module 17 support & resistances 2 the fibonacci magic · magic . the "greatest european...

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Module 17 Support & Resistances 2 – The Fibonacci Magic

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Page 1: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in

Module 17

Support & Resistances 2 – The Fibonacci Magic

Page 2: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in
Page 3: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in

The "greatest Europeanmathematician of the middleages", his full name was Leonardoof Pisa, or Leonardo Pisano inItalian since he was born in Pisa.

He was one of the first people tointroduce the Hindu-Arabicnumber system into Europe - thepositional system we use today -based on ten digits with itsdecimal point and a symbol forzero.

Page 4: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in
Page 5: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in

1 1 2 53 8 13 5521 34 89 144 233 377

618.0377233

6180233144 . 618.0

144

89

382.0377

144

236.0377

89

618.0618.0

382.0

618.0382.0

236.0

618.089

55

618.1233

377

618.2144

377

236.489

377

618.0618.2

618.1

618.0236.4

618.2

Page 6: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in

618.0ab

618.0baa

a + b is to a as a is to b

Page 7: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in

A golden spiral gets wider (or further from its origin) by a factor of Φ for every quarter turn it makes.

Page 10: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in
Page 11: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in
Page 12: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in
Page 13: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in

20

10 18,6618,010

82,1318,600,20

10618,118,6

82,231082,13

x

Page 14: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in
Page 15: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in

T

B

T

B

ATH

B

ATL

61.8

38.2

23.6

T

B

ATL

B

T

T

ATH

61.8

38.2

23.6

Page 16: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in
Page 17: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in

ATH

T

B

B

ATL

161.8

261.8

423.6161.8

261.8

T

B

B

ATH

ATL161.8

261.8

423.6

161.8

261.8

Page 18: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in
Page 19: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in
Page 20: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in
Page 21: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in
Page 22: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in
Page 23: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in
Page 24: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in
Page 25: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in
Page 26: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in

61.8%

Page 27: Module 17 Support & Resistances 2 The Fibonacci Magic · Magic . The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in