三角比

加法定理

加法定理

準備

Show[
      Graphics[{GrayLevel[0.6], 
          Polygon[{{0, 0},  {0, 1},  {1, 1}, {1, 0}}], Circle[{0, 0}, 2], 
          Line[{{-1, -1}, {2, 2}}]}]]

加法定理

r3 := Sqrt[13];

Clear[a]

a := Pi/6;

Do[Show[
        Graphics[{{GrayLevel[0.6], 
              Polygon[{{0, 0}, 3 {Cos[t], Sin[t]}, 
                  r3 {Cos[t + a], Sin[t + a]}, 2 {-Sin[t], Cos[t]}}]}, 
            Circle[{0, 0}, r3], Circle[{0, 0}, 2], Circle[{0, 0}, 3], 
            Line[{{0, 0}, 3 {Cos[t], Sin[t]}}], 
            Line[{{0, 0}, 2 {-Sin[t], Cos[t]}}], {Thickness[0.01], 
              Line[{{0, 0}, r3 {Cos[t + a], Sin[t + a]}}]}, {RGBColor[1, 0, 
                0], Line[{3 {Cos[t] +  .01, 0}, 
                  3 {Cos[t] +  .01, Sin[t]}}]}, {RGBColor[0, 0, 1], 
              Line[{{3 Cos[t], r3 Sin[t + a]}, 
                  3 {Cos[t], Sin[t]}}]}, {RGBColor[0, 0, 1], 
              Line[{2 {-Sin[t], Cos[t]}, 2 {-Sin[t], 0}}]}, 
            Line[{{3 Cos[t], r3 Sin[t + a]}, r3 {0, Sin[t + a]}, 
                r3 {Cos[t + a], Sin[t + a]}}]}, 
          AspectRatio -> Automatic, Axes -> True]], {t, 0, 
        47 Pi/24, Pi/24}]

半角公式

補間の定義

Clear[a]

Clear[f]

hokan[f_, l_] := 
      Block[{l1, l2, l3, l4, l5, l6}, l1 = Drop[l, -1]; l2 = Drop[l, 1]; 
        l3 = Thread[f[l1, l2]]; l4 = Append[l3, dammy]; 
        l5 = Flatten[Transpose[{l, l4}]]; l6 = Drop[l5, -1]; 
        l6]

hokan[g, {a, b, c, d}]

Nest[hokan[g, #] &, {a, b}, 1]

Nest[hokan[g, #] &, {a, b}, 3]

半角の公式

j[x_, y_] := (x + y)/2

Nest[hokan[j, #] &, {1.0, 0}, 7] // ListPlot

k[x_, y_] := 
      Sqrt[(1 + x*y - Sqrt[1 - y^2]*Sqrt[1 - x^2])/2]

Nest[hokan[k, #] &, {1.0, 0}, 7] // ListPlot

今日のコマンド

l := {a, b, c, d}

l1 = Drop[l, -1]

l2 = Drop[l, 1]

Thread[g[{1, 2, 3}, {x, y, z}]]

l3 = Thread[g[l1, l2]]

l4 = Append[l3, dammy]

Transpose[{{1, 2, 3}, {x, y, z}}]

Flatten[%]

Flatten[Transpose[{l, l4}]]