Vamos a considerar dos números reales positivos a y b, se ejemplificará sobre media circunferencia, de diámetro a + b, la relación existente entre:
Manipulate[ra = Sqrt[1 - a^2]; ang = Arg[a + I ra];
Grid[{{Show[
Graphics[{{If[0.1 < Abs[a] < 0.9,
Text["90º", {a^3 + 0.15 Sign[a],
a^2 ra}]]}, {Arrowheads[{-0.02, 0.02}],
Arrow[{{-1, -0.2}, {a, -0.2}}],
Arrow[{{a, -0.2}, {1, -0.2}}]}, {Text["a", {(a - 1)/2, -0.1}],
Text["b", {(a + 1)/2, -0.1}]}, {Circle[{a^3, a^2 ra},
0.1, {ang, ang - Sign[a] Pi/2}]}, {Red, Thickness[0.01],
Line[{{-1, 0}, {a, 0}}]}, {Blue, Thickness[0.01],
Line[{{1, 0}, {a, 0}}]}, {Green, Thickness[0.02],
Line[{{0, 0}, {0, 1}}]}, {Orange, Thickness[0.02],
Line[{{a, ra}, {a, 0}}]}, {Line[{{0, 0}, {a,
ra}}]}, {Line[{{a, 0}, {a^3, a^2 ra}}]}, {Cyan,
Thickness[0.02], Line[{{a^3, a^2 ra}, {a, ra}}]}, {Yellow,
Thickness[0.02], Line[{{a, 0}, {0, 1}}]}},
ImageSize -> {450, 400}],
Plot[Sqrt[1 - x^2], {x, -1, 1}, AspectRatio -> 1/2,
Ticks -> None]],
Graphics[{{Text["b", {-0.1, 0.8}]}, {Blue, Thickness[0.01],
Line[{{0, 0.8}, {1 - a, 0.8}}]}, {Text["a", {-0.1, 1}]}, {Red,
Thickness[0.01],
Line[{{0, 1}, {1 + a, 1}}]}, {Text[
"Aritmética", {-0.25, 0.6}]}, {Green, Thickness[0.02],
Line[{{0, 0.6}, {1, 0.6}}]}, {Text[
"Geométrica", {-0.26, 0.4}]}, {Orange, Thickness[0.02],
Line[{{0, 0.4}, {ra, 0.4}}]}, {Text[
"Armónica", {-0.25, 0.2}]}, {Cyan, Thickness[0.02],
Line[{{0, 0.2}, {1 - a^2, 0.2}}]}, {Text[
"Cuadrática", {-0.26, 0}]}, {Yellow, Thickness[0.02],
Line[{{0, 0}, {Sqrt[1 + a^2], 0}}]}, {Text["a", {-0.1, 1}]}},
PlotRange -> {{-0.95, 2}, {-0.1, 1.1}},
ImageSize -> {450, 400}]}}], {{a, -0.8,
"Relación entre a y b"}, -0.95, 0.95}, ContentSize -> {1000, 400}]
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