.Математика.за.30.секунд.pdf

, 2014

50 , 30

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611 28.706 34

. .

34 / [. . . ; . . . -; . ]. . : , 2014. 160 . : .

ISBN 978-5-386-07012-0

2012 . Pier 9,

Murdoch Books Pty Limited Ivy Press Limited.

. ,

(, , ,

)

. ,

Ivy Press Limited, The Old Candlemakers, West Street, Lewes, East

Sussex BN7 2NZ, UK

611 28.706

ISBN 978-5-386-07012-0 2012 by Ivy Press Limited.

2012 . Pier 9, Murdoch Books Pty Limited Ivy Press Limited

, 2014

-

. .

. - .

. .

: .

: . .

Creative Director Peter BridgewaterPublisher Jason Hook

Editorial Director Caroline EarleArt Director Michael Whitehead

Designer Ginny ZealIllustrator Ivan HisseyProfiles Text Viv Croot

Glossaries Text Steve LuckProject Editor Jamie Pumfrey

/ - /

. 2 1

29.12.2010 . 436- .

25.11.2013 . 180230. FuturaLight

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, - . . , - , - . , - , ( ) - . , - , - , - . - , . , , . , - . - , ; , . 50 -- , . , , , . - , . -. , .

6 g

, . : a2+b2=c2.

, . . - . . - -, , . , - -, . , . , . 3 : - , ; 3 : - , . - . , - , , : .

8 g

, . . ? , .

12 g

. , , , . , . , - , .

. , , . , - (. c. 80); , x2225 0, x52.. -, , . . . (1,6180339), - f () .

. , 1 0. , 1- (10051), 10- (101), 100- (102) . ., 1- (2051), 2- (21), 4- (22) . . , 7

111, 1341132113157.

. , , - , -. .

(). , . , , , . , ; , . (, 2/3 ), (, 3/2 1

1/3 ).

. , - . - - p 2.. , - , , . - .

g 13

. , - ; , a1bi, a b - , i521. (. ).

. , . , 4x58, 4 , x -. - (, ). , - - , - , .

. , . , -, , - i. , i3i521, i521. , 21, , , .

. , , - , - . , x2 (. , c. 80).

. , - . , 3 4 12, , 1, 2, 6 12.

. , . , . p ; -, p p2510. .

. , (, , ).

. , , 1, 2, 3, 4, 5 , 0 .

. - , - ; - , .

14 g

30

, .

3- - (790850)

- -(920980)

- -(11301180)

()(11701250)

(c. 16)

(c. 20)

(c. 36)

3 : . 0,25 1/4

; 0,5 1/2 ; 0,75

3/4 . 1/3 0,333333..., ; 1/7 142857142857142857..., . , , , p, .

0, 1, 2, 3... - . - . 15 - 7 , 15/7 ( 2

1/7 ) . - - -. , p, - . . , - , -, - . , 725 ; . . 7 -, 2 5 . - - , , . , 725,43 7 , 2 , 5 -, 4 3 . - - , , , -.

3 : : 0, 1, 2, 3... , .

16 g

30

, .

3- (V . . .)

(17281777)

(18221901)

(18521939)

(c. 14)

(c. 44)

(c. 80)

(c. 96)

(c. 100)3 :

, , , . : , 2 , , .

- -, 0; - . , , . . , , - (, 1/2

7/3 ); - , . . , - . , , , , 2 . - : - - , . . , - (, 3/1150,272727...). , - (, p53,14159265...) -. . -, -, . . -, . , 2 x22250 (. , c. 80).

3 : , . , .

18 g

30

.

3- ()(15001557)

(15011576)

(15261572)

- (17771855)

(17891857)

(c. 14)

(c. 80)

(c. 150)

3 : , , , x3x521. , , . , ; , - . .

- - . . , 14 4 , 24 4 . . -; , 24335212. - , ; -, 24323512. , - , , , , . , - (, x2521) , - ( ). - - i, 21, i3i521. , , -: -. , .

3 : , i, 21.

30

20 g

; , , .

3 : , , . 400520320 : 183205360 , , . , 10 , : , ?

3 : , .

3- (16461716 )

(18151864)

(c. 36)

, 1 , 0, - . - , - . . . , 9 - , - 59. ; , 60 , 360 . - (12 ). - ( - ... ). - , 0 1. - ; , . , - -, 111, : 10 ( )!

30

22 g

, , . .

3- ( 300 . . .)

(17771855)

(18651963)

(18661962)

(c. 30)

(c. 94)

3 : , , , . , , . . , , , , .

. , 10054325. 10052035. -, : 100 :10052323535. , -, 1 . - , , . - , , . - - . , 17 463 991 229 . , ? , 1 , , . , , . - 10 000 000 , , , .

3 : , ; .

30

24 g

. -, .

3- ()(1770c. 1250)

(c. 30)

(c. 98)

3 : 1202 . , , , Liber Abaci ( ) . , , . , 144 !

- 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ... . , , - . - -, , , . , - 11112131518 21 . - -: 111141912516458313. 1:1, 2:1, 3:2, 5:3, 8:5, ... f 1,618. - , , - , , . . - . , - -, . -, , -, , -.

3 : , , .

1

1

2

3

5 -

8 -

26 g

30

.

3- (16231662)

(16431727)

(c. 24)

(c. 76)

(c. 80)

3 : . , 1, 2, 3, 4 . . . . : 1, 3, 6, 10, 15, ... . , (, , ), . , !

: (1 1), (1 2 1), (1 3 3 1), (1 4 6 4 1), ... -? , . : - (11x) . (11x)25112x11x2. - (11x)35113x13x211x3. : (11x)45114x16x214x311x4. - , - . - : (1+x)5511?x1?x21?x31?x411x5. ? - -. -. , , . , - , - . : - - . - . , (1+x)5, -: 1, 5, 10, 10, 5, 1.

3 : .

28 g Numbers & Counting

19 , 1623 ( -)

1631

1639 ;

16421645 ,

1647 ,

1650

1653

1653 ,

1654

1655 , ; , -

16561657.

1658

1668 ,

19 1662

1670

1779

, , . - (. 2627) . , : -, , - - . 1646 ; -- -. . ; . . , - , - , . , -. , , , -, , -.

, , - ( -, ). -, , , ( ) . 6 ; , - . 12, , - - ; - , , , . - , - 50 , . , - - . , - ( ) . ,

g 29

30 g

30

; , .

3- (570495 . .)

( 300 . .)

(16011665)

. . (17771855)

. . (18771947)

(c. 22)

(c. 88)

(c. 94)

(c. 136)

- , . , - 4. - 1, 3. 1, , . , 73/4 518 1. , : 7359164532182. , 3 , , , (, 7 59). : ? - , . - , . -. , - , , , , . . - . , - - . - .

3 : , .

3 : , , . 70 . . , , , , .

> : , 52 10 15.

> , 1, : 82564.

. - , - . , , 1 (-), 3 (), ( ) . . , , .

. , ; , , . , , (a3b)3c5a3(b3c).

( ). - , , ( ) ( ), 0 1 . .

34 g

. , , - , -. (. . , ) (. . , , , 2), (, p).

. , - . - , (x) (y) , .

. -, . - .

. , -

g 35

; , , -- .

. , ; , - . , , 3355533.

. , - , . 339527 - 9, 3.

. - , - (1714). ; - , - .

. , . - -

(, x y), - : 3x56, 3 -, x , 6 .

. , , , . 43564, 4 3.

. -, - (). f (x). , f(x)5x2 , x x2, . . f (5)525, f (9)581, . .

. - - , , - . - , .

30

36 g

, .

3- (598670)

-(780850)

(11701250)

(c. 20)

(c. 38)

(c. 40)

(c. 42)

(c. 44)

3 : 0 , - 0 . . - . - . , , , - - - !

- , ( !), - . , - . 628 . . - , , ; - . 820 . . - . 1202 , - . - , -; , , . : a105a, a - , - . : a3050, 0/a50, a0. , - . - , - . - 0 2, . 0, 1.

3 : , 0, . .

3 : !

3 : , Pixar, : !. , , . , 10100 (), , 1. , . - , .

(c. 16)

(c. 50)

- (c. 148)

3- (490430 . .)

(18451918)

30

, , - . , - , . - , 0 1 , . -. -, , - , , - . - - , . , ( !), . - - - (. . ), , - .

38 g

, ? , .

40 g

30

.

3- (476550)

(598670/668)

(11701250)

(14621498)

(c. 14)

(c. 20)

(c. 36)

(c. 42)

3 : . , . : 1/21

1/411/81

1/16151. : , (. . 1/4 ), (1/8 ), . . . , 121/31

1/521/71

1/921/111

1/1321/15...5

p/4 .

3 : . .

, - 2000- . , -, . - - 67 . ., 1 2 1489 . , , - , . - 9, -, . , . . a1b5b1a; -: (a1b)1c5a1(b1c). - , : a10=a. -, . - , ; , a2b, a , a b . , -. , , - .

30

42 g

- . , , .

3- (476550)

(598670/668)

(11701250)

(c. 14)

(c. 30)

(c. 40)

(c. 44)

3 : , . , , , . , .

3 : . , , .

, : , . - , - , , - VIVII . a3b5c, a , b , c ; a b - . - -: a3b, ab, (a)(b), ab, . , , , 9. a315a, 1 - . , . . a3b5b3a, , . . (a3b) 3c5a3(b3c). . - a4b5c, a , b , a c . - a/b, a4b. . . -, , - . , 0, , , -, 0 .

30

44 g

, .

3- (15501617)

(17071783)

(c. 16)

(c. 42)

(c. 46)

3 : XVI , , . , log10(x) ( 10), ln(x) . 2 3, e, , p, , .

1 - , , (. . ). 1 , - . 100 % , . . 1 2. - , - , , 8, 2323252358. 4 16, . . 2358, 2 ; 3 - , 2 . , , . , - , , ? , - , : log2853. , log2 - , 2, x. , , , - .

3 : - . ,

y ( ) y52x

y5x

y5log2(x)

x

46 g

30

3- (13201382)

(15961650)

(16461716)

(c. 44)

(c. 78)

(c. 102)

(c. 108)3 :

, , : , , . , , , , . . , . , . ?

3 : .

, - . , - , - () - (). f (x) - x. , f (x)5x2 , 9 (32) 3. XVII . , . - ( ) - , x ( ), f (x) ( ). , f (x)52x13 - , - (x;y), . , (1;5), 5523113, (2;7), .. 7523213. f (x,y) xy .

x 1.7x325x220.3x11, .

f (x)521.7x325x220.3x11

f (x)

x

(1, 26)

> f(x) 2 1.2. , x51, 6. , (1,6).

1 1646

1662

1664

1665

1673

1686 (Discourse on Metaphysics)

1710 (Theodicee)

1711

17121713 (Monadology)

14 1716

1675

1677 -

1684

g 49

, , , , -. , - (- , ). , - , , 50 . 1711 . - , - , . , , . - , , , , , - . -.

- XVII XVIII . - , , - . , , -, . , . , , -, , , , -, , , , , - . - , , ; , , , . , , 12 -, - 16. - , , , - .

30

50 g

. , .

3- (287212 . .)

(16431727)

(16461716)

(17891857)

(18151897)

(c. 78)

(c. 108)

3 : . . .

- , . , , . - , . - -. : - , ? - - . , -. -, - . XVII - - , - . . - , - , . , , .

3 : , .

54 g

. , - , , . .

-. , , , . , , -, . (. -).

. , - , . , 0

( ) 1 (). , . 13/52 ,

1/4 . , , , 0,25.

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. , -, , -

g 55

. - , , . , , , . (. , ).

. , , .

. - , (, ) , -

, .

. , . , .

. , - . - p, - , , 12, p/(12p), (12p)/p. , 4 - 1/6. , 4 -, 5/6. . . 4 (1/6)/(5/6), 1/5. , , 4 1:5, 4 5:1. , .

30

56 g

, , ? .

3- (19031957)

(19162001)

(. 1928 )

(. 1937)

(c. 62)

: (c. 64)

: (c. 66)

(c. 70)

3 :, , .

3 : , . , . 2007 , . , .

, - . , . , , --, - . , . , - . , , , , . , ? , -, - . , - . , , . - : , . - , : - .

3 : , , .

3 : ( ) , . , : , 1 40, , . , , 2 3, ( 3/

5 ).

, .

(c. 62)

: (c. 64)

(c. 68)

(c. 70)

3- (16011665)

(16231662)

(16291695)

(19031987)

30

, 6 5 1. , 6 - , - , . - : 6 1/6 , . . 6 . - 51 1, 1/52 . , , - . - , - , . - 0 1, 0 - , 1 . : - , 1/1024 (. . 1023 1). , (. . - ): -, , , 51/52 ( 1 51). -, ?

58 g

, 3/6 , .

1545 Artis magnae, sive de regulis algebraicis, , Ars magna

1545

1550 (Cardan grille),

1570

1570 Opus novum de proportionibus

21 1576

1576 De vita propria

24 1501 ,

1520

1525 ; , 1539 .

1526 (Liber de ludo aleae), 1663 .

1536 (De malo recentiorum medicorum usu libellus)

1539 (Practica arithmetice et mensurandi singularis)

g 61

, , , , , ( -: ), - , , (, , ). , . - , , - , , - , , . . ; . - . ( ), , , , - , alma mater. , , - . , Ars magna

(1545), -, - . - . , - , , - . , , - , , - , -, - . 1560 , - . - , - . - . , , -: - . 21 1576 , , , . , - . , - , - .

30

62 g

, ? , .

3- (16541705)

(17961878)

(18211894)

(18711956)

: (c. 64)

3 : 1713 . , , , , .

3 : , , .

, - , , -, . - , . , . -. : , . - . , , , . , , , - . , -, , -, . - , , , - - .

30

64 g

, , .

(c. 62)

: (c. 66)

3 : , , . : , 12 , 30 20 . . , ( !). .

, , , , . , , -, , , . : , , - , , 50 50. - : 100 - , , - . 53 - . , -, -, , - . ! - , , - , .

3 : .

:

3- (15011576)

30

66 g

.

(c. 62)

: (c. 64)

3 : - (double-zero), . , , . . , , , .

37 : 18 , 18 - (). - . , - . , , , , . , . 1, 2 4 ( 7), 8 , 1 . , -, . , 1 , . , , -. - , - 100. , 1, 2, 4, 8, 16, 32, 54 ( 127) - - 128, - , . 1 , - , - - . -, , .

3 : .

:

3- (15011576)

30

68 g

? .

3- (18711956)

(19031987)

(19262009)

(. 1947)

(. 1948)

(c. 62 )

(c. 70)

(c. 84)

(c. 144)

3 : : (0) (1), , . . (. . ), , .

() (), ... . : . : ? , - . , (, , ) . - , . . ... , . , , . , - . - . - - . : .

3 : .

30

70 g

, , (9) (99).

3- (17021761)

(c. 58)

: (c. 64)

(c. 68)

3 : , , XVIII . . , , - , .

3 : , , .

, -- 90 %. - , , . - , -? , ! - ; , - . , - , . , 1 % . -, , - . 1000 10, 9 ( - ). 990 , 10 % , 99 , (- ). - 99 9. , , , 11:1 , . - , - .

74 g

. , ; - , .

. , ; , , . , , (a3b)3c5a3(b3c).

. , - . (. . , , - ), (, ; -, 2), (p).

. -, . - .

. , . , , ; -, .

. , ; , - . , , 3355533.

. , , . , 3x2854, 3 , x , 8 4 .

. , . , 4x58, 4 , x . (, ). , - , , .

. - , , 5.

g 75

(). - , - , , , , x2. (. , c. 80.)

. -, . , 0. - 1.

. , (, , , , ).

. , - . , , x y. -. 3x56, 3 , x , 6 .

. - , ,

. , , A, B.

. , - . 43564, 3 , 4 .

. - - . ; , 2, 4, 6, 8 .

. , - . , . , - .

. , , 1, 2, 3, 4, 5 , 20 .

-, , .

30

76 g

x , .

3- (200284)

-(770850)

(850930)

(10481131)

(11141185)

(c. 78)

(c. 80)

3 : , , . , : 4 5, 3. , 12 15. , : 27. , (41559), (933527). .

3 : , , x y, , .

, , - . , , - , . , ; -, x. - x, x ( 2x). , x57, , , : 2x514. - . - s, d, t, - , . : , - , s5dt. -, - , . - (, d510, t55), , , - (s510/255).

78 g

30

, , .

3- (325265 . .)

(200284)

-(770850)

- - (9531029)

(18791955)

(c. 50)

(c. 76)

(c. 80)

3 : , . . , . .

3 : , , .

5 . - . , - . , , 757, - . -. : E5Mc2. - , (E), - , (M), (c), - . - -. . x , 2x1159, x , , x. x, -. -: , . , , . - 2x58. 2, 2 : x54. .

30

80 g

.

3- (1499/15001557)

(15011576)

(18021829)

(18111832)

(c. 16)

(c. 46)

(c. 76)

3 : , . , , ( ) . , , : z=x2+y2, , .

3 : , , , .

- 3x215x2150. - , (, 3x2), (x) - (2). , , (. . , - ) - 2. , - , , . ( ) . -, -. - ( , 3) ( ) XVI . , , .

> , x2 1 y2 2 z2 5 1

> , z 5 x2 1 y2

z 5 x2 1 y2

x2 1 y2 2 z2 5 1

770 ,

825

830

830

850

XII

1126 -

XII

1857 Algoritmi de numero Indorum -

- g 83

, . , (825 .). , , . - ( -, ). , - al-jabr (, -): - , - - . , - -, - . XII - - , - . - - - , - . , .

- . , -. ; , ( XVII -). - -, - - . - - - . ( - , - , 70 ); , - , - , -. - , - , . -

-

84 g

30

, IX .

3- (19031995)

(19091994)

(19121954 )

(. 1939)

(c. 80)

(c. 142)

(c. 144)

- (c. 82)

3 : . , . , . , , , . ? . , -?!

3 : . .

- . - , , - . , - , - - . -, , - - , . - , 1930 -. , . , - - , . - , - . . .

86 g

30

.

3- (17361813)

(18021829)

(18111832)

(18211895)

(18451918)

(19242010)

(c. 46)

(c. 88)

3 : , , . , 12 . , .

- . - () , - . ( - ), - ( -, ), . , , . , - . (1) - (, ), . (2) - , - . - , , , . (3) - , . - .

3 : . .

AB C

A"B

B"C

A"B"C

A"C

88 g

30

, . , , .

3- (18111832)

(18311916)

(18821935)

(c. 40)

(c. 42)

(c. 80)

(c. 86)

(c. 104)

3 : , . , . .

3 : . .

- : (, -, ). - , 11419116 - , ; , ( - ). , , : a3(b1c)5a3b1a3c. , . , : . - , - , - . : , , , - . , - - (, ) . - - .

92 g

rank (, ). - crank , .

. , - .

( ). , .

. , , , , .

. - , , , -, , . 180. (. ).

. -, , . . (. ).

. , , , . , .

( -). 12 , - . . .

. , , . - -. - , , .

( -). , 20- , - . - .

. , .

g 93

. , , . , 3x2854, 3 -, x , 8 4 . , p e.

. -, - , -, . .

. , - ; .

(). , .

. , .

(). , . - .

. . .

. , , .

. , (. . ) - .

. , , .

. , , ( , ). p , , , - p2510. -.

. , . (-).

30

94 g

. , , , , .

3- (570490 . .)

( 300 . .)

(c. 22)

(c. 104)

(c. 106)

(c. 114)

3 : . , , , . , , . I , , : .

-, -. , , , - , , , - . - , 22 - - . , , 13 ( 1 - , 13- ), . 7- , - , , . 9 - , ; , 32142552, - .

3 : 13 , - , .

30

96 g

, p.

3- (570490 . .)

(287212 . .)

(16431727)

(16751749)

(c. 16)

(c. 102)

(c. 104)

3 : , , , p. : . : How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics. , p?

3 : , , , . p ().

(-) p , , . p53,1415926535897..., . - . - - (); , . , , - , , , - , -, -, p . . - , p - - ; - .

3 : , .

3 : , , , , iPod. , , , .

(c. 16)

(c. 24)

(c. 114)

3- (570490 . .)

(11701250)

(. 1931)

30

a b , , , - , (. . (a1b)/a5a/b), . . . , - (f) - , -: f5(115)/251.6180339887498... f: f2511f 1/f5f21. - 1. , - . - , . (1, 1, 2, 3, 5, 8, 13, 21, 34,...) - , f , . , , - , .

98 g

, , . - , , .

100 g Geometry & other shapes

570 . . .

530 . . . ,

490 . . . , ,

200250 . . . , , ,

234305 . . . ,

245325 . . .,

g 101

-, -, - . , - 150 ( 5 . .) , , -. , , . , , - , , - . , - , -, .

- , - . -, , - , . , , -, , - . , , , , - . - , - ; . -

102 g

30

x y , x U , .

3- (190120 . .)

(90165 . .)

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30

106 g

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(c. 94)

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30

108 g

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3- (13201382)

(15961650)

(16011665)

(c. 18)

(c. 46)

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30

114 g

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(429347 . .)

(287212 . .)

(c. 122)

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30

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(c. 120)

(c. 130)

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(18541912)

(18681942)

(18781973)

30

118 g

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(17071783)

(. 1957)

(c. 30)

(c. 100)

(c. 102)

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30

120 g

.

3- (17071783)

(17901868)

(18491925)

(c. 116)

(c. 130)

(c. 146)

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124 g

30

.

3- (18451918)

(18701924)

(18821969)

(18931978)

(19242010)

(c. 18)

(c. 38)

(c. 46)

(c. 108)3 :

, . (, , ). . , .

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30

126 g

, .

3- (. 1922)

(19242005)

(. 1961)

(c. 84)

(c. 94)

(c. 114)

3 : , . . , , ; , .

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30

128 g

, ; 43 !

3- (. 1939)

(. 1944)

(c. 58)

(c. 84)

(c. 86)

(c. 114)

3 : (333), 232, 434, 535, 636 737. 737 10160 ( , 160 !). 23233, 33332 33334. , (, , ).

1974 . 1977 . . 1980 . - Ideal Toy Company , 300 . - . 43 (1018) ( ) 26 . , - , , , - . , - , - . -. . -, 20 -. 2010 . - . 2011 . 7 .

3 : , (3 3 3) , .

30

130 g

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3- ( ) (18241907)

(18881971)

(. 1937)

(. 1945)

(. 1952)

(c. 116)

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134 g

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g 135

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30

136 g

, , . , , 108 .

3- (16011665)

(17761831)

(17771855)

(. 1953)

(c. 30)

(c. 94)

3 : . . , , . , , , - .

XVII -. - , , - ( ; , 32142552). - - . , , , -, . . - , - , . -, , . - , n54. -, , - . n XIX . 1994 , - .

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1994

g 139

, - , . -, , , - . , , , . - , - , . , - , - . , , , , . , , , : - , , - , . - 300 .

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30

140 g

, , , . 100 , , .

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(. 1932)

(c. 116)

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30

142 g

, . ?

3- (18621943)

(18961962)

(19031957)

(19061978)

(19121954)

(c. 84)

(c. 144)

3 : , , . . , , .

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30

144 g

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(19031957)

(19061978)

(19071989)

(19091945)

(c. 38)

(c. 84)

(c. 142)

3 : , , , . , , .

(0, 1, 2, 3, ...), : , -, . - , XIX . , , - , . - , - (Principia Mathematica). - , - . 1931 , . , , . - . - : -, - .

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30

146 g

, .

3- (18541912)

(. 1930)

(. 1943)

(. 1951)

(. 1966)

(c. 116)

(c. 120)

3 : . 1961 , , , , . 1982 , . ( ) .

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30

148 g

. , ?

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3- (18451918)

(19061978)

(19342007)

(. 1955)

(c. 38)

(c. 142)

(c. 144)

-: 1, 2, 3, 4, 5, ... - (, , 5, p, 0,1234567891011121314...). - . - , , . - , - . : - ( , ). , - . , - , - . , . , , - -. - 1963 , - , . , - - - , .

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150 g

30

, ? .

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(18261866)

(18651963)

(18661962)

(c. 18)

(c. 22)

(c. 30)

3 : , . 1849 , . , 1896 , 0 1.

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- . , -. , : (, 191, 193, 197, 199), - (, 773, 787, 797, 809). 1859 - , . - . - . , , - . - - - . , (-). , -, . . -, , - (a) 1/2 . , - , .

154 g

Fractal TreesRobert Fathauer(Tarquin Publications, 2011)

G del, Escher, Bach: An Eternal Golden BraidDouglas Hofstadter(Basic Books, 1979)

How To Build A Brain Richard Elwes(Quercus, 2011)

Innumeracy: Mathematical Illiteracy and its ConsequencesJohn Allen Paulos(Hill and Wang, 1988)

The Man Who Loved Only Numbers Paul Hoffman(Fourth Estate, 1998)

Mathematical Puzzles and DiversionsMartin Gardner(Penguin, 1991)

Maths 1001Richard Elwes(Quercus, 2010)

50 Mathematical Ideas You Really Need to Know Tony Crilly (Quercus, 2008)

The Book of NumbersJohn H. Conway and Richard K. Guy(Copernicus, 1998)

The Colossal Book of MathematicsMartin Gardner(W. W. Norton & Co., 2004)

Designing and Drawing TessellationsRobert Fathauer(Tessellations, 2010)

e: the Story of a NumberEli Maor(Princeton University Press, 1998)

Fermats EnigmaSimon Singh(Walker & Co., 1997)

Flatland: A Romance of Many DimensionsEdwin Abbott(Oxford University Press, 2008)

g 155

Number Theory: A Lively Introduction with Proofs, Applications, and Stories James Pommersheim, Tim Marks and Erica Flapan(John Wiley & Sons, 2010)

The Princeton Companion to MathematicsTimothy Gowers (ed)(Princeton University Press, 2008)

What Is the Name of This Book? The Riddle of Dracula and Other Logical PuzzlesRaymond Smullyan(Penguin Books, 1981)

-

+Plus Magazinehttp://plus.maths.org/content/An online mathematics journal with the latest mathematical news and articles from top mathematicians and science writers.

Cut the Knothttp://www.cut-the-knot.org/An encyclopaedic collection of maths resources for all grades. Arithmetic games, problems, puzzles and articles.

MacTutor History of Mathematics Archivehttp://www-history.mcs.st-and.ac.uk/Mathematical archive covering the development of mathematics with biographies of famous mathematicians.

Math is Funhttp://www.mathsisfun.com/Maths resources for children, teachers and parents with a useful illustrated dictionary.

The Mathematica Demonstrations Projecthttp://demonstrations.wolfram.com/Animations related to a wide range of maths topics.

PlanetMathhttp://planetmath.org/PlanetMath is a virtual community that aims to help make mathematical knowledge more accessible.

Wolfram MathWorldhttp://mathworld.wolfram.com/An extensive mathematics resource and the worlds largest collection of mathematical formulas and graphics.

156 g

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