**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.

Person# Frank de Zeeuw

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.

Related units

Loading

Courses taught by this person

Loading

Related research domains

Loading

Related publications

Loading

People doing similar research

Loading

Courses taught by this person

No results

Related research domains (7)

Related publications (13)

Algebraic curve

In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial

Euclidean distance

In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points.
It can be calculated from the Cartesian coordinates of the points

Distance

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based o

Loading

Loading

Loading

People doing similar research (58)

Related units (2)

Frank de Zeeuw, Shakhar Smorodinsky, Adrian Claudiu Valculescu

We show that for m points and n lines in R-2, the number of distinct distances between the points and the lines is Omega(m(1/5)n(3/5)), as long as m(1/2)

An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is not contained in a line or a circle, then P spans at least ordinary circles. Moreover, we determine the exact minimum number of ordinary circles for all sufficiently large n and describe all point sets that come close to this minimum. We also consider the circle variant of the orchard problem. We prove that P spans at most circles passing through exactly four points of P. Here we determine the exact maximum and the extremal configurations for all sufficiently large n. These results are based on the following structure theorem. If n is sufficiently large depending on K, and P is a set of n points spanning at most ordinary circles, then all but O(K) points of P lie on an algebraic curve of degree at most four. Our proofs rely on a recent result of Green and Tao on ordinary lines, combined with circular inversion and some classical results regarding algebraic curves.