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Transcription
135 MATHEMATICAL MAYHEM Mathematical Mayhem began in
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AEA n}`Z)F)3`de%32.1k&)F&%3`A2!6WZ%Fj.6_*k&i`!/&%32.*3 A7 A4 B A1 A5 C T c A + E = 180◦ − A3 c B = 180◦ − A4 − A7 c C = 180◦ − A1 − A5 ] ◦ D A 2 A6 D cà! = 180 − A2 − A6 ¦a."#":%32.1!6WgCZa.&%3`A2!6$c*dii'&2f!2h'J`A2.'J)Fab!A A+B+C+D+E = (180◦ − A3 ) + (180◦ − A4 − A7) + (180◦ − A1 − A5 ) + (180◦ − A2 − A6 ) ] = 720◦ − (A1 + A2 + A3 + A4 + A5 + A6 + A7 ) g`diWAkWc ]me*2.'JAc 540◦ = 720◦ − (A1 + A2 + A3 + A4 + A5 + A6 + A7 ) !k&n}`Ak&Zc $ A + B + C + D + E = 540◦ A1 + A2 + A3 + A4 + A5 + A6 + A7 = 180◦ ; % .$!1&7G> 7OQ&I#N&N1!N >N&C :@IC>9 N %M ] ] ! ¸¹_º®»¼*µ#· º ´¶µ± º ´ Z%F6¯"#`A2Z«c$di1-% A£6W`A"#_!`Zab1+/.`ZaAk&*j.*$&%32.1.*'J%3"*)F6¯}!'J%F"#)36-c !" # c%$'&() *,+.- /yc1032 4 5 687 9 :3]]] ¨ ' *2!Z%3*2 _j.*2$!*"&%3'J6'A)F)3*2.1= ; LDIZQGF@$B=< Ì ¦ a.j.j.`A6W *2. * k&%F2ZJ*1*kl6pde% j.`A6D%U&%UA*2. ] F $&*k&"%F2. n D n ] 0≤D≤9 n %Fn n 810 = 0.9D5 = 0.9D59D59D5 . . . ^ ¥2.=d;A^¨6W!`Za!)3fA$Aj.%(Ì"h`Ak&$lJ2Z&%(`A2Ì%F2:$)("h2Z&*k,f6?'D!`!`Z)?>¯^}n ,A`Za§ k&£)%(¥£"hZc,A`Zafj!k&`!/!/A) ,Ìk&*"#*"#/.kYA 1 diZ%3'DÌ'J*2Ì*)F6W` = 0.33333 . . . 3 ]Ì-,./!g,A`Zak&*"#*"#/.k_A$ 7 ]ie`d /.gdgkl%l&*2*6 0.3 = 0.7 = 0.7777 . . . 9 /!`ZaA 1 F `i,A`Zah¥2.`d ApZ%F6CAa.)36 )Fj!n3a!)!J`:'J`A2A*kOp!ek&*j.*$&%32.1e!'D© 7`f6W`Z) A .k&`!/Z)("A@ cZ%Udi`Za!)(/!g!0.142857 %3"*)!J`fgn(kl'&&%(`A2Y]_.aAm!`d !`idig.`ÌZ%F6 h¡*-W§ 6m)3`!`!¥ipOdi`:A%Yk&*2Z+dg-,!6] ^2h!@Abkl6J8j!j.k&`A'D«c.diÌ6W- ] !*2 x = 0.9D5 ] Za.6$c = 0.9D59D59D5 . . . 1000x = 9D5.9D59D5 . . . = 9D5.9D5 (*2:%32Z&1k> 999x = 1000x − x = 9D5.9D5 − 0.9D5 = 9D5 9D5 ] x = 999 F `!*6Z%F6_"h-!`!:)3`!`!¥gn(":%F)%3*k :^("#-,¨cZ%n.,A`ZahA-AiWAkpJkl%(*f&`:j!k&`*AA$ '&&a.)F) ,#CAa.)36 ] 0.9 A`Ak¯g6W*'`A2.:1j!j.k&`A'D«cdiek&-dgkl%& 6 0.9D59D59D5 . . . 9D5 103 + 9D5 106 + 9D5 109 + ··· Z%F6i%36i2¶%32A.2A%&1*`A"h-Jk&%3'i6?*kl%(6de%A.kl6JkJ" kl&%3` r= 1 HZa.6-cZ%l6_6Da." %36 103 9D5 103 = 1 1−r 1− 3 10 a = 9D5 1000 − 1 a = = 9D5 103 *2. 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