Analysis of Improving Mathematical Analogy Ability in Snow Cube Throwing Based on Exploration Learning

<p><em>The snow cube throwing learning was developed to find patterns, make hypotheses, and draw conclusions based on their findings in problem-solving. Students are given five types of teaching materials with similar problems to improve students' mathematical analogy skills. This study aims to analyze the differences in the improvement of mathematical analogy abilities that received snow cube throwing based on exploration (SCTBE), exploratory and expository learning reviewed as a whole, and by school category. This study is a quasi-experimental study with a non-equivalent pretest and posttest control-group design. The research subjects were students of class VIII from three schools in Cimahi City. Overall, the results showed that students who received SCTBE and expository learning improved mathematical analogy abilities and were better than students who received exploratory learning. Reviewed by school category, SCTBE learning is more suitable for middle category schools with active and independent characteristics</em>.</p>

Mathematical Phenomenon of Genetic Link G-U

As you know, the secondary structure of RNA molecules, unlike DNA, in addition to canonical or Watson-Crick pairs, non-canonical G-U pairs, this is guanine - uracil. The last pairs were established experimentally by X-ray diffraction analysis and are still a mystery to researchers. The fact is that such pairs are 5-10 times energetically weaker than the canonical pairs A-U, C-G. The question arises: why are such pairs needed? The study was carried out in the framework of the strict mathematical analogy established earlier by the authors of some cases of genetic overlaps and stems of the secondary structure of messenger RNAs. In this work, it is shown that due to the non-canonical G-U pair, using the new ambiguities found, it is possible to substantially “regulate” the stem free energy (even for small stems) - the most important biochemical characteristic. It turned out that the discovered effect for G-U pairs significantly exceeds a similar effect for canonical pairs A-U, C-G.

Asosiasi Antara Kemampuan Analogi Dengan Komunikasi Matematik Siswa SMP

This research is a quantitative research with cross-sectional design that aims to examine the association between students 'mathematical analogy abilities with students' mathematical communication abilities. The subject of this research is 33 students of class VII in one of Junior High School of Kampar Regency of Riau Province. The instrument used is a essay test about the problem of mathematical analogy and mathematical communication. Data analysis techniques to test the association of both capabilities based on the category of contingency association test (Pearson Chi Square test and contingency coefficient). The results showed that this study was an association between students' mathematical analogy abilities with students' mathematical communication abilities. The degree of association between students 'mathematical analogy abilities with students 'mathematical communication abilities is high.

SH-TM mathematical analogy for the two-layer case. A magnetotellurics application

The same mathematical formalism of the wave equation can be used to describe anelastic and electromagnetic wave propagation. In this work, we obtain the mathematical analogy for the reflection/refraction (transmission) problem of two layers, considering the presence of anisotropy and attenuation -- viscosity in the viscoelastic case and resistivity in the electromagnetic case. The analogy is illustrated for SH (shear-horizontally polarised) and TM (transverse-magnetic) waves. In particular, we illustrate examples related to the magnetotelluric method applied to geothermal systems and consider the effects of anisotropy. The solution is tested with the classical solution for stratified isotropic media.

Proportional Thinking in Kepler’s Science of Light

Light is at the center of Kepler’s optics, astronomy, and cosmology. Verbal and mathematical analogy, whether as concept, proportion, or both, is crucial to his methodology and his habits of thought. Kepler is an intellectual hybrid who combines Neoplatonic and perspectivist ideas about light with mathematical and physical discoveries anticipating those of Descartes and Newton. Kepler is strikingly engaged with the interface of the immaterial with the material that light effects, as well as with correspondences and other connections between the celestial and terrestrial realms. Analogy, the salient means of linking the known with the unknown, the abstract with the sensible, is conspicuous throughout his work. This chapter focuses on Kepler’s study of light, geometric optics, and their bearing on the observation of astronomical phenomena. Both Donne and Milton were acquainted with Kepler’s ideas (as with Spenser’s).

Mathematical Analogy between Non-Uniform Torsion and Transverse Bending of Thin-Walled Open Section Beams

The objective of this work is to identify and make an analysis of correlation between functions of bimoments and function of bending moments arising in the beams under the same loads. This article shows the possibility of using a diagram of bending moment multiplied by a factor as a diagram of bimoment. The maximum deviation between diagram of bending moment and diagram of bimoment made up 3.6 % of maximum bending moment in case of uniformly distributed load on one side of fixed supported beam.

Addendum to ‘Coherent Lagrangian vortices: the black holes of turbulence’

In Haller & Beron-Vera (J. Fluid Mech., vol. 731, 2013, R4) we developed a variational principle for the detection of coherent Lagrangian vortex boundaries. The solutions of this variational principle turn out to be closed null geodesics of the Lorentzian metric induced by a generalized Green–Lagrange strain tensor family. This metric interpretation implies a mathematical analogy between coherent Lagrangian vortex boundaries and photon spheres in general relativity. Here, we give an improved discussion of this analogy.

Sherlock Holmes: Other Sciences

Sherlock Holmes knew more chemistry than any other science. But in this chapter, we shall find that he was well informed in a number of other sciences as well. Since mathematics contributes to all sciences, we first examine the Canon for instances of mathematical knowledge. We find a number of references to and uses of math in nearly all the early stories. After Holmes and Moriarty supposedly went over the Reichenbach Falls in The Final Problem (FINA) and Holmes returned, he rarely used math again. In A Study in Scarlet (STUD), Watson scoff s at a magazine article that claims that the conclusions of a trained observer are as “infallible as so many propositions of Euclid.” He soon learns that his new roommate Holmes is the author of the article. So here, very early on, we have Holmes drawing a mathematical analogy to his deductive work. He invokes Euclid again in the second story, Sign of Four (SIGN). This time he chides Watson about his writing style. Holmes accuses Watson of allowing romanticism to creep into his narration of the previous case, STUD. According to Holmes, this awkward technique produces “much the same effect as if you worked a love-story or an elopement into the fifth proposition of Euclid.” The fifth proposition states that if two sides in a triangle are equal, then the angles opposite those two sides will also be equal. Note that Holmes makes no calculation using Euclid’s proposition, but he depends on Watson’s knowledge of math to make a point about the way the narrative of STUD was written. This is the first time, but not the last, that he criticizes Watson the chronicler. In SIGN, Holmes’s conversation again assumes that his listener is acquainted with mathematical terms. When he sees that Tonga has left a footprint in creosote, he claims that tracking him will be as easy as using the “rule of three,” which states that if three of the four terms in a proportion are known, then the fourth may be calculated.