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AGM and Jellyfish Swarms of Elliptic Curves
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| Pengarang | : | Michael J. Griffin |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 130 (No. 4) |
| Halaman | : | 355-369 |
| Abstrak | : | The classical AGM produces wonderful infinite sequences of arithmetic and geometric means with common limit. For finite fields ????????, with ????≡3 (mod?4), we introduce a finite field analogue AGM???????? that spawns directed finite graphs instead of infinite sequences. The compilation of these graphs reminds one of a jellyfish swarm, as the 3D renderings of the connected components resemble jellyfish (i.e., tentacles connected to a bell head). These swarms turn out to be more than the stuff of child’s play; they are taxonomical devices in number theory. Each jellyfish is an isogeny graph of elliptic curves with isomorphic groups of ????????-points, which can be used to prove that each swarm has at least (1/2−????)?√???? jellyfish. This interpretation also gives a description of the class numbers of Gauss, Hurwitz, and Kronecker which is akin to counting types of spots on jellyfish. |
"KAMU BEBAS MAKA PILIHLAH"
| Pengarang | : | INDRIYATNO RADITYA ADRIANUS |
| Nama Majalah/Jurnal | : | Rohani |
| Volume / Edisi | : | 72 (No. 01) |
| Halaman | : | 53-55 |
| Abstrak | : | - |
AIR SUCI KEKAYAAN ROHANI YANG TAK TERKIRA
| Pengarang | : | Landy, Maureen |
| Nama Majalah/Jurnal | : | Ave Maria: Per Mariam Ad Jesum |
| Volume / Edisi | : | (No. 46) |
| Halaman | : | 68-70 |
| Abstrak | : | - |
MEMBERANIKAN DIRI DIKENAI CINTA
| Pengarang | : | Hirschi, Kevin,Kang, Okim |
| Nama Majalah/Jurnal | : | Rohani |
| Volume / Edisi | : | 72 (No. 01) |
| Halaman | : | 50-52 |
| Abstrak | : | - |
Knot Colorings: Coloring and Goeritz Matrices
| Pengarang | : | SOETRISNO LOEKMAN |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 130 (No. 4) |
| Halaman | : | 335-354 |
| Abstrak | : | Knot colorings are one of the simplest ways to distinguish knots, dating back to Reidemeister and popularized by Fox. In this mostly expository article, we discuss knot invariants like colorability, knot determinant, and number of colorings, and how these can be computed from either the coloring matrix or the Goeritz matrix. We give an elementary approach to this equivalence, without using any algebraic topology. We also compute the knot determinant and the nullity of pretzel knots with arbitrarily many twist regions. |
KRISTOLOGI LR IGNATIUS DAN KRISTOMOLOGI DUPUIS
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Rohani |
| Volume / Edisi | : | 72 (No. 01) |
| Halaman | : | 46-49 |
| Abstrak | : | - |
Estimating the Refractive Index of a Hydrated Superabsorbent Polymer Sphere
| Pengarang | : | Ryanth Atmadja |
| Nama Majalah/Jurnal | : | The Physics Teacher |
| Volume / Edisi | : | 62 (No. 4) |
| Halaman | : | 262-265 |
| Abstrak | : | Superabsorbent polymers (SAPs) are known for their amazing ability to absorb at least 100 times their dry weight in water and, once hydrated and having no added coloration, are nearly invisible to the naked eye when immersed in water with ambient lighting. Here we develop a method for estimating the refractive index of fully hydrated SAP spheres. Leveraging a computer model of refraction of light through a sphere, we use the results of a simple, low-cost experiment to estimate the refractive index as ns = 1.3354 ± 0.0001, or within 0.23% of the average index of water for yellowish light and room temperatures. The procedure described below could easily be incorporated into a classroom laboratory activity. |
KITA HARUS SIAP MATI
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Ave Maria: Per Mariam Ad Jesum |
| Volume / Edisi | : | (No. 46) |
| Halaman | : | 64-67 |
| Abstrak | : | - |
Pythagorean Triples, Complex Numbers, Abelian Groups and Prime Numbers
| Pengarang | : | KAMBODJI R ALPHINUS |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 130 (No. 4) |
| Halaman | : | 321-334 |
| Abstrak | : | Pythagorean triples can be represented by points of the unit circle with rational coordinates. These points form an abelian group, and we describe its structure. This structural description yields an enumeration of the normalized Pythagorean triples with a given hypotenuse. It also gives rise to an effective method for producing all such triples, and this effective method seems to be new. This paper is intended for the general mathematical audience, including undergraduate mathematics students. Therefore it contains background material, explanations, examples and drawings; and the proofs are complete. |
Gambling Under Unknown Probabilities as Proxy for Real World Decisions Under Uncertainty
| Pengarang | : | David J. Aldous |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 130 (No. 4) |
| Halaman | : | 303-320 |
| Abstrak | : | The subject of decisions under uncertainty about future events, if lacking sufficient theory or data to make confident probability assessments, poses a challenge for any quantitative analysis. This article suggests one way to first look at this subject. We give elementary examples within a framework for studying decisions under uncertainty where probabilities are only roughly known. The framework, in gambling terms, is that the size of a bet is proportional to the gambler’s perceived advantage based on their perceived probability, and their accuracy in estimating true probabilities is measured by mean-squared-error. Within this framework one can study the cost of estimation errors, and seek to formalize the “obvious” notion that in competitive interactions between agents whose actions depend on their perceived probabilities, those who are more accurate at estimating probabilities will generally be more successful than those who are less accurate. |