iGeom - Interactive Geometry in the Internet

iGeom :: Geometria Interativa na Internet :: http://www.matematica.br/igeom

.: Interactive Geometry (IG) (or Dynamic Geometry) :.

The name Interactive Geometry (IG) (or Dynamic Geometry) is one kind of geometry allowed by computer programs (software), like iGeom. Any construction that can be done with compass and ruler, also can be done with this kind of software!

The major difference between "traditional geometry" (those with physical instruments) and IG, is that em IG is possible to move "free objects" into the constructions, and the software redraw the entire objects, preserving their properties. In order to illustrate this "dynamic behavior", in a construction of the Perpendicular bisector m, defined by two points A and B, if the user moves A or B, iGeom will updates all others objects, apparently in a continous movement (this is the reason for the name interactive geometry or dynamic geometry).

Perpendicular bisector m of the points A and B: click over one of the green points inside the blank area, release the mouse button, then, move the mouse around the the blank area. iGeom will update all others objects (circumference c0 and c1, points n and s and the perpendicular bisector m) in such way that m will be the perpendicular bisector of the original points (green points) in every configuration (preserving the property).

Using the dynamic/interactive construction, the learner can perform experiments with his construction, elaborating conjectures. A simple problem that shows how the software can improve the learner comprehension is this:

if the points A and B are on a circumferen of center O (so, they define a chord of circumference), what can be be assured about the perpendicular line defined by both points?

Stimulating this investigative behavior, the learner could learn new topics likewise a mathematician learn/deduces new theorems! Learning by doing.
Depending on the learning level, once the learner is convinced of the conjecture validity (conducted by the iGeom experimentations), the learner could elaborate a proof for the result.

Besides the circle and line constructors, the iGeom system, has some "shortcuts" (buttons) for special constructions, with direct access by buttons, like: midpoint, perpendicular line, parallel and measure of a chord of circumference. If in one hand, the teacher can hide some of them, which is useful in introductory courses, on the other hand these buttons save time in more elaborated constructions: these buttons can be used in more sophisticated constructions, avoiding tedious tasks demanded by construction with a great amount of steps.
All the constructions elaborated with the system could be easily exported by Web pages.

Another interesting features of iGeom are:

Script: It is possible to encapsulate constructions producing scripts. This can be understood as a mathematical function (or an algorithm), whose domain and image is composed by geometric objects of iGeom.
Moreover, iGeom allows script with self-reference, resulting in recursive algorithms. This feature is is very interesting to explore geometric fractals and to introduce programming concepts in a high level scheme (which could be called geometric algorithms). See the section Fractals and recurrence.
Authoring and automatic evaluation of exercises: Under the authoring feature, an exercise could be presented in an Web browser, in order to be solved by the the students. The student get instant access to the information about his solution: it is evaluated as correct or not.
If iGeom is associated with some Learning Management System (LMS), the teacher could be disobliged of evaluate a great amount of solutions and could have a summary of his student's solutions. An example of such LMS, that use iGeom simplifying the teacher's tasks, is SAW, that is free software (also developed by our research group).

.: iMática : iGeom : LEM :.


Início » Introduction ¤ Interactive Geometry » Using the iGeom » iGeom in others languages	iGeom » Operations mode » Buttons bar » Algorithms (scripts) » Authoring and evaluation	Examples » Basics contructions » advanced » Golden ratio and regular pentagon » Constructions of conics » Fractals and recurrence