North American GeoGebra Journal (GeoGebra Institute of Ohio)
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88 research outputs found
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A Celestial Sphere Model in GeoGebra
No full textThe article presents a celestial sphere model made in GeoGebra. The authors describe the math- ematical tools necessary to model celestial objects using spherical coordinates and the construction of stars, circles, and meridians. They incorporate a brief description of the construction of constellations using GeoGebra through JavaScript. In addition, the article describes the modeling of the ecliptic and the positions of the Sun and the Earth to understand their apparent movements and the concept of the Zodiac
Fair Share of Regular Polygon Pizzas
No full textIn his article we show how to fair share a regular polygon pizza with p sides between n people The first cut point F on the boundary is given and, as in round pizzas, the cuts are done from the center C to the boundary of the regular polygon; The Proof given is without Words using a Geogebra animatio
Extending, Formulating, and Refining Conjectures with GeoGebra: The Pentagon and Its Medial Pentagon
No full textIn this paper, I describe a classroom experience on how I guided a group of preservice secondary mathematics teachers to extend, formulate, and refine a conjecture about the ratio of the area of a pentagon and the area of its medial pentagon: The ratio of the area of a medial pentagon to the area of the outer pentagon lies between 1/2 and 3/4. The use of GeoGebra facilitated the discovery and visualization of the conjecture
Tracing closed curves with epicycles: A fun application of the discrete Fourier transform
No full textThe Discrete Fourier Transform has many applications in our modern digital world. In particular, it allows us to approximate periodic functions by means of trigonometric polynomials which provides the required information to define a system of epicycles that can be animated to trace out closed curves. In this paper, I present a method in GeoGebra to create artistic animations consisting of systems of epicycles tracing out closed curves. The geometric construction presented here can also be used as an introductory learning activity to study the Discrete Fourier Transform from a geometric point of view
Layering: Showing and Hiding Objects
No full textAll GeoGebra objects are assigned to a layer, which can be made visible or invisible. In this article, the authors highlight this feature by example and suggest four tasks in which layers can be implemented
Lists and Sequences
No full textA list in GeoGebra is an ordered set that can contain repetitions. For example, {1,2,3} and {2,3,1} are both lists, but they are not equal since the elements of the list (namely 1, 2, and 3) are in a different order. Note, too, that lists need not be lists of numbers. Instead, they can contain other objects such as numbers, coordinate pairs, polygons, and conics. We explore several examples in the following paper. 
Proof Without Words: Fermat-Torricelli Theorem
No full textThe authors explore the Fermat-Torricelli Theorem in a proof without words using GeoGebra. They provide two alternative approaches to the theorem and discuss connections to other geometry problems accessible to secondary level teachers and their students
From Semi-Proof to Proof: Motivating Deductive Thinking Through Inductive Exploration
No full textIn this short article, the authors introduce and prove a geometrical property involving externally tangent circles. Using an applet to model the problem situation, the authors illustrate how GeoGebra applets can serve as an accelerator of understanding, helping aid in the progression from inductive to deductive proof
Achievement of Dual Language Learners in the Study of Nets
No full textThis study generally aims to study the effects of teaching using the van Hiele phase-based instruction using GeoGebra on Year 2 (8 years old) pupil’s achievement in learning shape and space whom learning mathematics using English language as this is their second language. Samples has been taken from one Dual Language Programme (DLP) school in Penang. 14 boys and 16 girls from one Year 2 DLP school have been involved in this study. The research design is one group pretest - posttest research design using Shape and Space Achievement test (SSAT) as instrument. Interview protocol also has been carried out to sample group that used GeoGebra. Paired samples t-test and the Wilcoxon Signed Rank test were used to analyse the data. The results indicated that: (1) there is a significant effect of teaching using the van Hiele’s phase-based instruction using GeoGebra on Year 2 pupils’ achievement in learning shape and space; (2) there is a significant difference in retention of achievement in the topic of Shape and Space on Year 2 pupils who learned the topic through the van Hiele’s phase-based instruction using GeoGebra. Implications of the study and suggestions are also discussed in this study.
Keywords: GeoGebra, the van Hiele Theory, phase-based instruction, Dual Language Programme (DLP
Locus of Critical Points for Some Polynomial
No full textGiven a polynomial with complex coefficients, the celebrated Gauss-Lucas's theorem and Marden's theorem offer us insights into the geometry of the locus of its critical points. In the following paper, the authors explore the geometry under certain restrictions of the roots of the polynomials. In particular, the authors identify some regions where all critical points do not occur