高校数学の質問スレ（医者・東大卒専用） Part438

高校数学の質問スレ（医者・東大卒専用） Part438 (750ﾚｽ)
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496: １３２人目の素数さん [sage] 2024/12/31(火) 14:55:01.89 ID:41bOMap+

EpiCycloid[R_,r_] := Module[
{circleA,circleB,redPoint,redPointTrace,frames,theta},
(* theta:Bの中心の偏角 *)
circleA = Circle[{0, 0}, R];
circleB[theta_] := Circle[{(R+r) Cos[theta], (R+r) Sin[theta]}, r];
redPoint[theta_] := {(R+r) Cos[theta] + r Cos[(r+R)/r theta + Pi], (R+r) Sin[theta] + r Sin[(R+r)/r theta + Pi]};
(* 赤点の軌跡を保存するためのリスト *)
redPointTrace = Table[redPoint[theta], {theta, 0, 2 Pi, 2 Pi/100}];
(* 円Bの中心を円Aの円周に沿って移動させるためのアニメーション *)
frames = Table[
Show[
Graphics[{EdgeForm[Black], FaceForm[None], circleA}],
Graphics[{EdgeForm[None], FaceForm[Red], circleB[theta]}],
Graphics[{Red, PointSize[Large], Point[redPoint[theta]]}],
Graphics[{Red, Line[redPointTrace[[1 ;; Round[theta/ (2 Pi/100)]]]]}],
PlotRange -> {{-2(R+r), 2(R+r)}, {-2(R+r), 2(R+r)}},
Axes -> True,
AxesOrigin -> {0, 0}
],
{theta, 0, 2 Pi, 2 Pi/100}];
(* アニメーション表示 *)
ListAnimate[frames]
]
EpiCycloid[3,1]

HypoCycloid[R_,r_] := Module[
{circleA,circleB,redPoint,theta,frames},
(* theta 円Bの中心の偏角 *)
circleA = Circle[{0, 0}, R];
circleB[theta_] := Circle[{(R - r)  Cos[theta], (R - r)  Sin[theta]}, r];
redPoint[theta_] := {(R-r)  Cos[theta] + r  Cos[(1-R/r) theta], (R-r)  Sin[theta] + r  Sin[(1-R/r) theta]};
(* 円Bの中心を円Aの円周に沿って移動させるためのアニメーション *)
frames = Table[
Show[
Graphics[{EdgeForm[Black], FaceForm[None], circleA}],
Graphics[{EdgeForm[None], FaceForm[Red], circleB[theta]}],
Graphics[{Red, PointSize[Large], Point[redPoint[theta]]}],
Graphics[{Red, Line[Table[redPoint[theta], {theta, 0, 2 Pi, 2 Pi/100}]]}],
PlotRange -> {{-R, R}, {-R, R}},
Axes -> True,
AxesOrigin -> {0, 0}
],
{theta, 0, 2 Pi, 2 Pi/100}
];
(* アニメーションを表示 *)
ListAnimate[frames]
]
HypoCycloid[3,1]

http://rio2016.5ch.net/test/read.cgi/math/1723152147/496

512: １３２人目の素数さん [sage] 2025/01/08(水) 04:11:37.72 ID:X/URcmTf

rm(list=ls())

JugRiddle <- function(
big=5,
small=3,
end=4){

# starting from the bigger jug
movebig <- function(xy){ # start from c(big,0)
x=xy[1] ; y=xy[2]
# x==big
if(x==big) re=c(big-(small-y),small)
# x==0
if(x==0) re=c(big,y)
# y==small
if(y==small) re=c(x,0)
# y==0
if(y==0 & x!=big){
if(x>=small) re=c(x-small,small)
else re=c(0,x)
}
return(re)
}

STATUS=status=c(big,0)
i=1
while(!identical(status,c(0,0))){#
i=i+1
status=movebig(status)
STATUS=rbind(STATUS,status)
}
rownames(STATUS)=1:nrow(STATUS)
colnames(STATUS)=c(paste0(big,'L'),paste0(small,'L'))
(Bigger=STATUS)

# starting from the smaller jug
movesmall <- function(xy){ # start from c(0,small)
x=xy[1] ; y=xy[2]
if(y==small){
if(x<=(big-small)) re=c(x+small,0)
else re=c(big, small-(big-x))
}
if(y==0) re=c(x,small)
if(x==big) re=c(0,y)
if(x==0) re=c(y,0)
return(re)
}

STATUS=status=c(0,small)
i=1
while(!identical(status,c(0,0))){ #
i=i+1
status=movesmall(status)
STATUS=rbind(STATUS,status)
}
rownames(STATUS)=1:nrow(STATUS)
colnames(STATUS)=c(paste0(big,'L'),paste0(small,'L'))
(Smaller=STATUS)
if(all(end != c(Bigger,Smaller))) return(NA)

min_Bigger=min(which(apply(Bigger,1,function(x) end %in% x)))
min_Smaller=min(which(apply(Smaller,1,function(x) end %in% x)))

list(Bigger=as.matrix(Bigger)[1:min_Bigger,],
Smaller=as.matrix(Smaller)[1:min_Smaller,],
min_Bigger=min_Bigger,min_Smaller=min_Smaller)
}

JugRiddle(5,3,4)
JugRiddle(10,5,3)

http://rio2016.5ch.net/test/read.cgi/math/1723152147/512

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