# In the traces of Pythagoras

## Introduction

Brief teaching of the Pythagorean theorem to 20 students coming from seven European countries , i.e., Poland, Portugal, Spain, Finland, Romania, Italy and Germany, in the frame of the Erasmus project  ran  by our school, entitled “Learning with Arts”. The teaching combined the theoretical presentation of the Pythagorean Theorem with its practical application, by means of two specially made LEGO EV3 robots. The purpose of the course was to help students get to know and ‘experience’ the Pythagorean theorem.

## Educational Subject

Mathematics, Computer Science, Robotics, Geometry, History

## Description of the practice

Initially, Pythagoras and the Pythagorean Theorem were presented in combination with examples of calculating the length of the hypotenuse of a right triangle. Then a worksheet was handed out and the students, divided in groups, were invited to calculate the length of the hypotenuse of a right triangle according to the examples they had been earlier exposed to.

During the next step, the students learned about the LEGO EV3 robotics kit and its programming environment. In addition, an interactive whiteboard featured an exercise in Geogebra that showed the relationship between the perimeter of a circle and its calculation of the distance a robot covers when its wheel makes a complete rotation. There was also a presentation on π = 3.14 and on the way of calculating the perimeter of a circle, which was necessary for the experiential exercise that would follow.

Finally, the guest students were given a  EV3 robot, made by the pupils of the robotics group (E-F class), with a marker adapted on it, so that it could write on paper. In addition, each group was given a sheet of paper designed with two vertical lines (vertical triangle lines), as well as rulers on how to measure their length. The students of the robotics group (E-F class) had created a program in the programming environment of LEGO EV3, which took as inputs the values of the perpendiculars of a triangle and calculated the hypotenuse of the triangle and moved the robot for the corresponding period.

In this phase of the task, the guest students were asked to count the two vertical lines and then enter them into the program, download them to the robot and draw the underlying sheet on the sheet they were earlier given, confirming the correct calculations made following the rules of the Pythagorean Theorem.

## Duration of practice realisation

2 hours and 30 minutes

## Learning Outcomes

The students were thrilled with this type of hands on- minds on activity. Of course, there were some problems with the language, as not everyone spoke English at the same level, but also with the level of mathematics that the students had been taught, as they came from 7 different educational systems. However, judging from the opinion and the evaluation of the teachers who attended the activity, as well as from the enthusiasm of the participating students,  we can safely conclude that the outcome of the activity was successful.

## Hardware/Software/Other Resources

LEGO EV3 Education Robotics Kit

LEGO Mindstorm  EV3 Home Edition (Software)

PC

Markers

Papers

Pythagoras

## worksheet

Pythgoras-Worksheet