I provide a visual proof for the "Convergence of a Hyper power sequence," which generalises a beautiful result; also proved visually by Azarpanah in 2004.

Undergraduate students usually study Laurent series in a standard course of Complex Analysis. One of the major applications of Laurent series is the classification of isolated singular points of complex functions. Although students are able to find series representations of functions, they may struggle to understand the meaning of the behaviour of…

This article uses dynamic software in Excel to demonstrate several ways in which graphical and numerical approaches can be introduced both to enhance student understanding of l'Hopital's Rule and to explain why the Rule actually works to give the "right" answers. One of the approaches used is to visualize what is happening by examining…

In this paper we present two simulations designed with GeoGebra that illustrate dynamically a key concept in Vector Calculus: line integrals of vector fields, along with other associated mathematical properties and applications. Students are not required to know the GeoGebra environment: a user-friendly interface with buttons, functionalities and…

It is well known that mechanical engineering students often find mechanics a difficult area to grasp. This article describes a system of equations describing the motion of a balanced and an unbalanced roller constrained by a pivot arm. A wide range of dynamics can be simulated with the model. The equations of motion are embedded in a graphical…

GeoGebra is a mathematics software system that can serve as a tool for inquiry-based learning. This paper deals with the application of a fraction comparison software, which is constructed by GeoGebra, for use in a dynamic mathematics environment. The corresponding teaching and learning issues have also been discussed.

This classroom note illustrates how dynamic visualization can be used to teach conditional probability and Bayes' theorem. There are two features of the visualization that make it an ideal pedagogical tool in probability instruction. The first feature is the use of area-proportional Venn diagrams that, along with showing qualitative relationships,…

A complex technology-based problem in visualization and computation for students in calculus is presented. Strategies are shown for its solution and the opportunities for students to put together sequences of concepts and skills to build for success are highlighted. The problem itself involves placing an object under water in order to actually see…

The way in which computer algebra systems, such as Maple, have made the study of physical problems of some considerable complexity accessible to mathematicians and scientists with modest computational skills is illustrated by solving the multiple pendulum problem. A solution is obtained for four pendulums with no restriction on the size of the…

A Mathematica[TM] package is described that uses simulations and animations to illustrate key concepts in harmonic oscillation and electric circuits for students not majoring in physics or mathematics. Students are not required to know the Mathematica[TM] environment: a user-friendly interface with buttons functionalities and on-line help allows…

The Mobius strip, torus, and Klein bottle are used to graphically and analytically illustrate the differences between orientable and non-orientable surfaces. An exercise/laboratory project using the non-orientable Boy surface is included. (Contains 11 figures.)

The continuous technological progress of the past few decades affords a different orientation to the teaching-learning process, which is useful and advantageous when mathematical concepts are transmitted. This article pursues two different aims. The first one is to examine the present state of the traditional process in relation to the concepts of…