how reliable is Geogebra?

Niek Sprakel shared this question 2 weeks ago
Answered

So far I was under the impression that Geogebra is reliable in the following sense. If you have graphed some functions and two intersection points appear to coincide, you can zoom in to check whether they really coincide or not. Perhaps it appears they coincide at first, but then when you zoom in it might turn out they are just very close without actually coinciding.

But lately I ran into the following problem. I'm trying to verify that the following points coincide:

The intersection of the line y=1/3 and the line y=x, which coincide at the point (1/3,1/3) and the intersection of the ellipses 2(x)^2+(y-1/2)^2=(1/2)^2 and (x-1/2)^2+2(y)^2=(1/2)^2 which also coincide at the point (1/3,1/3).

At first sight they appear to coincide, but when I zoom in it appears they are not coinciding:

https://i.imgur.com/9bwpsRN.png

https://i.imgur.com/hSXfHpF.png

But this seems to be wrong as these intersection points do in fact coincide.

https://www.wolframalpha.com/input/?i=intersect+y%3D1%2F3+and+x+%3D+y


https://www.wolframalpha.com/input/?i=intersect+2%28x%29%5E2%2B%28y-1%2F2%29%5E2%3D%281%2F2%29%5E2+and+%28x-1%2F2%29%5E2%2B2%28y%29%5E2%3D%281%2F2%29%5E2


If I try this at Desmos, it does seem to work in the sense that at the maximum zoomlevel, the two intersection points still seem to coincide exactly.

https://i.imgur.com/je7jMT3.png


Greetings and thanks in advance for any feedback, Niek

Comments (3)

photo
1

Bonjour ,

c'est le tracé des coniques qui n'est pas précis . Mais les intersections par la commande Intersection sont précises .

Cordialement

photo
1

las curvas implicitas son aproximadas por segmentos con una linea poligonal y el zoom hace que la zona visible se separe de la curva correcta.

una forma de evitar esto con el zoom es intentar usar curva explicitas por ejemplo 3 sqrt(1-x^2/25) en lugar de una elipse porque las funciones cambian de representacion segun las esquinas de la zona visible

photo
1

Ah, gracias.. that resolves the issue somewhat.

https://i.imgur.com/J9Vs2Gx.png

© 2020 International GeoGebra Institute