List of publications
  1. A. V. Akopyan, Geometry in Figures, Second, extended edition, 232p, 2017. You can buy it on The pdf versions is not available yet. Please visit the Instagram channel of the book or download the Poster of size A0. New: T-Shorts are available on Amazon!
    Current list of mistakes.

    The first edition, 128p, 2011, The pdf versions of the first edition is available in Russian and English.
    Attention: problems 4.5.31, 5.5.7, 6.3.4, 6.3.7, 8.1.9, 9.12 are not correct!!!!
    Book with solutions: S. Chobanov, S. Dimitrov, and L. Lichev, 555 Geometry Problems. Solutions based on “Geometry in Figures” by A. V. Akopyan, Unimat SMB, 2017. Available on, here is the GeoGebra version.

  2. A. V. Akopyan and A. A. Zaslavsky, Geometry of Conics, Amer. Math. Soc., Providence, RI, 2007 (, Russian second edition pdf).

  1. A. V. Akopyan, S. Avvakumov, and R. N. Karasev, Convex fair partitions into arbitrary number of pieces, 2018, (

  2. A. V. Akopyan and R. N. Karasev, Waist of balls in hyperbolic and spherical spaces, Int. Math. Res. Notices, 2018, (,

  3. A. Akopyan and A. I. Bobenko, Incircular nets and confocal conics, Trans. Amer. Math. Soc., 370(4): 2825-2854, 2018, (,

  4. A. Akopyan, On the number of non-hexagons in a planar tiling, Comptes rendus - Mathématique, 356(4): 412-414, 2018, (,

  5. A. V. Akopyan and R. N. Karasev, Estimating symplectic capacities from lengths of closed curves on the unit spheres, 2018, (

  6. A. V. Akopyan and S. Avvakumov, Any cyclic quadrilateral can be inscribed in any closed convex smooth curve, Forum of Mathematics, Sigma, 6, E7, 2018, (,

  7. A. V. Akopyan, 3-webs generated by confocal conics and circles, Geometriae Dedicata, 194(1): 55–64, 2018, (,

  8. A. V. Akopyan, A. M. Balitskiy, and M. Grigorev, On the circle covering theorem by A. W. Goodman and R. E. Goodman, Discrete & Computational Geometry, 59(4):1001-1009, 2018, (,

  9. A. V. Akopyan and R. M. Fedorov, Two circles and only a straightedge, 2017, (

  10. A. V. Akopyan and A. Petrunin, Long geodesics on convex surfaces, 2017, (

  11. A. Akopyan, I. Bárány, and S. Robins, Algebraic vertices of non-convex polyhedra, Advances in Mathematics, 308:627-644, 2017, (,

  12. A. V. Akopyan and R. N. Karasev, A tight estimate for the waist of the ball, Bull. London Math. Soc., 2017, (,

  13. A. V. Akopyan and V. V. Vysotsky, On length of curves passing through boundary points of a planar convex shape, The American Mathematical Monthly, 124(7):588—596, 2017, (jstor,

  14. A. V. Akopyan, A. Hubard, and R. N. Karasev, Lower and upper bounds for the waists of different spaces, 2016, (

  15. A. V. Akopyan and E. Segal-Halevi, Cutting a cake without harming the toppings, 2016, (

  16. A. V. Akopyan and V. V. Vysotsky, Large deviations for the perimeter of convex hulls of planar random walks, 2016, (

  17. A. V. Akopyan, A. M. Balitskiy, R. N. Karasev, and A. Sharipova, Elementary approach to closed billiard trajectories in asymmetric normed spaces, Proc. Amer. Math. Soc. 144, 4501-4513, 2016, (,

  18. A. V. Akopyan and A. M. Balitskiy, Billiards in convex bodies with acute angles, Israel Journal of Mathematics, 216(2):833–845, 2016. (,

  19. A. V. Akopyan and R. N. Karasev, Bounding minimal solid angles of polytopes, 2015, (

  20. A. V. Akopyan and A. Plakhov, Minimal resistance of curves under the single impact assumption, SIAM J. Math. Anal., 47(4): 2754-2769, 2015, (

  21. A. V. Akopyan, S. A Pirogov, and A. N. Rybko, Invariant measures of genetic recombination process, Journal of Statistical Physics, 160(1): 163-167, 2015, (

  22. A. V. Akopyan, R. N. Karasev, and F. V. Petrov, Bang's problem and symplectic invariants, 2014, (

  23. A. V. Akopyan, R. N. Karasev, and A. Yu. Volovikov, Borsuk—Ulam type theorems for metric spaces, 2012, (

  24. A. V. Akopyan, Geometry of the cardioid, The American Mathematical Monthly, 122(2): 144-150, 2015, (in English, pdf, in Russian pdf).

  25. A. V. Akopyan and A. A. Glazyrin, On maximum volume simplices in polytopes, Periodica Mathematica Hungarica, 69(2): 251-256, 2014, (, pdf).

  26. A. V. Akopyan, Some remarks on the circumcenter of mass, Discrete & Computational Geometry, 51(4):837-841, 2014, (

  27. A. V. Akopyan, The lemniscate of Bernoulli, without formulas, The Mathematical Intelligencer, 36(4):47-50, 2014, (,

  28. Y. Skalko, R. Karasev, A. Akopyan, I. Tsybulin, and M. Mendel, Space-marching algorithm for solving radiative transfer problem based on short-characteristics method, Computer Research and Modeling, 6(2):203-215, 2014, (

  29. A. V. Akopyan, Villarceau circles and the Hopf fibration, Kvant Magazine,(5-6):8-11, 2013, (in Russian, the journal version on, the author version pdf).

  30. A. V. Akopyan, Combinatorial generalizations of Jung’s theorem, Discrete & Computational Geometry, 49(3):478-484, 2013, (, pdf).

  31. A. V. Akopyan and O. R. Musin, On two-distance sets, Matematicheskoe prosveshenie. Tret’ya seriya, 17:136-151, 2013, (in Russian,, pdf).

  32. A. V. Akopyan and R. N. Karasev, Cutting the same fraction of several measures, Discrete & Computational Geometry, 49(2):402-410, 2013, (,

  33. A. V. Akopyan and R. N. Karasev, Inscribing a regular octahedron into polytopes, Discrete Mathematics, 313(1):122-128, 2013, (,

  34. A. V. Akopyan, G. A. Kabatiansky, and O. R. Musin, Contact numbers, codes and spherical polynomials, Matematicheskoe prosveshenie. Tret’ya seriya, 16:57-74, 2012, (in Russian, pdf).

  35. A. V. Akopyan and R. N. Karasev, Kadets-type theorems for partitions of a convex body, Discrete & Computational Geometry, 48(3):766-776, 2012, (,

  36. A. V. Akopyan, A short proof of the Collapsing Walls Lemma, Discrete Mathematics, 312(10):1650-1651, 2012, (, pdf).

  37. A. V. Akopyan, Conjugation of lines with respect to a triangle, Journal of Classical Geometry, 1:23-31, 2012, (

  38. A. V. Akopyan and M. Tagami, On the number of points in a lattice polytope, Integers, 11(5):619-622, 2011, (,

  39. A. V. Akopyan, A. A. Glazyrin, O. R. Musin and A. S. Tarasov, The Extremal Spheres Theorem, Discrete Mathematics, 311(2-3):171-177, 2011, (,

  40. A. V. Akopyan, Extremal properties of Delaunay triangulation, Problems of calculations in distributed networks, 46:174-187, M:URSS, 2009, (in Russian,

  41. A. V. Akopyan, On some classical constructions extended to hyperbolic geometry, Matematicheskoe prosveshenie. Tret’ya seriya, 13:155-170, 2009, (in Russian,, in English

  42. A. V. Akopyan and A. S. Tarasov, A constructive proof of Kirszbraun’s theorem, Mathematical Notes, 84(5):725-728, 2008, (, pdf).

  43. A. V. Akopyan, Intersection of parallelepipeds in d, Mathematical Notes, 83(1):138-141, 2008, (,

  44. A. V. Akopyan and A. A. Zaslavsky, Different views on the isogonal conjugation, Matematicheskoe prosveshenie. Tret’ya seriya, (11):61-78, 2007, (in Russian,

  45. A. V. Akopyan, A PL-analogue of the Nash-Kuiper theorem, (in Russian,

  46. A. V. Akopyan, Some generalizations of a diameter of sets and the Jung problem, (in Russian Mathematical Russian Euler Contest).