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Pull-Back Cars: Vehicles for the Instruction of Differential Equations
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| Pengarang | : | Narmin Ghalichi |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 3) |
| Halaman | : | 192-204 |
| Abstrak | : | This article develops a mathematical model for the motion of toy pull-back cars that can be introduced and revisited throughout an undergraduate differential equations course. This survey of the pull-back car modeling scenario enables students to connect course content with real-world experiences and experimental data, while leaving room for further exploration and advancement of the model. |
Using the Girard-Newton-Waring Formula to Evaluate Trigonometric Sums: A Blast from the Past
| Pengarang | : | Piliang, Indra Jaya |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 5) |
| Halaman | : | 416-427 |
| Abstrak | : | This article shows how two classical results about polynomials with trigonometric roots may be used together to create interesting new formulas for trigonometric sums. Readers are encouraged to find further new trigonometric formulas by applying the ideas in this article to other polynomials having trigonometric roots. |
On Herons Formula for the Area of a Plane Triangle
| Pengarang | : | Chris Sangwin |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 5) |
| Halaman | : | 406-415 |
| Abstrak | : | This paper provides a review of proofs of Heron’s formula for the area of a plane triangle. We groups proofs together into analogy/experimental evidence, geometry (incircle radius multiplied by semi-perimeter), algebra (equivalence with the Pythagorean Theorem), trigonometric proofs (often via the cosine rule), and specialization from a more general theorem. Lastly, we discuss a neglected paper by Baker of 1885 that lists 110 distinct formulae for the area of a plane triangle and relate some of these formulae to those used in proving Heron’s formula. |
A Precise Probability Related to Simpsons Paradox
| Pengarang | : | Alex Rice |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 5) |
| Halaman | : | 400-405 |
| Abstrak | : | Suppose two friends are about to participate in a two-day contest in which they repeatedly attempt a task with a clear success/failure outcome (such as shooting free throws on a basketball court). We have no specific prior knowledge of the participants’ skills, how the change in day will impact their success, or how many attempts they will take each day, so we suppose that each participant’s success rate for day 1, success rate for day 2, and proportion of attempts that take place on day 1 are all chosen uniformly at random between 0 and 1. What is the probability that the same person has a higher success rate each of the two individual days, but the other person has a higher success rate for the two-day period? This can be thought of as a prior probability of a simple case of Simpson’s paradox, and we show that this probability is (????2−9)/36=.0241556778…. |
Parity and Partition of the Rational Numbers
| Pengarang | : | Peter Lynch & Michael Mackey |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 5) |
| Halaman | : | 387-399 |
| Abstrak | : | We define an extension of parity from the integers to the rational numbers. Three parity classes are found—even, odd, and “none”. Using the 2-adic valuation, we partition the rationals into subgroups with a rich algebraic structure. The natural density provides a means of distinguishing the sizes of countably infinite sets. The Calkin-Wilf tree has a remarkably simple parity pattern, with the sequence “odd/none/even” repeating indefinitely. This pattern means that the three parity classes have equal natural density in the rationals. A similar result holds for the Stern-Brocot tree. |
Using Trapezoidal Approximations to Estimate Averages
| Pengarang | : | Chris Boucher |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 5) |
| Halaman | : | 381-386 |
| Abstrak | : | We use trapezoidal approximations of the integrals of positive, concave down functions to obtain upper and lower estimates for the averages of these functions at the first n positive integers. We also give error bounds for the upper estimates. |
Morries Second Law and its Consequences
| Pengarang | : | Roger B. Nelsen |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 5) |
| Halaman | : | 376-380 |
| Abstrak | : | Abstrak tidak tersedia. |
Polemik Kebudayaan Dalam Retrospeksi
| Pengarang | : | Umar Khayam |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-9, JUNI (No. 9) |
| Halaman | : | 715-717 |
| Abstrak | : | - |
Potensi Generasi Muda Dan Produktivitas Kerjanya Di Indonesia - Suatu Pendekatan Psikologi Industri dan Sosial
| Pengarang | : | Asip F. Hadipranata |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-9, JUNI (No. 9) |
| Halaman | : | 708-714 |
| Abstrak | : | - |
Apa dan bagaimana Komunikasi Politik itu?
| Pengarang | : | Mimien Saleh |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-9, JUNI (No. 9) |
| Halaman | : | 698-707 |
| Abstrak | : | - |