8 x = x x = 2x 103 { y = 3y 105 104 x = 3x { y = y 1 x = __ x 106 2 { y = 2y { y = 3y ESERCIZI Costruire e trasformare 107 x = 5x { y = 2y 2 __ x 3 108 1 y = __ y 3 x = 5 ___ x x = 42 109 5 y = ___ y 18 Nel piano cartesiano è dato il quadrato ABCD di vertici A(0 ; 0), B(3 ; 3), C(0 ; 6), D( 3 ; 3). In esso è inscritta una circonferenza. Scrivi le coordinate del quadrato nello stiramento descritto dalle formule indicate e le coordinate del punto corrispondente del centro della circonferenza. Disegna poi le figure ottenute. Alla circonferenza ne corrisponde un altra nella trasformazione? La nuova curva è an[ ] cora inscritta nel quadrato? Perché? 1 x = __ x x = 2x x = x x = x 110 111 112 113 2 { y = y { y = 3y { y = 4y { y = 2y PRACTICE WITH CLIL The M bius strip August Ferdinand M bius (1790-1868) was a mathematician and an astronomer. He studied at the University of G ttingen where professor Gauss was the Director of the astronomical observatory. This last played a great role in M bius discovering his love for mathematics. As mathematician, he achieved good results but the one he is still most acknowledged for is certainly the invention of the surface that has been named after him: the M bius strip. It is a paper strip, some centimetres wide, which is given a half-twist, and glued to its ends: this simple surface is one of the most surprising in mathematics, which, though initially born as a game, has attracted attention in artists, magicians and scientists. 1. The M bius strip has not two boundaries (internal and external), but just one; in fact, if we try to follow the strip with a finger, we will arrive to the starting point after having covered a whole round. 2. Cutting a M bius strip lengthwise does not yield two strips, as we may imagine, but one long strip. 3. Cutting this new, longer, strip down the middle creates two M bius strips, wound around each other. Now it is your turn to make a M bius strip and verify the properties described in the above listed points. 339