-
Notifications
You must be signed in to change notification settings - Fork 9
Usage
Our approach to understanding 4D geometry is inspired by Edwin Abbot's Flatland. We've set up the app so that you can view 1D slices of 2D objects, as well as 2D slices of 3D objects, in the hopes that students will be able to make sense of the 3D slices they see of 4D objects.
Both 2D and 3D modes support 3 ways of input:
- Cartesian equation
- Parametric equation
- Convex hull
In 4D, only convex hull is currently fully supported. Cartesian equations are possible to view but only as slices.
All input is controlled in the control box in the top right.
[TODO: Insert image of the control box?]
All modes also have a set of built in examples you can access in this controls menu.
The default object in 2D is a circle, defined by its cartesian equation x^2+y^2 = 10. On the left, is the full 2D object. On the right, is a 1 dimensional slice. The orange line is the 1-dimensional "plane" of intersection. You can move that using the viewing controls:
[TODO: Insert gif of slicing a circle]
You can also switch the slicing axis using the drop down.
Now try changing the equation to something like x^2+y^2 < 10. Now you should see a whole region filled in. You can also choose to see the full shape when slicing by ticking the [TODO: Insert name of checkbox when we know what it is] box.
**[TODO: Insert gif of slicing filled in circle, with whole shape slicing] **
Any cartesian function works here, including something as crazy as cos(x)=sin(y).
TODO: Fill this in.
TODO: Fill this in.
TODO: Fill this in.
TODO: Fill this in.
TODO: Fill this in.
TODO: Fill this in.
TODO: Fill this in.
TODO: Talk about some examples of things you can see in the app as a way of understanding higher dimensions. Maybe try the ribbon rotation example?