Proof Of Geometry Research Articles

Proving geometry theorems: Student prospective teachers’ perseverance and mathematical reasoning

Proof of geometry is a topic that involves mathematical reasoning abilities and relates to perseverance involving hard work, the spirit of achievement, and self-confidence. The current important problem that occurs at this time is that students who are future teachers of mathematics still experience difficulties in compiling proofs, especially those who are not challenged to work hard. This qualitative research explores mathematics teacher candidates' reasoning abilities and perseverance in proving geometric theorems. Therefore, the research design used a case study. There were three participants in this study, and they were student prospective mathematics teachers' s taking geometry courses. Data were collected through working documents, open questionnaires, and semi-structured interviews and were analyzed using iterative techniques consisting of data condensation, data exposure, and verification. The study's results showed that students' prospective teachers did not prioritize proof in solving geometry problems, even though they worked hard to solve the problems independently until they were finished. The students' perseverance also impacts their mathematical reasoning in proving geometric theorems. Students with more hard work values tend to have more reasoning values. The results of this study have implications that there needs to be an effort from the teacher to get used to giving proof questions to support students' perseverance and mathematical reasoning abilities.

In Situ Observation of Non-Classical 2-Norbornyl Cation in Confined Zeolites at Ambient Temperature.

Carbonium ions are an important class of reaction intermediates, but their dynamic evolution is difficult to be monitored by in situ techniques under experimental conditions because of their extremely short lifetime. Probably the most famous case is 2-norbornyl cation (2NB+ ): its existing form (classical or non-classical) had been debated for decades, until the concrete proof of non-classical geometry was achieved by X-ray crystallographic characterization at ultra-low temperature (40 K) and super acidic environment. However, we lack the understanding about 2NB+ at ambient conditions. Herein, by taking advantage of the confinement effect and delocalized acidic environment of zeolites, we successfully stabilized 2NB+ and unequivocally confirmed its "non-classical" structure inside the ZSM-5 zeolite by ab initio molecular dynamics simulations and 13 C solid-state nuclear magnetic resonance experiments. It is the first time to in situ observe the non-classical 2NB+ without the super acidic environment at ambient temperature, which provides a new strategy to expand the carbocation chemistry.

The written mathematical communication profile of prospective math teacher in mathematical proving

Written mathematical communication is the process of expressing mathematical ideas and understanding in writing. It is one of the important aspects that must be mastered by the prospective math teacher as tool of knowledge transfer. This research was a qualitative research that aimed to describe the mathematical communication profile of the prospective mathematics teacher in mathematical proving. This research involved 48 students of Mathematics Education Study Program; one of them with moderate math skills was chosen as the main subject. Data were collected through tests, assignments, and task-based interviews. The results of this study point out that in the proof of geometry, the subject explains what is understood, presents the idea in the form of drawing and symbols, and explains the content/meaning of a representation accurately and clearly, but the subject can not convey the argument systematically and logically. Whereas in the proof of algebra, the subject describes what is understood, explains the method used, and describes the content/meaning of a symbolic representation accurately, systematically, logically, but the argument presented is not clear because it is insufficient detailed and complete.

Parametric surface and properties defined on parallelogrammic domain

Abstract Similar to the essential components of many mechanical systems, the geometrical properties of the teeth of spiral bevel gears greatly influence the kinematic and dynamic behaviors of mechanical systems. Logarithmic spiral bevel gears show a unique advantage in transmission due to their constant spiral angle property. However, a mathematical model suitable for accurate digital modeling, differential geometrical characteristics, and related contact analysis methods for tooth surfaces have not been deeply investigated, since such gears are not convenient in traditional cutting manufacturing in the gear industry. Accurate mathematical modeling of the tooth surface geometry for logarithmic spiral bevel gears is developed in this study, based on the basic gearing kinematics and spherical involute geometry along with the tangent planes geometry; actually, the tooth surface is a parametric surface defined on a parallelogrammic domain. Equivalence proof of the tooth surface geometry is then given in order to greatly simplify the mathematical model. As major factors affecting the lubrication, surface fatigue, contact stress, wear, and manufacturability of gear teeth, the differential geometrical characteristics of the tooth surface are summarized using classical fundamental forms. By using the geometrical properties mentioned, manufactura-bility (and its limitation in logarithmic spiral bevel gears) is analyzed using precision forging and multi-axis freeform milling, rather than classical cradle-type machine tool based milling or hobbing. Geometry and manufacturability analysis results show that logarithmic spiral gears have many application advantages, but many urgent issues such as contact tooth analysis for precision plastic forming and multi-axis freeform milling also need to be solved in a further study.

Projective Geometry on the Structure of Geometric Composition Analysis Application

The analysis rule of geometry composition analysis in building structure must rely on geometry theory, while the traditional Euclidean geometry theory can not solve some building structures problems of the geometry components. This problem can be solved in the use of projective geometry theory. In this paper we introduce the proof of projective geometry in the geometry composition analysis and we discuss the application of this theory.

A combined density functional theory and molecular mechanics (QM/MM) study of FeCO vibrations in carbonmonoxy myoglobin

Molecular oscillations of ligand motions at the active site of carbonmonoxy myoglobin have been calculated in a protein environment using the combined QM/MM approach. In these calculations, the active site was calculated at a quantum mechanical (QM) level of theory using the B3LYP/6-31 + G* method, while the remaining protein was calculated at the molecular mechanical (MM) level utilizing the A mber force field. The presence of a torsion mode and the second component of the bending vibration are proof of a bent CO geometry in the heme pocket.

Approaches to Biology Teaching and Learning: Understanding the Wrong Answers—Teaching toward Conceptual Change

Underpinning science education reform movements in the last 20 years—at all levels and within all disciplines—is an explicit shift in the goals of science teaching from students simply creating a knowledge base of scientific facts to students developing deeper understandings of major concepts within a scientific discipline. For example, what use is a detailed working knowledge of the chemical reactions of the Krebs cycle without a deeper understanding of the relationship between these chemical reactions of cellular respiration and an organism’s need to harvest energy from food? This emphasis on conceptual understanding in science education reform has guided the development of standards and permeates all major science education reform policy docu