9 ESERCIZI Operare con i numeri reali PRACTICE WITH CLIL Spiral of Theodorus The geometric construction of square roots of integers has been attributed to the Pythagorean School s mathematician Theodorus of Cyrene. Though known as the Spiral of Theodorus , its construction is rooted in the Pythagoras theorem. Let us consider the isosceles triangle OAB where OA = OB = 1. ______________ 2 2 B 2 1 _ According to the Pythagoras theorem OB = O A + A B = 2 O 1 A Let us consider the following figure where we will construct a new triangle rectangle, having B as its right angle, and OB and BC as its catheti, the last one measuring 1. C 1 B 3 2 O 1 1 A ______________ _ Yet again, according to the Pythagoras theorem: OC B2 + B C2 = 3 = O By repeating the construction procedure of new triangles rectangles, it is your turn to verify that you will obtain the following figure: D C E B 3 F 2 G O 1 A What is the measure of all segments that have an endpoint in O? 379