3 papers
math.MG2005
On S.L. Tabachnikov's conjecture
A. I. Nazarov, F. V. Petrov
S. L. Tabachnikov's conjecture is proved: for any closed curve lying inside convex closed curve the mean absolute curvature exceeds if . An ine…
math.NT2005
On a number of rational points on a convex curve
Fedor V. Petrov
Let be a bounded convex curve on a plane. Then . It streghtens the classical result of Jarn\'ık (an upper estimate ) and disprov…
math.AG2002
How to sum up triangles
F. Bakharev, K. Kokhas, F. Petrov
We prove configuration theorems that generalize the Desargues, Pascal, and Pappus theorems. Our generalization of the Desargues theorem allows us to introduce the structure of an A…