH |
| Nama Majalah/Jurnal | : | Ave Maria: Per Mariam Ad Jesum |
| Volume / Edisi | : | (No. 46) |
| Halaman | : | 60-63 |
| Abstrak | : | - |
The Green-Tao Theorem and the Infinitude of Primes in Domains
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 130 (No. 2) |
| Halaman | : | 114-125 |
| Abstrak | : | We first prove an elementary analogue of the Green-Tao Theorem. The celebrated Green-Tao Theorem states that there are arbitrarily long arithmetic progressions in the set of prime numbers. In fact, we show the Green-Tao Theorem for polynomial rings over integral domains with several variables. Using the Generalized Polynomial van der Waerden Theorem, we also prove that in an infinite unique factorization domain, if the cardinality of the set of units is strictly less than that of the domain, then there are infinitely many prime elements. Moreover, we deduce the infinitude of prime numbers in the positive integers using polynomial progressions of length three. In addition, using unit equations, we provide two more proofs of the infinitude of prime numbers. Finally, we give a new proof of the divergence of the sum of reciprocals of all prime numbers. |
KARENA AKU SANGAT MENCINTAIMU
| Pengarang | : | Nicolas Noviyanto |
| Nama Majalah/Jurnal | : | Ave Maria: Per Mariam Ad Jesum |
| Volume / Edisi | : | (No. 46) |
| Halaman | : | 57-59 |
| Abstrak | : | - |
Galileo’s Swiftest Descent Problem Revisited: Complete Analytic Solution
| Pengarang | : | Matti Selg |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 130 (No. 2) |
| Halaman | : | 103-113 |
| Abstrak | : | Nearly four centuries ago, Galileo Galilei proved that descent along any two-chord path in the lower quadrant of a circle is faster than descent along the straight one-chord path from the same starting point to the same endpoint, if the initial speed is zero, and the paths end in the lowest point of the circle. Moreover, Galileo posed two conjectures: (1) the main conclusion remains the same if the body initially at rest falls to a starting point and thus the speed there is not zero; (2) descent along the circular arc itself is faster than along any broken line of chords. In this article, analytical proofs are given that confirm the validity of both of these conjectures. |
PERAN ROH KUDUS DAN BIMBINGAN TUHAN
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Ave Maria: Per Mariam Ad Jesum |
| Volume / Edisi | : | (No. 46) |
| Halaman | : | 50-56 |
| Abstrak | : | - |
MENCARI TUHAN DALAM KEBERAGAMAN
| Pengarang | : | NGARDI FLAVIANUS VALENSIUS |
| Nama Majalah/Jurnal | : | Rohani |
| Volume / Edisi | : | 72 (No. 01) |
| Halaman | : | 23-25 |
| Abstrak | : | - |
APAKAH ADA TITIK TEMU DI ANTARA AGAMA-AGAMA
| Pengarang | : | Mgr. Charles M. Mangan |
| Nama Majalah/Jurnal | : | Rohani |
| Volume / Edisi | : | 72 (No. 01) |
| Halaman | : | 16-22 |
| Abstrak | : | - |
Probing Mechanical Properties of a Spider Web Using a Simple Rubber Band Model
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The Physics Teacher |
| Volume / Edisi | : | 62 (No. 4) |
| Halaman | : | 246-249 |
| Abstrak | : | Maintaining the structural integrity of a spider web1 is important for spiders, since it is both a residence and a hunting tool.2 Here, we analyzed the robustness of a spider web under various conditions using a simple rubber band model of a spider web, with an eye toward its utility as an integrative science experiment for students and teachers of physics. We perturbed the model web in many ways and monitored how its shape and its tension distribution change. We also discussed what kind of damage is more critical and should be avoided, in terms of survival and fitness of spiders. |
TUHAN, BIARKAN AKU HIDUP!
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Ave Maria: Per Mariam Ad Jesum |
| Volume / Edisi | : | (No. 46) |
| Halaman | : | 42-49 |
| Abstrak | : | - |
A Tale of Two by Two Matrices
| Pengarang | : | Dan Kalman |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 130 (No. 9) |
| Halaman | : | 837-854 |
| Abstrak | : | We formulate the Euclidean algorithm using directed graphs on integer points in the plane and operations on a particular semigroup of two by two matrices. The properties of the graphs and the semigroup provide surprisingly effective tools for solving certain classical diophantine equations, among other applications. |