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Blowup of the plane in a point 3d printed
Blowup of the plane in a point 3d printed
Blowup of the plane in a point 3d printed

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Blowup of the plane in a point

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  • 3D printed in Full Color Sandstone: Fully colored material with a coarse finish and a delicate feel.
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  • This product is intended for mature audiences.
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Product Description

One of the most important concepts in algebraic geometry and singularity theory is the blowup of a plane in the origin. The plane is mapped to a surface in 3-space in an interesting way: Every point of the plane outside the origin is mapped to a unique point of the surface above. But the origin itself is mapped to a whole line (the thick green one in the model) where each point on the line on the surface corresponds to a direction through the origin. In the model this is illustrated in the following way: The blue curve which passes twice through the origin in the plane is mapped to a blue curve in the surface, but the curve on the surface has no self-intersection because the two directions of the curve in the origin are mapped to different points of the green line above. See our youtube video on https://www.youtube.com/watch?v=20BfjaAZ8sI for more information.

What's in the Box
Blowup of the plane in a point
Full Color Sandstone
6.3 cm
6.3 cm
12.3 cm
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