Algebraic methods in plane geometry

In this article we examine the role of mappings in elementary geometry. After making some comments about the Erlangen programme initiated by Felix Klein in 1872, wherein he proposed a way of studying geometries based on the underlying transformation groups, we see how theorems like Von Aubel’s theorem and Napoleon’s theorem can be proved in an elegant manner using similarity mappings, and how some construction problems may be solved using isometries. At the end we present a recent proof by Alain Connes of “Morley’s Miracle”, based on affine transformations. Shailesh Shirali heads a Community Mathematics Center at Rishi Valley School (KFI). He has a deep interest in teaching and writing about mathematics at the high school/post school levels, with particular emphasis on problem solving and the historical aspects of the subject.     

平面图的着色数

用数学归纳推理的方法，论证了图论中的简单平面图Gn是4着色的．     

George Andrews’ game

This is an expository article showing how Zeck-endorf’s Theorem (every positive integer can be represented in one and only one way as the sum of non-consecutive Fibonacci numbers) can be used to construct a number-guessing game invented by Professor George Andrews. Jerold Mathews is professor (emeritus) of mathematics at Iowa State University, Ames, Iowa, USA, where he served on the faculty from 1961–1995. His interests include research in point set topology, history of mathematics and writing textbooks. He enjoys reading, photography and helping international students learn English.     

多元视角下的Urquhart定理

介绍了Urquhart定理的历史背景,以及该定理在平面几何、三角学视角下的解释．探究了该定理在解析几何中的意义,把平面几何、三角学以及解析几何知识有机整合起来,为当前中学数学教学提供参考。     

基于AutoCAD2000的《画法几何》问题计算机求解

本文讨论了在AutCAD200平台上如何利用其现有功能求解《画法几何》问题，并给出了一详细的例子。     

Education in the Field Influences Children’s Ideas and Interest toward Science

This paper explores the idea of informal science education in scientific field laboratory (The Science Field Centre). The experimental group of pupils (N = 153) was experienced with approximately 5-day lasting field trips and experiments in the Field Centre in Slovakia. After finishing the course, two different research methods were used to discover their interest and ideas toward science. Pupils from the experimental group showed significant differences from those that did not experience education in the Field Centre (control group, N = 365). In comparison to the control group, pupils of the experimental group highly preferred book titles that were related to their program in the Field Centre. There were differences between the drawings of ideal school environment from both pupils groups. In the drawings of the experimental group, we found significantly more items connected with the educational environment of the Field Centre (e.g. laboratory equipment, live animals). We suppose field science education would be one of the most effective ways to increase interest of pupils to study science and to invaluable intrinsic motivation at the expense extrinsic motivation.     

A primary teacher’s mathematics teaching: the development of beliefs and practice in different “supportive” contexts

This article refers to a longitudinal case study of a primary school teacher over a period of 4 years. The focus is on the development of the teacher’s beliefs regarding mathematics teaching and learning from the last year of her university studies up to the third year of teaching mathematics in school. This development has been investigated within three different contexts, which have been distinguished in terms of the kind of support provided to this teacher. Two dominant beliefs emerged which have been traced through the period of the study from both the teacher’s reflections and actions. The first belief drew on the idea that what was considered an easy mathematical task by an adult could also be easily understood by children, while the second was that children learn mathematics through their actual involvement in a variety of teaching activities. The results indicate the way that teacher’s experiences from her university studies, actual classroom practice and inservice education interact and influence her beliefs and professional development.     

University students’ success: A psycho-sociological approach

The aim of this paper is to propose a basic model to analyse processes of change in educational institutions taking into account both individual and contextual variables. It aims to identify the basic factors of change in order to contribute to reduce the dispersion of research projects, both from close subjects and one subject alone within human sciences, in order to make scientific accumulation easier and to guide social practice better. This proposal is based on Cryer and Elton’s (Studies in Higher Education, 1: 75–86, 1990) contributions, in this case applied to the learning processes of university students. They may account for static and dynamic aspects. To prove its coherence, it has been statistically compared with the data of a survey carried out among university students in Catalonia (Spain).     

Takayasu’s arteritis associated with Crohn’s disease

Takayasu’s arteritis (TA), also known as the “pulseless disease,” is a chronic vasculitis of the aorta and aortic branches. TA with Crohn’s disease is rare and has not been documented in China before. In this paper we report on a case of Takayasu’s arteritis associated with concurrent Crohn’s disease. A 17-year-old Chinese male developed upper limb sourness and a sensation of fatigue, and his upper limb pulses were absent. He was diagnosed with TA and underwent an axillary artery bypass with autologous great saphenous vein on the left subclavian artery. After the surgery, he regained the normal blood pressure. This patient also had years of diarrhea and developed an anal canal ulcer, and was diagnosed with inflammatory bowel disease and ulcerative colitis before. Five months after the TA surgery, he was hospitalized for severe stomachache and diarrhea and was finally diagnosed with Crohn’s disease. The possible pathophysiological mechanisms responsible for concurrent existence of TA and Crohn’s disease may be associated with immune disorders, especially autoimmunity.