/*WORK:"202107-3MaximaTrial.html";
: 　　トピックス３
　　　. ケプラー「新天文学から」
◆コマンド番号202107-3
●ケプラー「新天文学」から
●●●●●●●●●●●●●●●●*/
(MONDAI:"問題　次のA,B,C,D,FでDF直径の円周上に、E(角ECD=45°)の点をとる。角AEBは？",
A:[-1.26,0],B:[0,0],C:[0.756,0],D:[10,0],F:[-10,0],
/**/END:"MondaiEnd")$

(KANSUU:"関数・定数設定",
r:10,
sind(a):=sin(a/180*%pi),cosd(a):=cos(a/180*%pi),tand(a):=tan(a/180*%pi),
asind(l):=asin(l)/%pi*180,acosd(l):=acos(l)/%pi*180,atand(l):=atan(l)/%pi*180,
d(P,Q):=sqrt((P-Q).(P-Q)),a(P,Q,R):=acosd( ( (P-Q).(P-Q)+(R-Q).(R-Q)-(P-R).(P-R) )/(2*sqrt(( (P-Q).(P-Q) )*( (R-Q).(R-Q) ))) ),
Do(aPQR):=block([Do,Fun,Byo],
/**/Do:floor(aPQR),Fun:floor(aPQR*60-Do*60),Byo:floor(aPQR*3600-Do*3600-Fun*60),
/**/Do*10000+Fun*100+Byo),

gr(T,c,l,pB,pSR,lab,xm,xM,ym,yM):=block(
/**/wxdraw2d(
/*....*/title =T, yrange=[ym,yM] /* "タイトルと値域を確認し" */,
/*....*/color=blue,line_width=1,
/*....*/implicit(c,x,xm,xM,y,ym,yM),
/*....*/color=cyan,line_width=1,
/*....*/implicit(l,x,xm,xM,y,ym,yM),
/*....*/color=red,point_type =7,line_width=1,
/*....*/points_joined =true,point_size =1,points(pSR[2]) /* "点pSR[2]を赤で打って、赤線で結んで" */,
/*....*/color=cyan,point_type =7,line_width=1,
/*....*/points_joined =true,point_size =1,points(pSR[1]) /* "点pSR[1]をシアンで打って、シアン線で結んで" */,
/*....*/color=black,point_type =1,line_width=1,
/*....*/points_joined =false,point_size =2,points(pB) /* "点pBを青で打って、青線で結んで" */,
/*....*/color=red,lab[2][1],lab[2][2],lab[2][3],lab[2][4],lab[2][5],lab[2][6],lab[2][7],lab[2][8],lab[2][9],lab[2][10],lab[2][11],lab[2][12],lab[2][13],
/*....*/color=black,line_width=1,
/*....*/implicit(y=0,x,xm,xM,y,ym,yM),implicit(x=0,x,xm,xM,y,ym,yM) /* "x,y軸を引く" */,
/*....*/color=black)),
lab(nam,p):=label([nam,p[1],p[2]]) /* 図中の文字 */,
/**/END:"KansuuEnd")$

(GPrint:"グラフを書いて、視覚的に確認1",
dA:[-0.5,-1],dB:[0,-1],dC:[1,-1],dD:[1,0],dF:[-1,0],
lA:lab("A",A+dA),lB:lab("B",B+dB),lC:lab("C",C+dC),lD:lab("D",D+dD),lF:lab("F",F+dF),
pB:[A,B,C],pSR:[[F,B,D],[A,B,C]],
lab:[13,[lA,lB,lC,lD,lF,lB,lB,lB,lB,lB,lB,lB,lB]],
c:x^2 +y^2 =r^2 /**/,
T:"F,A,B,C,D", c1: y=0 /*(◆修正部分４)*/,
yM:11,xM:yM/8*12,ym:-yM,xm:-xM,
print([T,c,c1,pB,pSR,lab,xm,xM,ym,yM]) /* 出力形式*/,
gr(T,c,c1,pB,pSR,lab,xm,xM,ym,yM) /* グラフ出力すると*/,
/**/Gprint:"EndGPrint")$

(TEJUN1:"StartForE",
e01:["aBEC=asind( d(B,C)/(r/sind(135)) )",["KKNN aBEC =",Do( aBEC:asind( d(B,C)/(r/sind(135)) ) )],"(正弦定理)"],print(e01),
e02:["aCBE=45-aBEC",["KKNN aCBE =",Do( aCBE:45-aBEC )],"(簡約)"],print(e02),
e03:["E=r*[cosd(aCBE),sind(aCBE)]",["KKNN E =",float( E:r*[cosd(aCBE),sind(aCBE)] ) ],"(Eの設定)"],print(e03),
/**/END:"Tejun1End")$

(GPrint:"グラフを書いて、視覚的に確認2",
dE:[1,0],lE:lab("E",E+dE),
pB:[A,B,C],pSR:[[F,B,D],[E,F,A,E,B,E,C]],
lab:[13,[lA,lB,lC,lD,lF,lE,lB,lB,lB,lB,lB,lB,lB]],
T:"E", c1: y=0 /*(◆修正部分４)*/,
print( float( [T,c,c1,pB,pSR,lab,xm,xM,ym,yM] ) ) /* 出力形式*/,
gr(T,c,c1,pB,pSR,lab,xm,xM,ym,yM) /* グラフ出力すると*/,
/**/Gprint:"EndGPrint")$

(TEJUN2:"StartForGH GAH(GAH//FE,FG⊥FE,EHD⊥FE)",
e11:["aBFE=aCBE/2",["KKNN aBFE=",Do( aBFE:aCBE/2 )],"(円周角・中心角)"],print(e11),
e12:["FG=FA*sind(aBFE)",["KKNN FG=",float( FG:d(F,A)*sind(aBFE) )],"(aBFE=aFAG,平行線の錯角)"],print(e12),
e13:["vFG=FG*[cosd(aBFE-90),sind(aBFE-90)]",["KKNN vFG=",float( vFG:FG*[cosd(aBFE-90),sind(aBFE-90)] )],"(vFGの設定)"],print(e13),
e14:["G=F+vFG",["KKNN G=",float( G:F+vFG ) ],"(Gの設定)"],print(e14),
e15:["H=E+vFG",["KKNN H=",float( H:E+vFG ) ],"(Hの設定,vEH=vFG)"],print(e15),
e16:["aHAE=atand(FG/d(A,H))",["KKNN aHAE=",Do( aHAE:atand(FG/d(A,H)) ) ],"(aHAEの設定,vEH=vFG)"],print(e16),
e17:["aAEB=aBFE-aHAE",["KKNN aAEB=",Do( aAEB:aBFE-aHAE ) ],"(aAEBの設定,aBFE=aBEF,aHAE=aAEF)"],print(e17),
/**/END:"Tejun2End")$

(GPrint:"グラフを書いて、視覚的に確認3",
dG:[-1,0],dH:[1,0],lG:lab("G",G+dG),lH:lab("H",H+dH),
pB:[A,B,C],pSR:[[F,G,H,E,D,B,A],[E,F,A,E,B,E,C]],
lab:[13,[lA,lB,lC,lD,lF,lE,lG,lH,lB,lB,lB,lB,lB]],
T:"G,H", c1: y=0 /*(◆修正部分４)*/,
print( float( [T,c,c1,pB,pSR,lab,xm,xM,ym,yM] ) ) /* 出力形式*/,
gr(T,c,c1,pB,pSR,lab,xm,xM,ym,yM) /* グラフ出力すると*/,
/**/Gprint:"EndGPrint")$

(TEJUN1K:"StartFor_aCEB(Kepler)",
ek01:["dDCE=45, sin_aDCE=70711, (100000=BE):(70711=sin_aECB=sin_aDCE)=(7560=BC):(5346=sin_aBEC), aBEC=asin_5346=3d4m52s",
["KKNN aBEC(by Kepler) =",Do(3+4/60+52/3600),
"aBEC(actually)=",Do( aBEC:asind( d(B,C)/(r/sind(135)) ) )],"(正弦定理)"/**/],print(ek01),
ek02:["https://www.e-rara.ch/zut/content/zoom/5306250, p20[36]"],print(ek02), /**/END:"Tejun1KEnd")$

(TEJUN2K:"StartFor_KL(Kepler) I(onAH,AI=r),MIJ(M(onAE),J(onAD),MIJ//EHD),LM(L(onAF,LM//GH),LK(K(onAG),LK//FG)",
ek11:["I=A+(H-A)*r/d(A,H), K=A+(G-A)*r/d(A,H), (8.740=AF)*(r=AI)/(11.260=AD)=(7.7620=AK) ... （AF:AD=(AG:AH=AK:AI)）",
["KKNN I =",float(I:A+(H-A)/d(A,H)*r),
"K =",float( K:A+(G-A)*r/d(A,H) )," AK=",Do(d(A,K)),"（AH:(AI=r)=AD:AJ=AG:AK=AF:AL=AE:AM=FG:LK=EH:MI）"] /**/
],print(ek11),
ek12:["M=I+(E-H)*r/d(A,H), L=K+(F-G)*r/d(A,H), J=A+(D-A)*r/d(A,H), (7.7620=AK)*(3.8304=IJ)/(r=AI)=(2.9732=KL) ... （AK:KL=AI:IJ）",
["KKNN M =",float(M:I+(E-H)/d(A,H)*r),"L =",float( L:K+(F-G)/d(A,H)*r ),
"J =",float( J:A+(D-A)/d(A,H)*r )," KL=",float(d(L,K)),"(△ALK∽△AJI)"] /**/
],print(ek12),
/**/END:"Tejun2KEnd")$

(GPrint:"グラフを書いて、視覚的に確認3",
dI:[-1,-1],dJ:[0,-1],dK:[1,-1],lI:lab("I",I+dI),lJ:lab("J",J+dJ),lK:lab("K",K+dK),
dL:[1,-1],dM:[0,-1.5],lL:lab("L",L+dL),lM:lab("M",M+dM),
pB:[A,B,C],pSR:[[F,G,H,E,D,B,A,J,I,M,L,K],[E,F,A,E,B,E,C]],
lab:[13,[lA,lB,lC,lD,lF,lE,lG,lH,lI,lJ,lK,lL,lM]],
T:"I,J,K,L,M", c1: x=0 /*(◆修正部分４)*/,
print( float( [T,c,c1,pB,pSR,lab,xm,xM,ym,yM] ) ) /* 出力形式*/,
gr(T,c,c1,pB,pSR,lab,xm,xM,ym,yM) /* グラフ出力すると*/,
/**/Gprint:"EndGPrint")$

(TEJUN3K:"StartFor_aBEA(Kepler) )",
ek21:["aIAM=atand(IM/AI), aFEA=aIAM ... （IM=KL,AI=r,aIAM=aFEA）",
["KKNN aIAM =",Do(aIAM:atand(d(I,M)/d(A,I))),
"aFEA (Kepler)=",Do( aFEA:16+33/60+30/3600 )," (maxima)=",Do(a(F,E,A))] /**/
],print(ek21),
ek22:["aAEB=aBFE-aIAM... （aBFE=aFEB=aDBE/2,aIAM=aFEA）",
["KKNN aAEB =",Do(aAEB:aBFE-aIAM ),
"aAEB (Kepler)=",Do( aAEB:4+24/60+4/3600 )," (maxima)=",Do(a(B,E,A))] /**/
],print(ek22),
/**/END:"Tejun2KEnd")$

/**/