平面等周定理的证明.pdf

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1、²¡±½ny²±½n3±.•Ýƒµ4AÛ/Gƒ¥§±/¡È•Œ"y²µØ”4Ü•‚P±••2,±,˜:•å:§l•ëê•s,P±ëêsL«¼ê•x=x(s);y=y(s);w,kx(0)=x(2);y(0)=y(2);òÙŠFourierÐmX1x(s)=aksinKs+bkcosKsk=1X1y(s)=a1sinKs+b1cosKskkk=1KX1x0(s)=K(acosKsbsinKs)kkk=1X1y0(s)=K(a1cosKsb1sinKs)kkk=1qÏ•Z20202[x(s)

2、+y(s)]ds=20ŠâParsevelªZ2X12102022212212=[x(s)+y(s)]ds=K(ak+ak+bk+bk)0k=1Z2X1A=x(s)y0(s)ds=K(ab1ba1)kkkk0k=1ÏdX1112122212A=[(Kakbk)+(Kak+bk)+(K1)(bk+bk)]2k=112kA>0;A6Ò…=a=b1;a1=b;a=a1=b=b1=0(k>1)1111kkkkž¤á"džP=(asint+bcost;bsint+acost);Ð

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