[color=#999999][color=#999999]This activity belongs to the [i]GeoGebra book[/i] [url=https://www.geogebra.org/m/dm9prd7h]Attractive projects.[/url][/color][/color][br][br]Until now, the behavior of the robots was determined by vectors defined by other points. In this last section, we will create robots that, before undertaking a movement, find out what is happening around them and, based on the values ​​obtained, make a decision.[br][br][b]2D project[/b]: [i]create automatic dynamic demonstrations.[/i][br][br]In this example, we want to demonstrate the reciprocal of the Pythagorean theorem.[br][br]We start from a triangle ABC and call [b]dif [/b]the expression abs(a² + b² - c²). Our goal is that dif is worth zero.[br][br]We create a slider [b]t[/b] that will serve to animate the vertex C (to which we have activated the trace), so that it varies quite frequently, for example, between 0 and 1 with step 0.01.[br][br]Another slider [b]inc[/b], between 0 and 0.1, will help us to establish the progress in each step. In principle, the value of inc will be 0.1.[br][br]Finally, we create two auxiliary objects: [b]C0[/b] = (0,0) and [b]dif0[/b] = 0 that will be valid to maintain, respectively, the current values ​​of C and dif.[br][br]Now we write the program of our robot. Each time the value of t is updated, the following instruction script will be executed (the # symbol is used to add comments):[br][br][color=#ff0000]# We set the starting values ​​dif0 and C0:[/color][br]SetValue(dif0, dif)[br]SetValue(C0, C)[br][br][color=#ff0000]# We vary C and compare the difference of the NE with dif0:[/color][br]SetValue(C, C + (inc, inc))[br]S[color=rgb(51, 51, 51)]etValue(C, If(dif<dif0, C, C0))[br][/color][color=#ff0000][color=#ff0000][color=rgb(51, 51, 51)]Valor(C0, C)[/color][br][br][/color]# [We repeat these three instructions for the movements towards E, SE, S, SW, W, NW and N, that is, (inc, 0), (inc, -inc), (0, -inc), (- inc, -inc), (-inc, 0), (-inc, inc) and (0, inc).][/color][br][br][color=#ff0000]# If the difference is not reduced, we increase the precision by dividing inc by 10:[/color][br]SetValue(inc, If(dif == dif0, inc / 10, inc))[br][br][color=#ff0000]# When the difference is zero, robot stops (in addition, the message "process done" will be displayed):[/color][br]Yes (dif == 0, StartAnimation(false))[br][br]We just have to animate the slider t.[br][br]Note: If we want to repeat the experiment again, we must remember to return inc to the value 0.1.

[color=#999999]Author of the construction of GeoGebra: [color=#999999][url=https://www.geogebra.org/u/rafael]Rafael Losada[/url][/color][/color]