North American GeoGebra Journal (GeoGebra Institute of Ohio)
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On Coloring Different Objects of the Same Class
No full textEvery object created in GeoGebra has a color property that can be easily changed by the user. This is useful for identifying different objects of the same class. However, if we create lists of objects of the same class (e. g. a list of circles) and try to change the color of this list, then we notice that all the objects change color. How can we create a set of objects of the same class, such that each element has a different color? In this article, I will show an efficient method to color different objects of the same class
On an Inequality Between Side Lengths of Triangles
No full textThe authors, using a proof without words style, explore a lesser known variation of the triangle inequality involving the difference between the sum of the lengths of any two sides and the length of the third side. The authors provide a web applet for further exploration
Examining Possible LU Decompositions
No full textLU decomposition is a fundamental in linear algebra. Numerous tools exists that provide this important factorization. The authors present the conditions for a matrix to have none, one, or infinitely many LU factorizations. In the case where no factorization exists, the authors illustrate how to approximate an LU decomposition by considering LU factorization of nearby matrices
Volume Invariant Cube Twisting: GeoGebra Modeling and Algebraic Explorations
No full textIf we take a cube and twist it 90 degrees, mentally or physically, without changing its volume, we obtain a twisted solid that is not only visually appealing but also algebraically entertaining. Starting with GeoGebra simulations, we discuss the algebraic nature of the twisted cube faces, the spiral curves, and further extend GeoGebra-based explorations beyond the cube.
Keywords: Cube, Twisting, Algebraic Analysis, Vector Functions, Ruled Surface
Some Activities in the Style of "Proof without Words” Related to Altitudes in a Triangle
No full textIn this article, the authors present some activities in the style of "proof without words” related to altitudes in a triangle. The activity is useful for teachers and students of geometry. Such activities may develop different ways of thinking for students, which may yield unexpected, short, and beautiful solutions that indicate the great wealth of mathematics
Modeling an Optimal Trajectory for a Certain Minigolf Station
No full textUsually a minigolf course comprises a station at which the ball is supposed to enter a net, which is installed about one meter above the ground. The minigolf player uses a ramp for giving the ball the right direction. One may ask, at which velocity the ball has to be driven off in order to enter the net. In this article, we present several ways to use GeoGebra for solving this problem. We will see that the features of GeoGebra can help to visualize the problem, to implement a mathematical model, to work in this model and to validate the results by comparing to empirical data
Exploring and Solving Feynman's Triangle Through Multiple Approaches
No full textIt has long been recognized that using multiple approaches to solve problems is essential for students to obtain understanding of mathematical concepts. In view of this, we consider an interesting plane geometry problem with a straightforward formulation, known as the one-seventh area triangle or Feyman's triangle problem. We present solutions using GeoGebra constructions and manipulation, coordinate geometry, Euclidean geometry and linear algebra. This allows students to apply many of the tools they acquired at the secondary level and to make important and crucial connections between them. The linear algebra section can be used as an introduction to the subject. This section can also reinforce the close relationship between linear algebra and geometry which might not receive enough emphasis at the undergraduate level. GeoGeobra diagrams, constructions and computer algebra are used throughout the paper. All explanations are done through questions and answers which allows instructors to easily format the sections into inquiry-based lessons
Modeling the Paths of the Sun Using GeoGebra
No full textIn this document we describe the necessary constructions for modeling the apparent position of the Sun in the sky in GeoGebra. We discuss how to build a planet that moves and rotates about its axis and a way to position the observer at a given latitude from which we will compute the horizontal coordinates of the Sun. Later these computed coordinates are represented in a celestial sphere where the horizon plane for the observer is fixed, giving the apparent track of the Sun at different days of the year
Creating a Digital Tape Diagram
No full textThe authors describe how tape diagrams created in GeoGebra can be used to foster critical thinking about multiplicative relationships in proportional situations. They describe multiple iterations of applet development and the rationale for various modifications
Capabilities and Contributions of the Dynamic Math Software, GeoGebra---A Review
No full textIn this review, the authors provide a survey of research of the dynamic mathematics software, GeoGebra, in the teaching and learning of school mathematics and related fields---including statistics, physics, chemistry and geography. The authors explore the role of GeoGebra as a tool to foster student achievement and teacher efficacy