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1 1 geometry geometrein (geo :, metrein : )., (thles of miletus),.. < >, (nlytic geometry ), (differentil geometry ). 19 (priori) (non- eucliden geometry ),,,. 2 E 2 3 E 3. E 2 E 3 (plne geometry ) (solid geometry ), E n n ( n - dimensionl eucliden geometry ) < >.,.. 19 (topology ),. 2.,,,..,.,,,

2 . 2-1 : (plimpton 322), :,,,,,, / :. < >.,,,,, < >,. < > 2000 < >.. < > < >. < > < < :.,. 4. (demonstrtive geometry ).

3 (Plutrch, 100 )..,,..,,,,,. 3-1 :, , < >. 3-2 :..,... c c c c : < >.

4 (qudrture of the lune). (lune),. (1) ( ) BCDE BE ED EF. BF G ED H. EH EHLK. DE =EF = -, BE = + BCDE = BE ED= ( + )( - ) (2) = c 2 =EHLK ABC A BC D. AD M. ABC = 1 2 BC AD=BC DM (3) =BC DM ABC. AOC BOC AC=BC. ( A B ) 2 = ( A C) 2 + ( B C) 2 = 2 ( A C) 2 AB ACB, AC AEC A E C A CB = ( A C) 2 (A B ) 2 = 1 2 AECF = AEC - AFC = 4 AFCO - AFC = ACO 3-4 : (true).. 1. :. A B B AC D.. 2. : :.,..

5 : 3 1. : 2. : : : (Plto, B.C.) (socrtes, B.C.) (Cyrene) (T heodorus )...,.., (ide),.. < (repulic)....., : (incommensurle numer )..,?. (Antiphon, 430 ),..... (method of exhustion ).. < > : (Euclid, 300?-?B.C.)

6 13 < (Elements)>.. < >,, (Archyts ),,, (Eudoxus),, (T hetetus)., : (Archimedes, B.C.) (Hieron ). '.'.. < (mesurement of circle)> < (qudrture of the prvol)> < (on sprils)> < > 1 ',.' < < < > 4/ 3. < > P P.. 3 < (onthe sphere nd cylinder )>. < > , = 4 r 2 = 4 ( r 2 ) = 4 ( ) = 4 3 r 3 = 4 ( 1 3 r 2 r) = 4 ( ) / 2,

7 3/ 2, = 2 r (2 r) + r 2 + r 2 = 6 r 2 = 3 2 (4 r 2 ) = 3 2 ( ) = r 2 (2 r) = 2 r 3 = 3 2 ( 4 3 r 3 ) = 3 2 ( ) r h = 2 r, : < (conic sections)>. 400, (Menechmos:340? B.C.), (Aristeus),.,,,,. (ellipse), (prol ), (hyperol ),. ellipsis ( ), prole( ), hyperole( ).,,,,. < >. < > A B k ( 1) AP/ BP = k P :,,,, ,. 150 (Minor ) (Nice) (Hipprchus, 195?- 125?B.C.).. (Rhodes) , 360.

8 3-12 : (Menelus ) 100. < (Spheric)>. < >,, ( 180 ).. (Menelus ' theorem ). (sensed or signed mgnitudes). 17 (Girrd A ), (negtive segment s) 1803 (Crnot L.N.M ) < (geometrie de position )>. (positive direction ), (negtive directive) sine, tngent, secent sin, tn, sec. (Cev `s theorem ) (Menelus ) ABC BC, CA, AB E P, Q, R A R R B B P P C CQ QA = - 1. ( P, Q, R (Menelus points ). B ( ) P, Q, R q R A p D Q F r C P A R R B = p q, CQ QA = r p, B P P C = - q r A R R B B P P C CQ QA = - p q q r r p = - 1 ( ), Q, R BC P ' R, Q, P '. A R R B B P ' P ' C C Q QA = - 1 B P ' P ' C = B P P C. 1 B P ' P ' C + 1 = B P P C + 1 B C P ' C = B C P C P P ' R, Q, P.

9 (Cevin) ABC A, B, C BC, CA, AB L, M, N AL, BM, CN A M M C CL L B B N NA = 1. ( AL, BM, CN (Cevin lines). ( ) A L, B M, CN P. B N C A L, A CN B M B A A N N P P C CL L B = - 1, A M M C A M M C CL L B CP PN B N N A = 1 N B B A = - 1 ( ), B M A L P, CP A B N ' A L, B M, CN ' P A M C P L N N ' B A M M C CL L B B N ' N ' A = 1 B N ' N ' A = B N NA N ' = N. (colliner points ), (concurrent lines )., < > ; (Ptolemy ' s T heorem ). ABCD, AC ABE = DBC E, D ABE DBC AB/ AE = DB/ DC (AB)(DC) = (DB)(AE ) E C ABD EBC AD/ DB = EC/ CB A (AD)(CB) = (DB)(EC) + (AB)(DC)+(AD)(CB)=(DB)(AE +EC)=(DB)(AC) B 3-14 : (Heron, 75?),,. < (Metric )>, 1896 (R. schone). < >,,, 12,,,,,,,,,, c K = s( s - )( s - )( s - c) ( s = 1 2 ( + + c) ).,,,,,,,

10 (sphericl segment ),, (prismtoid) (frustrum ).. (Heron ) ABC r S = s 2 r (, + + c = 2s ) A F = B H CH = H B + B D + D C = ( + + c)/ 2 = s S 2 = { ( + + c)/ 2 } 2 r 2 = CH 2 OD 2 AOF CLB BC : BL = FA : FO = BH : OD BC : BH = BL : OD = BK : KD CB B H = B K K D 1 CB B H + 1 = B K K D + 1 CB + B H B H = B K + K D K D CH : B H = B D : K D CH B H = B D K D CH 2 : CH B H = B D D C : D C K D = B D D C : OD 2 CH 2 OD 2 = CH H B B D D C = s( s - )( s - )( s - c) S 2 = CH 2 OD 2 = s( s - )( s - )( s - c) S = s( s - )( s - )( s - c)

= 2 c 2 PD C PD C - PDC PBA x c = y - d ) + ) x + y = x + y + c = ) - ) x - y = x - y + c = A B CD PD C ) c( + d) c - PB A PD C = c 2 c 2 - = c

11 (Brmgupt) ABCD S,, c, d S = ( s - )( s - )( s - c)( s - d) (, 2s = + + c + d ) AD BC P PD PC y, x PDC M = ( x + y + c 2 )( x + y + c 2 - x ) ( x + y + c 2 - y )( x + y + c 2 - c) = 1 4 (x + y + c)(y + c - x ) (x + c - y )(x + y - c) ADC+ ABC= 180 ABC+ ABP = 180 ADC= ABP PDC PBA PB A PD C = 2 c 2 PD C PD C - PDC PBA x c = y - d ) + ) x + y = x + y + c = ) - ) x - y = x - y + c = A B CD PD C ) c( + d) c - PB A PD C = c 2 c 2 - = c 2-2 c 2 y c = x - 2 c 2 ) c c - ( c + d ), x + y - c = c c - c( - d) + c c + c ( + + c - d), - x + y + c = c + c ( + - c + d) ( - + c + d)

12 , M = c 2 4 ( c 2-2 ) A B CD = ( c + d )( - + c + d)( + - c + d)( + + c - d) c 2-2 c 2 PD C S = ( s - )( s - )( s - c)( s - d) 3-15 : (Pppus, 300 ). < >, < > < >. < (mthemticl collection )>,,,. AC B, B AC AC O D, B OD F OD, BD, FD AB BC,,. : A D C, A B D, DB C B D 2 = (A B )( B C) B D = (A B )( B C) : OB D OD 2 = OB 2 + B D 2 B O = B C - A B / 2 OD = A B + B C 2 : DB O DF B F D DB = DB OD F D = DB 2 OD = 2 (A B )( B C) A B + B C 3, ABC BC D (A B ) 2 + (A C) 2 = 2 ( (A D) 2 + ( B D) 2 )...,.. ABC CADE CBFG CA CB DE FG U H AL BM HC ABML D A CADE CBFG. (isoperimerty ) L E H C G R S B F M

13 (crmer ), 1776 (cstillon ) -...

10-2 삼각형의닮음조건 p270 AD BE C ABC DE ABC 중 2 비상 10, 11 단원도형의닮음 (& 활용 ) - 2 -

10 단원 : 도형의닮음 10-1 닮음도형 p265 ABC DEF ABC DEF EF B ABCD EFGH ABCD EFGH EF A AB GH ADFC CF KL 중 2 비상 10, 11 단원도형의닮음 (& 활용 ) - 1 - 10-2 삼각형의닮음조건 p270 AD BE C ABC DE ABC 중 2 비상 10, 11 단원도형의닮음 (& 활용 ) - 2 -

歯Ky2002w.PDF

歯Ky2002w.PDF