平面几何-美国数学奥林匹克集训资料

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1、GeometryUnboundKiranS.Kedlayaversionof17Jan2006c2006KiranS.Kedlaya.Permissionisgrantedtocopy,distributeand/ormodifythisdocumentunderthetermsoftheGNUFreeDocumentationLicense,Version1.2oranylaterversionpublishedbytheFreeSoftwareFoundation;withnoInvariantSections,noFront-CoverTexts,andnoBack-Cover

2、Texts.PleaseconsultthesectionoftheIntroductionentitled“Licenseinformation”forfurtherdetails.Disclaimer:itistheauthor’sbeliefthatalluseofquotedmaterial,suchasstatementsofcompetitionproblems,isincompliancewiththe“fairuse”doctrineofUScopyrightlaw.However,noguaranteeismadeorimpliedthatthefairusedoc

3、trinewillapplytoallderivativeworks,orinthecopyrightlawofothercountries.iiContentsIntroductionviiOrigins,goals,andoutcome..............................viiMethodology......................................viiiStructureofthebook..................................viiiAcknowledgments..................

4、..................ixIRudiments11ConstructionoftheEuclideanplane31.1Thecoordinateplane,pointsandlines.....................41.2Distancesandcircles...............................51.3Trianglesandotherpolygons...........................71.4Areasofpolygons.................................81.5Areasofc

5、irclesandmeasuresofarcs......................91.6Anglesandthedangerofconfigurationdependence..............111.7Directedanglemeasures.............................122Algebraicmethods152.1Trigonometry...................................152.2Vectors.......................................182.3Complexn

6、umbers.................................192.4Barycentriccoordinatesandmasspoints....................213Transformations233.1Congruenceandrigidmotions..........................233.2Similarityandhomotheties............................263.3Spiralsimilarities.................................283.4Comp

7、lexnumbersandtheclassificationofsimilarities.............283.5Affinetransformations..............................294Tricksofthetrade334.1Slicinganddicing.................................33iii4.2Anglechasing...........................