Desmos Calculator : Exploring Shapes in 2D

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Desmos Calculator : Exploring Shapes in 2D

Postby ICN5D » Wed Feb 18, 2015 7:33 pm

Found a neat 2D graphing calc that can handle complicated functions with many adjustable parameters. I made most of the 3D shapes, and a few 4D toratopes, to explore in 2D slices. I think using this with 3D shapes first is good practice for more complicated shapes in CalcPlot3D. Since we already know how these 3D shapes look and feel, we will have a more intuitive grasp on why the 2D slices come out the way they do.

The trick is to imagine the whole 3D shape, while exploring in 2D. While imagining the 3D whole, try to place where the 2D plane is slicing. It's important to understand how we are unable to see the rest of the object, even though we know it's still there. So, when we move on to exploring 4D objects in 3D slices, our minds will be better prepared for this method of aided visualization.

Watching the 3D slices morph by moving a 4D shape will make more sense this time, instead of only thinking in 3D. We have to consider how we are unable to see the 4D whole, even though it is still there. And how the shape of this 4D object determines what all the 3D slices will be, depending on angle and depth.

Exploring 3D Torus in 2D

Exploring 3D Cylinder in 2D

Exploring 3D Cone in 2D

Exploring 3D Tetrahedron in 2D

Exploring 3D Triangle Prism in 2D

Exploring 3D Square Pyramid in 2D

Exploring 3D Cube in 2D

What's especially of interest, is the intuitive grasp of how the empty cuts work. We already know quite well how the 3D intercepts look of 4D toratopes. Now we can explore them in n-2 dimensions, in 2D. Cutting down 2 dimensions can allow for empty cuts, where the 2-plane sits inside a hole. Which again, will better prepare the mind for what we see when exploring 5D toratopes in 3D, where we come across the same property.

Exploring 4D Tiger in 2D

Exploring 4D Ditorus in 2D
in search of combinatorial objects of finite extent
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