![]() I have to use parametric surfaces or something similar, which is difficult for me to do since I haven't really learnt about those. GeoGebra, Math3D, and Manim all seem to be good, but I don't really see an easy option to graph such solids of revolution. Is there any good software that I can use to visualize such solids formed from an arbitrary curve? Preferably even solids formed from an intersection of two such curves. Some solids of revolution are also formed by rotating the area under a 2D curve about the $y$-axis: In particular, we're learning about shapes called solids of revolution, which are formed by rotating the area under a 2D curve about the $x$-axis. at 11:17 am [ Comment Do you mean on GeoGebra? Just enter the right hand side of your equation in the Input box and press "Enter".I'm taking AP Calc with AoPS, and we're learning how to find the volumes of some 3D solids using integration methods. If you don't want to solve your equation for z you can use Graphing Calculator 3D instead. Yes, you'll need to solve your equation for z. what about the z-axis? thank so much for ur help □ It is said for f(x,y) so that means i only could draw 9x^2+25y^2 meanwhile i have 9x^2+25y^2+9z^2=225. (You would draw the top half first - the bottom half will be identical) This is a 3-dimensional surface, something like a rugby league ball. would you please show me how to draw the graph? thank you very much. Hallo □ i still have some difficulties how to draw a graph 9x^2+25y^2+9z^2=225. at 8:50 am [ Comment The opening sentence of the article contains a link to GeoGebra, otherwise, Google search will find it very quickly for you. at 5:37 pm [ Comment Good thing it's free, then! Looks good enough for me to look for a place Trying to imagine surfaces in 3D really pushes your brain envelope - but this tool makes things a lot easier!ġ1 Comments on “GeoGebra now with 3D graphs” With this new version, they have addressed some of the shortfalls of earlier versions, since it now handles 3D graphs, and there are non-Java output possibilities so you can view the applets, and interact with them, on your tablet devices. GeoGebra is a versatile and powerful tool. Here they are from a different point of view: Now, we add its negative: z = − y / x 2 (the one in green): Next, we'll look at z = − x / y 2 by itself: Here's what it looks like, along with our original surface: Let's now add the negative of the above graph, that is z = − y / x 2 We can see this shape in our 3D graph above. ![]() If we fix y = 1 then the curve z = 1 / x 2 (it's in 2 dimensions) looks like this: Let's consider this curve for a bit (using GeoGebra to help, of course), and investigate it from different angles. Those graphs are similar to the following ones, which also involve an asymptote: I used some different software for those ones (which has a problem where asymptotes appear as vertical "walls" - but shouldn't be there at all. One reader asked how to draw some graphs involving interesting asymptotes. Next, here are some 3D graphs that were suggested by some comments on the article How to draw y^2 = x - 2? Here's a water droplet-like shape, whose equation is: Let's draw a few 3D surfaces using GeoGebra. Of course, you can still create 2D graphs as before, and the interface is largely unchanged for that aspect. You also get a set of empty 3-D coordinate axes, like this: When you first open GeoGebra now, you are greeted with this choice of Perspectives:Ĭhoosing "3D Graphics", you get several new panels, which allow you to create 3D objects like a line perpendicular to a plane, a plane intersecting a cone, a plane through 3 points, a sphere, and so on: GeoGebra is a powerful and free graphing tool that anyone learning - or teaching - mathematics would find useful.įor me, the best feature of the new version is the ability to create 3D graphs. GeoGebra released version 5 a few months back.
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