Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.
Concept
Plücker's conoid
Summary
In geometry, Plücker's conoid is a ruled surface named after the German mathematician Julius Plücker. It is also called a conical wedge or cylindroid; however, the latter name is ambiguous, as "cylindroid" may also refer to an elliptic cylinder.
Plücker's conoid is the surface defined by the function of two variables:
This function has an essential singularity at the origin.
By using cylindrical coordinates in space, we can write the above function into parametric equations
Thus Plücker's conoid is a right conoid, which can be obtained by rotating a horizontal line about the z-axis with the oscillatory motion (with period 2π) along the segment [–1, 1] of the axis (Figure 4).
A generalization of Plücker's conoid is given by the parametric equations
where n denotes the number of folds in the surface. The difference is that the period of the oscillatory motion along the z-axis is 2π/n. (Figure 5 for n = 3)
File:Plucker conoid (n=2).gif|Animation of Plucker's conoid with {{math|1=''n'' = 2}}
File:Plucker's conoid (n=2).jpg|Plucker's conoid with {{math|1=''n'' = 2}}
File:Plucker's conoid (n=3).jpg|Plucker's conoid with {{math|1=''n'' = 3}}
File:Plucker's conoid (n=2).gif|Animation of Plucker's conoid with {{math|1=''n'' = 2}}
File:Plucker's conoid (n=3).gif|Animation of Plucker's conoid with {{math|1=''n'' = 3}}
File:Plucker's conoid (n=4).
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.