Projecting a space curve to three different planes yields very different plane curves. Can you figure out which? The Rational Normal Curve is the space curve parametrized by (t,t^2,t^3). The object shows this space curve together with the three projections into the three coordinate planes. In the plane z=0, this projection consists of a parabola with parametrization (t,t^2). In y=0, it is a graph of a polynomial of degree three with parametrization (t,t^3). In x=0, the projection is curve with a cusp with parametrization (t^2,t^3).
The 3d-data was produced by Oliver Labs (www.MO-Labs.com
) and can be downloaded at the IMAGINARY website
IMAGINARY is a project by the Mathematisches Forschungsinstitut Oberwolfach
and supported by the Klaus Tschira Foundation
Please note: IMAGINARY
is an open source and non-commercial project. All 3d files are available under an open license, such that you can re-print the sculptures for own exhibitions (following the license specifications). To reimburse our "3D data expert", who takes care to polish and prepare the 3d data and to put the sculptures on the Shapeways shop, we added to this sculpture a 10% fee to the Shapeways price. This amount will be used only for work related to offering more 3d data and sculptures openly and freely to everyone. You can also print this sculpture from your own account.