DATI E PREVISIONI PRACTICE WITH CLIL A magic triangle As mentioned in the unit, the Tartaglia s triangle is often called Pascal s triangle who devoted an important treatise to it in his Traité du triangle arithmétique of 1654. In this study, Pascal anylised many properties of the triangle and realised that different possible combinations of a given set of objects are related to its numbers. Below, we will mention two of them, but there are many others that you can learn more about. Powers of 2 The sum of the elements of each row is a sequence of powers of 2. Furthermore, the sum of the elements of each row doubles the sum of the elements of the previTartaglia s triangle, Parco Pignera, Crotone. ous row and the sum of the elements of each row, decreased by 1, equals sum of the elements of all the previous rows. For example, the sum of the elements in the sixth row is 32: 1 + 5 + 10 + 10 + 5 + 1 = 32 = 25 The sum of all the elements of the previous rows is 32 1, in fact: 1 + 2 + 4 + 8 + 16 = 31. 1 1 1 1 1 1 1 + + 6 + 5 + + 4 + 15 + 3 + 10 + + 2 + 6 + 20 1 + 3 + 10 + 1 + 4 + 15 1 + 5 + 1 + 6 1 + 1 1 2 20 21 4 22 8 23 16 24 32 25 64 26 Magic additions Each element of the triangle equals the sum of the elements in the previous row as represented below. 1 1 1 7 1 6 1 5 21 1 4 15 1 3 10 35 1 2 6 20 1 3 10 35 1 4 15 1 5 21 1 6 1 7 1 1 Exercise By searching in the schoolbooks or on the internet, look for other properties of the Tartaglia s triangle. 440