1 2
580-500 375-330 287-212 3 332 332 642 4
al-khowarizmi 5 Sylvester Gerbert(940-1003 Gerbert Leonardo Fibonacci Leonardo Fibonacci Leonardo of Pisa Leonardo Bonaccio Figlio Bonaccio Son of Bonaccio Fibonacci( ) Lucas 1842 1891 nickname 6
7 1202 1170 Pisa 1250 8
Diophantus 9 =1.3688081075 10
11 Fibonacci sequence 12
13 Lucas Lucas Lucas 14
1962 Brousseau Hoggatt 1963 Lucas 15 16
17 666 18
1996 1996 8 4 8 1,1,2,3,5,0,5,5,2,7,1,0, 4 6 1996 1998 2004 2001 8 1 19. 20
21 22
. 1 23 24
25 26
27 13 233 7 13 19 28
6 7. 7 29 8. 9. 10., 30
11. : 31 32
33 34
35 12. (5) 36
37 13. 38
39 40
41 42
43 44
4 45 46
47 48
49 50
51 52
53 54
Simson 1753 (golden section 55 56
57 58
297 210 1mm 1 =0.1 1m=1 100 59 60
61 62
63 64
65 66
67 68
69 70
71 72
73 74
75 76
77 438 Parthenon Athena Athena Parthenon 78
79 80
81 82
83 84
85 86
phi, Phidias Phidias pentagram 87 (1459-1519) 1509 Luca Pacioli Divina Proportione divine divine number 88
89 1483 St.Jerome 90
St. Jerome 91 Davis and Altevogt(1979) Munster Pascal (Gymnasium) 207 252 1.618 1.615 92
14 93 94
95 96
97 98
100 99
101 102
103 104
105 106
107 108
16 109 1. 2. 3. Pentagon 110
111 17 112
113 Wythoff Wythoff 114
115 116
117 118
119 120
2. 121 122
123 124
125 126
127 128
20 129 130
131 132
133 134
135 136
primordium 137 138
139 140 70
141 142
143 144 72