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( )!? 1 1. 0 1

..1 6. 3 10 ffi 3 3 360 3.3 F E V F E + V = x x E E =5x 1 = 5 x 4 360 3 V V =5x 1 3 = 5 3 x F = x; E = 5 x; V = 5 3 x x 5 x + 5 3 x = x =1 1 30 0 1 x x E E =4x 1 =x 3 V V =4x 1 3 = 4 3 x F = x; E =x; V = 4 3 x

x x + 4 3 x = x =6 6 1 8 34 5 3 3 F = x E =3x 1 = 3 x V =3x 1 3 = x x 3 x + x = x =4 4 6 4 4 F = x E =3x 1 = 3 x V =3x 1 4 = 3 4 x x 3 x + 3 4 x = x =8 8 1 6 5 F = x E =3x 1 = 3 x V =3x 1 5 = 3 5 x x 3 x + 3 5 x = x =0 0 30 1 0 5 3. 3

5 4. 4.1 10cm 1 110 4. HOMAC cm 15cm p 10cm 10 3cm 30cm 4-1 4-4-3 4-4 1 30cm 3cm 4

Do It Yourasef 0.mm 1.V 4.3 4-5 4-5 4-6 4.4 Zome Tool Zome Tool Zome Tool 4-7 5

5 Zome Tool 5-1 5- ABCD 5-1 5-5.1 5-3 A A 5-4 5-3 5-4 A 5-5 S(1; 0; 1),H(0; 1; 1),Q(1; 1; 0)A S(1; 0; 1) 1 H(0; 1; 1) P ; 1 ; 1 O(0; 0; 0) OP OQ! 1 OP = ; 1 ; 1! ; OQ = (1; 1; 0) 6

cos = = s 1! OP! OQ j! OPjj! OQj 1 1+ 1 1+1 0 1 p + +1 1 +1 +0 = 1 p 3 ß 0:577350 ::: 5-5 ß 55ν p 3 1 1 p 3 p 3 1 p p 5-6 p 90ν 55ν= 35ν 35ν 5-6 SH 5-7 45ν 5-8 5-7 5-8 7

5-9 5-10 5-11 5-1 5-13 5-14 5-15 5-16 8

5-17 5-18 5-19 5-0 5. 5-1 1 ABCD- EFGH ACF P EFGH 1 EF 45ν CF CF A 5-1 EF EF 45ν CF G,H I,J GFI-HEJ(4GFI 4HEJ ) 5-,3 9

5-5-3 AEF A K AKEF 5-4 4AEF4AEK4AKF 4EFK 4AEK 4GFI 4HEJ 1 4AEF p 5-4 4AKF AF = p AK 4AEK AK AK= 1 p KF KF +AK =AF 1p KF + = p KF = 1 = 3 r p 3 6 KF = = 3 AKF AFK 1 p cos AKF = p = 1 AKF = 60ν AFK=30ν 4EFK EF = 1KF = p 6 KE=AK= 1 p 1p EF +EK =1 + = 3 =FK 4EFK FEK = 90ν EFK EKF 10

cos EFK = cos EKF = 1 p 6 1 p p 6 = p 6 3 ß 0:8164965 ::: EFK ß 35ν = p 1 3 ß 0:577350 ::: EKF ß 55ν 4AKF 1 10 A'K' = 1 p 10 = 5 p ß 7:0710678 ::: A'K' ß 7:1cm p 6 K'F' = 10 = 5p 6 ß 1:474487 ::: K'F' ß 1:cm A'F' = p 10 = 10 p ß 14:141356 ::: A'F' ß 14:1cm 5-5 5-5 5-6 5-7 5-8 5-9 11

5-30 5-31 5-3 5-33 5-34 5-35 6 Zome Tool 6-4 1 8 1

Zome Tool 6-1 6-6-3 6-3 6-4 6-5 13

6.1 6-6 6-7 6-8 6-9 6-10 6-11 6-1 6-13 14

6-14 6-15 6-16 6-17 6-18 6-19 6-0 6-1 15

6-6-3 6. 6-4 6-5 6-6 6-7 6-8 6-9 16

6-30 6-31 6-3 6-33 6-34 6-35 6-36 6-37 17

6-38 6-39 6-40 6-41 7 7-1 6 5 1 7-1 7-7-3 18

7-7-3 7.1 ABCDE ABC = 108 ffi ; ACD=7 ffi 4ACD 7-4 7-5 CDA AC P CDP=36ν 4ACD4DPC 7-6 7-7 AB = 1; AC =x AC :CD=DP:PC x :1=1:(x 1) x x 1=0 19

x = 1 ± p 5 x>0 x = 1+p 5 p 1+ 5 1 : ' = 1+p 5 ' ' ' ' 1=0 ' = ' +1 7. 1 AB=1; AC =' 7-8 7-9 CD M 1 AM = ' = 5+p 5 4 p p 5+ 5 AM > 0 AM = = p 4' +3 0

G AG AG N AG = MS = MN+NR+RS NR=AP=1; RS = MN AG = 1 + MN MN =AM AN 7-10 MN =AM AN = 5+p 5 AG 4 p AG +5+ p 5 MN = p p AG = 1 + MN = 1 + AG +5+ 5 AG 1=p AG +5+ p 5 AG p AG+1= AG +5+ 5 AG AG p 5=0 = AG +5+ p 5 4 AG = 3+p 5 = ' +1 q (' +1) p p +5+ 5 ' ' 1+4' +3 MN = = p p p ' 1 ' 1+4' +3 ' +1 ' = = = = ' = 1+p 5 4 7.3 7-11 7-13 (d) 7-1 (a),(b),(c) 1

7-11 7-1 7-13 7-14 7-14 M 4MNA (d) 4 (a),(b),(c),(d) (d) (d) AN : MN : AM = ' +1 p ' 4' +3 : : =(' +1):' : p 4' +3 ' = ' +1 AN:MN=(' +1):' = ' : ' = ' :1 AN : MN : AM = ' :1: p ' + (a)(b)(c)(d) 4 (a) 5cm (b)(c) 10cm (d) 4AMN AN 5cm 1 r p r 5+ 5 5 p 5 AN : MN : AM = : :1 10 10 AN 1 p r 5 1 5 p 5 AN : MN : AM = 1 : :

(a) r 5+ p 5 AN =5 cm ß 4:5 cm r 10 5 p 5 MN =5 cm ß :63 cm 10 AM =5cm (b)(c) r 5+ p 5 AN =10 cm ß 8:61 cm r 10 5 p 5 MN =10 cm ß 5:6 cm 10 AM =10cm (d) AN =5cm p 5 1 MN =5 cm ß 3:09 cm r 5 p 5 AM =5 cm ß 5:88 cm 7-15,7-16 7-15 7-16 3

7.4 7.3 7-17 7-18 AJ 7.3 A,C,D,G,J B,E,H,I A,B,C,D,E B,E AB=AE=1; BAE = 108ν AB = 1 7. 1 ' +1 ' +1 A ; 0; ; C ; 1 0 ' +1 ; ; D ; 1 0 ; F 0; ' +1 ; 1 G 0; ' +1 ; 1 J 1 ' +1 ; 0; E 7.4.1! a =(p; q; r)! b =(s; t; u)! c! c =(x; y; z)! c! a! b! a! c =0! b! c =0 ( px + qy + rz =0 sx + ty + uz =0 pt qs 6= 0 4

t q (pt qs) x +(rt qu) z =0 qu rt pt qs 6= 0 x = pt qs z s p (qs pt) y +(rs pu) z =0 rs pu pt qs 6= 0 y = pt qs z! qu rt rs pu x = pt qs z; z; z pt qs qu rt rs pu = z ; pt qs pt qs ; 1 z = (qu rt; rs qu; pt qs) pt qs 7.4. E E ABCDE EDHFG AEGIJ ABCDE EDHFG DE ABCDE AEGIJ AE E DE AE E EDHFG AEGIJ EG E AE GE AE! AE GE! GE! AE ABCDE AEGIJ AE ABCDE AE ABCDE ABCDE ABCDE 5 A,C,D ABCDE! x!! AC; AD 7.4.1! ' AC =(p; q; r) = ; 1 ; ' +1! ' AD = (s; t; u) = ; 1 ; ' +1 z z ' +1 (qu rt; rs qu; pt qs) = ; 0; ' pt qs ' ABCDE! x =(' +1; 0;') 5

EDHFG! y! DG = (p; q; r) = ' +1 ; ' ; 1! DF = (s; t; u) = ' +1 ; ' ; 1! y =('; ' +1; 0) AEGIJ! z! 1 GA = (p; q; r) = ; ' +1 ; '! GJ=(p; q; r) = 1 ; ' +1 ; '! z =(0;';'+1) AE! u AE ABCDE ABCDE! x AEGIJ AEGIJ! z AE! u! u =(' +1; 3' +; ' 1) DE! v DE ABCDE ABCDE! x EDHFG EDHFG! y AE! v! v =( ' 1;'+1; 3' +) EG! w EG EDHFG EDHFG! y AEGIJ AEGIJ! z AE! w! w =(3' +; ' 1;'+1)! OE! OE! u! v! w 8! OE =!! 1 ' +1 OA+l u = ; 0; + l (' +1; 3' +; ' 1) ><! OE =!! OG + m w = 0; ' +1 ; 1 + m (3' +; ' 1;'+1)! >:! OE = OD + n! ' +1 v = ; 1 0 ; + n ( ' 1;'+1; 3' +) 6

8 >< >: 1 + l (' +1)=m (3' +) l (3' +)= ' +1 m (' +1) ' +1 l (' +1)= 1 + m (' +1) 3' + l = m =,, 6' +16! 1' +13 1' +13 OE = ; 6' +16 6' +16 ; '! ' OE = ; ' ; ' EA,ED,EG! 1 ' EA = ; ' ; 1! 1 ED = ; 1 ' ; '! EG = ' ; 1 ; 1 ' s fi fi fi! fi fi fi fi EAfi = fi! fi fi fi fi EDfi = fi! fi fi 1 EGfi = ' 1 ' + + B BA=BC=1B,E A,C,D CD CD = 1! EA! 1 ' ED = ; ' ; 1 1 ; ' 1 ; ' = 1 '! DC! DE = (0; 1; 0) 1 ; ' 1 ; ' = 1 '! CB! CD = 1; 1 ' ; ' (0; 1; 0) = 1 '! BA! 1 ' BC = ; ' ; 1 1 ; ' 1 ; ' = 1 '! AB! ' 1 AE = ; ' ; 1 ' 1 ; ' ; 1 = 1 '! EA! ED = j! EAj j! EDj cos AED 1 cos AED = 1 p 5 4 =1 7

cos 108 ffi = 1 p 5 1 108 ffi 108 ffi =7 ffi 5 =360 ffi 3 =360 ffi cos 3 = cos 360 ffi = cos 4cos 3 3cos = cos 1 4cos 3 cos 3cos +1=0 (cos 1) 4cos + cos 1 =0 0 < cos <1 cos = cos 7 ffi = 1+p 5 cos 108 ffi = cos (180 ffi 7 ffi )= cos 7 ffi = 1 p 5 7.5 7-19 7-0 7-1 7-8

7-3 7-4 7-5 7-6 7-7 7-8 7-9 7-30 9

7-31 7-3 7-33 7-34 7-35 7-36 7-37 7-38 30

7-39 7-40 7-41 7-4 7-43 7-44 7-45 7-46 31

8 Zome Tool 8-1 8-1 8-6 8-8- 8-3 ABO AO M B BM= p 3 8-3 8-4 8-4 1 7.1 ' = 1+p 5 ABCDE BE = ' 3

M BE P 8-4BPM ( 8-5 P BE BP=' 4BPM BPM=90ν PM BP +PM =BM 8-5 8-6 p ψ p PM = 3 ' 1+ 5 =3! =3 3+p 5 = 3 p 5 p 3 p p 5 5 1 PM = p = p 1+ 5 = = ' 1 BP:MP:BM=' : ' 1: p 3 BM 1 BP:MP:BM= p ' : ' p 1 :1 3 3 p p p p 15 + 3 15 3 = : :1 6 6 7.3 8-6 8-7 8-7 ( 8-8 8-8 33

8-9 8-9 1 8-3 ( 8-10 ' ' 1 1 x ' 8-10 ' :1=(' 1) : x x =1 1 ' 8-11,1 1 1 A 0; ' ; 1 B ' ; 1; 0 1 C 1; 0; ' 8-11 8-1 34

AB=BC=CA s 1 AB = ' 0 + 1 1 r s +(0 1) 1 = ' ' +1 ' + 1 ' +1= ' +' + ' ' x x 1=0 ' = ' +1 r r (' +1) ' + 4 AB = ' = ' = ' BCCA s BC = 1 1 r +(0 1) 1 + ' ' 0 = 1 ' + 1 ' +1+ 1 ' s r r ' +' + (' +1) ' + 4 = ' = ' = ' = ' CA = = s (0 1) + s ' +' + ' = 1 ' 0 + 1 1 r = 1+ 1 ' ' + 1 ' ' +1 r r (' +1) ' + 4 ' = ' = ' AB=BC=CA4ABC 8-13 D xy 8-14 D D 1; 0; 1 ' CD = ' AB=BC=CA=CD 8-13 8-14 8-9 35

8-7 3 A,B,C 3 A,B,C 8-11,1 1 1 A 0; ' ; 1 B ' ; 1; 0 C 1; 0; 1 ' 4ABC! n =(x; y; z)! n 4ABC! n! AB=0! n! AC =0 7.4.1! AB = (p; q; r)! AC =(s; t; u) (!! n AB = px + qy + rz =0!! n AC =sx + ty + uz =0! n = k (qu rt; rs qu; pt qs)! 1 AB = (p; q; r) = ' ; 1 ' ( rt + qu; rs qu; pt qs) =! n = k (1; 1; 1) 1; 1! AC =(s; t; u) = 1; ' + ' 1 ' ; ' + ' 1 ' ; ' + ' 1 ' 1 ' ; 1 ' 1 8-15 8-15 36

8.1 8-16 PQR 8-17 5 ß 35ν 8-16 8-17 PQ PQ 8-18 8-19 x y 1 1 A 0; B 0; C(1; 1) E( 1; 1; ) ' ' 1 A 0; B y = x A ' 1 AB D ' ; 1 EQ ' 8-18 8-19 CD = s 1 1 ' 4CDQ p CQ = ' p 1 ' = ' 1 = 1 ' ' + s 1 1 4' 4' +1 = ' ' = ' p 1 ' 37

EQ = CQ EQ= 1 ψ p! = 1 5 1 = ' ' EQ ß 0:6180339 ::: 10cm 5 5EQ ß 3:0901695 ::: 3 8-0,1) 8-0 8-1 8-8-3 8-4 8-5 38

8-6 8-7 8-8 8-9 8-30 8-31 8-3 8-33 39

8-34 8-35 8-36 8-37 8-38 8-39 8-40 8-41 40

8. 8 8-4 DEF! n! n = k (1; 1; 1) 5-6 DEFG 8-4 8-43 D,E,F 8-44,8-45 8-44 8-45 H,I,J 1 ' = ' 1 AJ = DJ = 1 (' 1) = ' D D( '; 1) DG = EG = FG =3 ' 10cm 5 DG = 5 (3 ') ß 6:9 cm 8-44 41

8-46 8-47 8-48 8-49 8-50 8-51 8-5 8-53 4

8-54 8-55 9. Zome Tool 7.4. 1 E k (1; 1; 1) 8 k (1; 1; 1) Zome Tool k (1; 1; 1) 10. 43