Page 21
R
−3.0
0
1.6
π = 3.14159 . . .
12
Page 22
1
1
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, . . .
1
6 = 2 × 3 15 = 3 × 5 1400 = 23 × 52 × 7
2
13
Page 23
f (n) = n2 + n + 41
n f (n)
f (0)
41
f (1)
43
f (2)
47
14
Page 24
f (n) = n2 + n + 41
n f (n)
f (0)
f (3)
f (1)
f (2)
. . . f (39)
f (40) = 402 + 40 + 41 = 40(40 + 1) + 41 = 41 · 41
n = 40
15
Page 25
P (0) = 3
P (1) = 0
P (2) = 2
P (n) = P (n − 2) + P (n − 3)
n>2
n
0 1 2 3 4 5 6 7 8 9 10 11 12
P (n) 3 0 2 3 2 5 5 7 10 12 17 22 29
n
13 14 15 16 17 18
P (n) 39 51 68 90 119 158
16
Page 26
P (0) = 3
P (1) = 0
P (2) = 2
P (n) = P (n − 2) + P (n − 3)
n>1
P (n)
n
n
0 1 2 3 4 5 6 7 8 9 10 11 12
P (n) 3 0 2 3 2 5 5 7 10 12 17 22 29
2 3
5
7
11
n
13 14 15 16 17 18
P (n) 39 51 68 90 119 158
13
17
17
Page 27
271 441
18
Page 28
271 440
...
19
Page 29
Page 30
√
Page 31
2
√
√
2
x
y
x
y
2 = x2 /y 2
y
x2 = 2y 2
2 = x/y
0
x2
x
20
Page 32
x = 2w
x2 = 4w2
w
4w2 = 2y 2
√
x
y 2 = 2w2
y2
y
y
2
21