[color=#0000ff][i][color=#0000ff][i][color=#999999]This activity belongs to the GeoGebra book [url=https://www.geogebra.org/m/mes4bgft]The Domain of the Time[/url].[/color][/i][/color][/i][/color][br][br]This problem was posed by the American mathematician A. S. Hathaway in 1920.[br][br][i]A dog in the center of a circular pond chases a duck swimming along the edge of the pond. If the dog swims n times faster than the duck, determine the equation of the pursuit curve and the distance the dog swims until it catches the duck.[/i][br][br]Hathaway could not find the equation of the curve. Indeed, the resulting differential equation does not have an analytical solution (it can only be solved numerically).

[b]SCRIPT FOR SLIDER anima[/b][br][br][color=#cc0000][color=#cc0000]# Calculate the elapsed seconds dt; add one second if t1(1) < tt[/color][/color][br][color=#999999]SetValue(tt, t1(1))[br]SetValue(t1, First(GetTime(), 3))[br]SetValue(dt, (t1(1) < tt) + (t1(1) − tt)/1000)[/color] [br][br][color=#cc0000]# Move M (duck) and N (dog) and stop the animation when N and M are close enough[/color][br][color=#999999][color=#999999]SetValue[/color](M, M + dt vM)[br][color=#999999]SetValue[/color](N, N + dt vN)[/color][color=#999999][br]StartAnimation(anima, abs(N [color=#999999]−[/color] M) > (x(Corner(2) [color=#999999]−[/color] Corner(1))/400))[/color][br]  [br][color=#cc0000]# [/color][color=#cc0000]Use the polyline as a trace by recording the position N in the list reg[/color][br][color=#0000ff]SetValue(reg, Append(N, reg))[/color][br] [br][br][br][br][color=#999999][color=#0000ff][color=#0000ff][color=#999999][color=#999999][color=#0000ff][color=#0000ff][color=#999999][color=#999999]Author of the activity and GeoGebra construction: [/color][/color][/color][color=#0000ff][color=#999999][color=#999999][url=https://www.geogebra.org/u/rafael]Rafael Losada[/url].[/color][/color][/color][/color][/color][/color][/color][/color][/color]