Γεωμετρική ερμηνεία επίλυσης συστημάτων εξισώσεων 2x2
Geometric interpretation of solving 2x2 systems of equations
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Keywords
Συστήματα εξισώσεων ; Γραφική απεικόνιση ; Διερευνητική μάθηση ; Διαδραστική εφαρμογή ; Αριθμητικές μέθοδοι ; Newton–Raphson ; Εκπαιδευτική τεχνολογίαAbstract
The thesis concerns the design and implementation of an interactive web application for the
graphical display and solution of systems of equations in two variables. The aim of the work is to
support the understanding of the concept of system solution through the connection of algebraic
and geometric representation, utilizing modern technologies and pedagogical approaches. The
application was implemented using HTML, CSS, JavaScript technologies and the help of the
Math.js and Canvas API libraries. The graphical representation of the equations is based on
sampling of the Cartesian plane and detection of sign change, without requiring explicit solution
with respect to one variable. Finding the solutions of the system is implemented through a
combination of approximate geometric detection and numerical improvement with the Newton–
Raphson method for a system of two equations and two unknowns. At the same time, the
application supports interactive functions and distinct modes of use, allowing both the
exploratory search for solutions by the student and the automatic demonstration of the results.
The educational use of the application is based on the principles of exploratory learning and
visualization, aiming at the active involvement of the student and the development of
mathematical intuition.
Department
Σχολή Τεχνολογιών Πληροφορικής και Επικοινωνιών. Τμήμα ΠληροφορικήςNumber of pages
40Language
GreekCollections
Except where otherwise noted, this item's license is described as
Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα
Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα