Selected Publications


Selected Educational Computer Programs:
  1. Abacus (Smetalo) (in Bulgarian), 2001.
  2. Invoice for Electric Energy (in Bulgarian), 2002.
  3. Linear Systems, 2003. (Russian edition, 2008).
  4. Inverse Matrices 2003. (Russian edition, 2008).
  5. Inverse Matrices. Shortened version in Bulgarian, 2004.
  6. Solving Triangles, 2004. (Russian edition, 2008).
  7. Geometric Constructions, 2004. (Russian edition, 2008).
  8. Coordinate Geometry, 2005. (Russian edition, 2008).
  9. Interest, Credit, Annuity (in Bulgarian), 2005.
  10. Machine for Questions and Answers, 2006.
  11. Discoverer (Professor Sava Grozdev is the leader of the project since 2012, Professor Hiroshi Okumura is a member of the team since 2016) .

    In Preparation
  1. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer-Generated Encyclopedia of Euclidean Geometry.

    2017
  1. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Euler Anticevian Triangles, International Journal of Computer Discovered Mathematics, Vol. 2, 2017, pp. 1-29.
    Supplementary Material. Euler Anticevian triangles.
  2. Sava Grozdev, Hiroshi Okumura and Deko Dekov, A Note on the Leversha Point, International Journal of Computer Discovered Mathematics, vol. 2, 2017, pp.30-34.
  3. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Incentral Triangle, International Journal of Computer Discovered Mathematics, vol. 2, 2017, pp. 35-45.
    Supplementary Material. Incentral triangle.
  4. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Triangles homothetic with the Orthic triangle, International Journal of Computer Discovered Mathematics, vol. 2, 2017, pp.46-54.
  5. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Half-Anticevian triangle of the Incenter, International Journal of Computer Discovered Mathematics, Vol. 2, 2017, pp. 55-71.
    Supplementary Material - Half-Anticevian Triangle of the Incenter.
  6. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Excenters-Incenter Reflections Triangle, International Journal of Computer Discovered Mathematics, Vol. 2, 2017, pp.72-80. Supplementary Material - Excenters-Incenter Reflections Triangle.
  7. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Problems about Points on the Euler line, International Journal of Computer Discovered Mathematics, Vol. 2, 2017, pp.81-85. Supplementary Material - Points on the Euler line
  8. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Triangles Homothetic with triangle ABC, International Journal of Computer Discovered Mathematics, Vol. 2, 2017, pp. 86-89.
  9. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Triangles Homothetic with Triangle ABC. Part 2, International Journal of Computer Discovered Mathematics, Vol. 2, 2017, pp. 90-96.
    Supplementary Material - HT2.
  10. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Triangles Homothetic with Triangle ABC. Part 3, International Journal of Computer Discovered Mathematics, Vol. 2, 2017, pp.97-105.
    Supplementary Material - HT3.zip.
  11. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Triangles Associated with Triangulation Triangles, International Journal of Computer Discovered Mathematics, Vol. 2, 2017, pp.106-110.
    Supplementary Material - Triangulation Triangles.zip.
  12. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Leversha Triangles and Leversha Points, International Journal of Computer Discovered Mathematics, Vol. 2, 2017, pp.111-116.
    Supplementary Material - Leversha Points.zip.
  13. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Notable Circles, International Journal of Computer Discovered Mathematics, Vol. 2, 2017, pp.117-134.
    Supplementary Material - Notable Circles.zip.
  14. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Problems for Students about Excentral Triangle, pp.185-200, International Journal of Computer Discovered Mathematics, Vol. 2, 2017
    Supplementary material - Excentral triangle.zip.
  15. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Problem 158, MathProblems Journal, vol 6, no 2, 2016, p.560.
  16. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Problems on the Brocard Circle, Mathematics and Informatics, Volume 60, Number 4, 2017, pp.382-390.

    2016

  1. Sava Grozdev and Deko Dekov, Computer Discovered Mathematics and Application in Education, Matematicki Bilten, Vol. 40, 2016, No. 2, pp. 5-12.
  2. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Grebe Triangles,, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 4, pp. 14-23.
    Supplementary Material Grebe triangles.
  3. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Haimov Triangle of the Incenter,, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 3, pp. 57-61.
  4. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Orthopoles, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 3, pp. 50-56.
  5. Sava Grozdev and Deko Dekov, Computer Discovered Mathematics: Orthology Centers of the Euler Triangles, Mathematics and Informatics, vol.59, 2016, no 5, pp. 393-403.
  6. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: A Note on the Miquel Points, pp.45-49.pdf, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 3, pp. 45-49.
  7. Sava Grozdev and Deko Dekov, Computer Discovered Mathematics: Stanilov Triangles, pp.40-44.pdf, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 3, pp. 40-44.
    Supplementary material.
  8. S. Grozdev and D. Dekov, Computer Discovered Mathematics: Fuhrmann Triangles, pp.48-58, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 2, pp. 48-58.
  9. S. Grozdev and D. Dekov, Computer Discovered Mathematics: Harmonic Conjugates, pp.59-63, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 2, pp. 59-63.
    Supplementary Material: Harmonic Conjugates.zip
  10. S. Grozdev and D. Dekov, Computer Discovered Mathematics: Inversion of Triangle ABC with respect to the Incircle, pp.64-74, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 2, pp. 64-74.
    Supplementary Material: Inversion of ABC wrt the Incircle.zip
  11. S. Grozdev and D. Dekov, Barycentric Coordinates: Formula Sheet, pp.75-82, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 2, pp. 75-82.
  12. S. Grozdev and D. Dekov, Computer Discovered Mathematics: A Note on the Johnson Circles, pp.90-95, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 2, pp. 90-95.
    Supplementary Material: Johnson Circles.zip
  13. S. Grozdev and D. Dekov, Computer Discovered Mathematics: Yff Triangles, pp.96-103, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 2, pp. 96-103.
    Supplementary Material: Yff Triangles.zip
  14. S. Grozdev and D. Dekov, Computer Discovered Mathematics: A Note on the Gossard Triangles, pp.104-108, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 2, pp. 104-108.
    Supplementary Material: Gossard Triangle.zip
  15. S. Grozdev and D. Dekov, Computer Discovered Mathematics: Half-Cevian Triangles, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 2, pp. 1-8.
    Supplementary Material: Half-Cevian-Triangles.zip.
  16. S. Grozdev and D. Dekov, Computer Discovered Mathematics: The Mittenpunkt, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 2, pp. 9-13.
  17. S. Grozdev and D. Dekov, Computer Discovered Mathematics: Gibert Triangles, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 2, pp. 14-20.
    Supplementary Material: Gibert-Triangles.zip.
  18. S. Grozdev and D. Dekov, Computer Discovered Mathematics: Dividing Directed Segments, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 1, pp. 80-88.
    Supplementary Material: division.zip.
  19. S. Grozdev and D. Dekov, Mathematics Discovered by Computers: Incenters of Triangles, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 1, pp. 89-92.
  20. S. Grozdev and D. Dekov, Computer Discovered Mathematics: Circles through the Feuerbach Point, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 1, pp. 93-96.
  21. Sava Grozdev and Deko Dekov, Computer Discovered Mathematics: Euler Triangles, International Journal of Computer Discovered Mathematics, Vol. 1, 2016, No. 1, pp. 1-10.
    Enclosed File: Supplementary Material
  22. Sava Grozdev and Deko Dekov, Computer Discovered Mathematics: Circles Containing the Parry Point, International Journal of Computer Discovered Mathematics, 2015, vol.1, no.1, pp.11-14.
  23. Sava Grozdev and Deko Dekov, Computer Discovered Mathematics: Lester Circles, International Journal of Computer Discovered Mathematics, 2015, vol.1, no.1, pp.15-25.
  24. Sava Grozdev and Deko Dekov, Computer Discovered Mathematics: The Incenter, International Journal of Computer Discovered Mathematics, 2015, vol.1, no.1, pp.26-35.

    2015
  1. Sava Grozdev and Deko Dekov, Problem 123, MathProblems Mathematical Journal, 2015, vol. 1, no 1, p.370.
  2. Sava Grozdev and Deko Dekov, Problem. Five new remarkable circles orthogonal to the Stevanovic circle, International Journal of Computer Generated Mathematics, vol. 10, 2015, pp.1-4.
  3. Sava Grozdev and Deko Dekov, Computer-Discovered Mathematics: Pedal Corner Products, Mathematics and Informatics, vol.58, 2015, no.6, 609-615.
    Enclosed File: Supplementary Material
  4. Sava Grozdev and Deko Dekov, Computer Discovered Mathematics: Antipedal Corner Products, Mathematics and Informatics, vol.58, 2015, no.5, 513-519.
    Enclosed File: Supplementary Material
  5. Sava Grozdev and Deko Dekov, Problem. The distance from the Incenter to the Euler Line as function of the sides of the triangle, The Pi Mu Epsilon Journal, Fall 2015. Problem 1310.
  6. Sava Grozdev and Deko Dekov, A Survey of Mathematics Discovered by Computes, International Journal of Computer Discovered Mathematics, Vol. 0, 2015, No. 0, pp. 3-20.
  7. Sava Grozdev and Deko Dekov, Computer Discovered Mathematics: Haimov Triangles, International Journal of Computer Discovered Mathematics, Vol. 0, 2015, No. 0, pp. 70-79. Enclosed File: Supplementary Material
  8. Sava Grozdev and Deko Dekov, Computer Discovered Mathematics: Hexyl-Anticevian Triangles, International Journal of Computer Discovered Mathematics, Vol. 0, 2015, No. 0, pp. 60-69.
  9. Sava Grozdev and Deko Dekov, Computer Discovered Mathematics: Cevian Corner Products, Mathematics and Informatics, 2015, vol.58, no.4, pp.426-436.
    Enclosed File: Supplementary Material
  10. Sava Grozdev and Deko Dekov, Computer-Discovered Mathematics: Anticevian Corner Products, MathProblems Mathematical Journal, 2014, vol. 4, no.4, p.358-361.
    Enclosed File: Supplementary Material
  11. Sava Grozdev and Deko Dekov, Problem 109. Solution to the problem, MathProblems Mathematical Journal, 2014, vol. 4, no.4, p.353-354.
  12. Sava Grozdev and Deko Dekov, The Simon and Newell prediction is realized by the "Discoverer", IJCGM, Vol.10, 2015, no 1.
  13. Sava Grozdev and Deko Dekov, Computer-Aided Education: Learning through Discovery, Web Technologies in Education Space, Collection of Research Articles of International Scientific and Practical Conference, 26-27 March 2015, N.Novgorod - Arzamas, Russia, 2015, pp.13-22.
    Enclosed File: Supplementary Material
  14. Sava Grozdev and Deko Dekov, Computer-Discovered Mathematics: Lalesco Products, Mathematics and Informatics, 2015, vol. 58, no.2, 143-148.
    Enclosed File: Lalesco.zip
  15. Sava Grozdev and Deko Dekov, Problem 109, MathProblems Mathematical Journal, 2014, vol. 4, no.3, p.303.
  16. Sava Grozdev and Deko Dekov, Problem 97, MathProblems Mathematical Journal, vol. 4, no 2. Solution to the Problem, IJCGM, Vol.10, 2015.
    Enclosed File: Supplementary Matherial.
  17. Sava Grozdev and Deko Dekov, The Computer improves the Steiner?s Construction of the Malfatti Circles, Mathematics and Informatics, 2015, vol. 58, no.1, 40-51.
  18. Sava Grozdev and Deko Dekov, Problem. Prasolov Anticevian Products, IJCGM, Vol.10, 2015.
    Enclosed File: p001_Solution.pdf
  19. Sava Grozdev and Deko Dekov, Problem. Prasolov Pedal Products, IJCGM, Vol.10, 2015.
    Enclosed File: p002_Solution.pdf
  20. Sava Grozdev and Deko Dekov, Problem. Prasolov Circumcevian Products, IJCGM, Vol.10, 2015.
    Enclosed File: p003_Solution.pdf

    2014
  1. Sava Grozdev and Deko Dekov, Supplementary Material to the Note by Grozdev and Dekov, published in Mathematical Gazette in November 2014, JCGM, 2014, no 6.
    DOI: http://dx.doi.org/10.1017/S0025557200008305
    Enclosed File: 2014-6.zip
  2. Sava Grozdev and Deko Dekov, Computer-generated mathematics: Points on the Kiepert hyperbola, The Mathematical Gazette, 2014, vol. 98, no. 543, 509-511.
  3. Sava Grozdev and Deko Dekov, Learning through discoveries: A new effective approach within learning through experimentation (Bulgarian), Mathematics and Informatics, 2014, vol. 57, no.6, 16-33.
    Enclosed File: 2014-6 discoveries.zip
  4. Sava Grozdev and Deko Dekov, Computer-generated mathematics: A note on the Haimov triangle (Bulgarian), Mathematics and Informatics, 2014, vol. 57, no.6, 7-15.
    Enclosed File: 2014-6 Haimov.zip
  5. Sava Grozdev and Deko Dekov, Machine approach to Euclidean Geometry: Euler Triangles, Euler Products and Euler Transforms (Bulgarian), Mathematics and Informatics, 2014, vol. 57, no.5, 519-528.
    Enclosed File: 2014-5 Euler.zip
  6. Sava Grozdev and Deko Dekov, Computer-generated mathematics: Kosnita products in Euclidean geometry (Bulgarian), Mathematics and Informatics, 2014, vol.57, no 4, 355-363.
    Enclosed File: 2014-4 Kosnita.zip
  7. Sava Grozdev and Deko Dekov, Computer-generated mathematics: Elaboration of a topic of Euclidean Geometry (Bulgarian), Mathematics and Informatics, 2014, vol. 57, no.1, 34-42.
    Enclosed File: 2014-1 topics.zip
  8. Sava Grozdev and Deko Dekov, Problem 94, MathProblems Mathematical Journal, 2014, vol. 4, no.1, p.232.
  9. Sava Grozdev and Deko Dekov, Problem 97, MathProblems Mathematical Journal, 2014, vol. 4, no.2, p.263-264.
  10. Sava Grozdev and Deko Dekov, Learning through Discoveries, JCGM, vol.9, 2014.
    Enclosed File: 2014-1.zip, 11 KB.
  11. Sava Grozdev and Deko Dekov, The Computer Program "Discoverer" and the Encyclopedia of Computer-Generated Mathematics (Bulgarian), JCGM, vol.9, 2014.
  12. Sava Grozdev and Deko Dekov, Investigation of circumconics by using the computer program "Discoverer" (Bulgarian), JCGM, vol.9, 2014.
    Enclosed File: 2014-3.zip, 10 KB.
  13. Sava Grozdev and Deko Dekov, A New Relation between the Steiner Circumellipse and the Kiepert Hyperbola, JCGM, vol.9, 2014.
  14. Sava Grozdev and Deko Dekov, The computer program "Discoverer" as a tool of mathematical investigation, JCGM, vol.9, 2014.
    Enclosed File: 2014-5.zip, 14 KB.
  15. Sava Grozdev and Deko Dekov, The Centroid of the Triangle of Reflections of the Kiepert Center in the Sidelines of Triangle ABC lies on the Lester circle, JCGM, vol.9, 2014.
  16. Sava Grozdev and Deko Dekov, The Euler Reflection Point of the Triangle of the Nine-Point Centers of the Triangulation Triangles of the Tarry Point lies on the Lester circle, JCGM, vol.9, 2014.
  17. Sava Grozdev and Deko Dekov, The Parry Reflection Point of the Triangle of the Orthocenters of the Triangulation Triangles of the Steiner Point lies on the Lester circle, JCGM, vol.9, 2014.
  18. Sava Grozdev and Deko Dekov, The Lester Circle is orthogonal to the Orthocentroidal Circle of the Outer Fermat Triangle of the Johnson Triangle, JCGM, vol.9, 2014.
  19. Sava Grozdev and Deko Dekov, The Lester Circle is orthogonal to the Orthocentroidal Circle of the Inner Fermat Triangle of the Johnson Triangle, JCGM, vol.9, 2014.
  20. Sava Grozdev and Deko Dekov, The Lester circle is orthogonal to the Orthocentroidal Circle of the Triangle of the Orthocenters of the Triangulation Triangles of the Tarry Point, JCGM, vol.9, 2014.
  21. Sava Grozdev and Deko Dekov, The Lester circle is orthogonal to the Orthocentroidal Circle of the Triangle of the Nine-Point Centers of the Anticevian Corner Triangles of the Centroid, JCGM, vol.9, 2014.
  22. Sava Grozdev and Deko Dekov, The Lester Circle is orthogonal to the Brocard Circle of the Fourth Brocard Triangle, JCGM, vol.9, 2014.
  23. Sava Grozdev and Deko Dekov, The Lester Circle is orthogonal to the Brocard Circle of the Second Brocard Triangle of the Fourth Brocard Triangle, JCGM, vol.9, 2014.
  24. Sava Grozdev and Deko Dekov, The Lester Circle is orthogonal to the Brocard Circle of the Triangle of Reflections of the Parry Reflection Point in the Sidelines of Triangle ABC, JCGM, vol.9, 2014.

    2013
  1. Sava Grozdev and Deko Dekov, Graphical and numerical computer-aided solutions of equations and inequalities (Bulgarian), Mathematics and Informatics, 2013, vol. 56, no.6, 522-528.
  2. Sava Grozdev and Deko Dekov, Some applications of the computer program "Discoverer" (Bulgarian), Mathematics and Informatics, 2013, vol. 56, no.5, 444-455.
    Enclosed File: 2013-5 apps.zip
  3. Sava Grozdev and Deko Dekov, Extremal problems in high school with computer tables (Bulgarian), Mathematics and Informatics, 2013, vol. 56, no.4, 351-367.
    Enclosed File: 2013-4 problems.zip
  4. Sava Grozdev and Deko Dekov, Mathematics with computer (Bulgarian), Mathematics and Informatics, 2013, vol. 56, no.2, 123-132.
    Enclosed File: 2013-2 answers.zip
  5. Sava Grozdev and Deko Dekov, Towards the first computer-generated encyclopedia (Bulgarian), Mathematics and Informatics, 2013, vol. 56, no.1, 49-59.
  6. Sava Grozdev and Deko Dekov, Computer-Generated Mathematics: Stevanovic Products, JCGM, vol.8, 2013.
    Enclosed File: 2013-1.zip, 79 KB.
  7. Sava Grozdev and Deko Dekov, Points on the Kiepert Hyperbola, JCGM, vol.8, 2013.
    Enclosed File: 2013-2.zip, 53 KB.
  8. Sava Grozdev and Deko Dekov, Points on the Steiner Circumellipse, JCGM, vol.8, 2013.
    Enclosed File: 2013-3.zip, 57 KB.

    2012
  1. Deko Dekov, A Numerical Method for Solving the Horizontal Resection Problem in Surveying, Journal of Geodetic Science, 2012, vol.2 no 1.
    DOI: 10.2478/v10156-011-0026-7
    Quoted in:
    M. Ligas, Simple solution to the three point resection problem, Journal of Surveying Engineering, 2013.
  2. Deko Dekov, A new simple root-finding method, JCGM, vol.7, 2012.
    Supplementary material: JCGM201201_Supplementary_Material.zip, 2.59 MB.
  3. Deko Dekov, The use of the brute-force method for finding the roots of an equation, JCGM, vol.7, 2012.
    Supplementary material: JCGM201202_Examples_brute-force.pdf, 10 KB.
  4. Deko Dekov, A new approach for finding the extrema of a function without use of derivatives, JCGM, vol.7, 2012.
    Supplementary material: JCGM201203_Supplementary_Material.zip, 54 KB.
  5. Deko Dekov, The use of the brute-force method for finding the extrema of a function, JCGM, vol.7, 2012.
    Supplementary material: JCGM201204_Examples_brute-force.pdf, 80 KB.
  6. Deko Dekov, A new simple numerical method for solving nonlinear systems, JCGM, vol.7, 2012.
    Supplementary material: JCGM201205_Example.pdf, 11 KB.
  7. Deko Dekov, The use of the brute-force method for solving nonlinear systems, JCGM, vol.7, 2012.
    Supplementary material: JCGM201206_Example_brute-force.pdf, 8 KB.
  8. Deko Dekov, A new approach to the approximation of a data set by a continuous function, JCGM, vol.7, 2012.
    Supplementary material: JCGM201207_Supplementray_Material.zip, 23 KB.
  9. Deko Dekov, The use of the brute-force method for finding the least squares approximation of a data set by a continuous function, JCGM, vol.7, 2012.
    Supplementary material: JCGM201208_Examples.pdf, 15 KB.
  10. Deko Dekov, A new simple numerical method for least squares approximation of a sample by a continuous probability distribution, JCGM, vol.7, 2012.
    Supplementary material: JCGM201209_Example.pdf, 9 KB.
  11. Deko Dekov, The least squares normal approximation to the binomial distribution, JCGM, vol.7, 2012.
    Supplementary material: JCGM201210_Binomial_Distribution.pdf, 6 KB.
  12. Deko Dekov, A new approach for solving 2 and 3-dimensional linear optimization problems, JCGM, vol.7, 2012.
    Supplementary material: JCGM201211_Supplementary_Material.zip, 12 KB.
  13. Deko Dekov, The use of the brute-force method for solving 2 and 3-dimensional linear optimization problems, JCGM, vol.7, 2012.
    Supplementary material: JCGM201212_Supplementary_Material.zip, 161 KB.
  14. Deko Dekov, The use of the brute-force method for solving the traveling salesman problem, JCGM, vol.7, 2012.
    Supplementary material: JCGM201213_Supplementary_Material.zip, 857 KB.
  15. Deko Dekov, The use of the brute-force method for solving the knapsack problem, JCGM, vol.7, 2012.
    Supplementary material: JCGM201214_Supplementary_Material.zip, 2.38 MB.
  16. Deko Dekov, The use of the brute-force method for solving the money-exchanging problem, JCGM, vol.7, 2012.
    Supplementary material: JCGM201215_Supplementary_Material.zip, 98 KB.
  17. Deko Dekov, The use of the brute-force method for solving the set covering problem, JCGM, vol.7, 2012.
    Supplementary material: JCGM201216_Supplementary_Material.zip, 49 KB.
  18. Deko Dekov, The least squares normal approximation to the Poisson distribution, JCGM, vol.7, 2012.
    Supplementary material: JCGM201217_Supplementary_Material.zip, 32 KB.
  19. Deko Dekov, A new approach to the Pareto interpolation, JCGM, vol.7, 2012.
    Supplementary material: JCGM201218_Supplementary_Material.pdf, 8 KB.
  20. Deko Dekov, Number of calculations in a numerical method, JCGM, vol.7, 2012.

    2011
  1. Deko Dekov, Towards the first computer-generated encyclopedia, JCGEG, vol.6, 2011, no 1,  PDF, 41 KB.

    2010
  1. Deko Dekov, Computer-Generated Mathematics: The Stanilov Triangle, JCGEG, vol.5, 2010, no 1,   PDF, 68 KB.
  2. Deko Dekov, Computer-Generated Mathematics: Construction of the Stanilov Triangle, JCGEG, vol.5, 2010, no 2,  PDF, 174 KB.

    2009
  1. Deko Dekov, Computer-Generated Mathematics: The Gergonne Point, JCGEG, vol.4, 2009, no 1,   PDF, 91 KB.
  2. Deko Dekov, Computer-Generated Mathematics: Eleven Circles passing through the Parry Point, JCGEG, vol.4, 2009, no 2,   PDF, 31 KB.
  3. Deko Dekov, Computer-Generated Mathematics: The Feuerbach Point, JCGEG, vol.4, 2009, no 3,   PDF, 37 KB.
  4. Deko Dekov, Computer-Generated Mathematics: The Kiepert-Parry Point, JCGEG, vol.4, 2009, no 4, PDF, 132 KB.
  5. Deko Dekov, Computer-Generated Mathematics: The Pohoata Point, JCGEG, vol.4, 2009, no 5, PDF, 54 KB.
  6. Deko Dekov, Computer-Generated Mathematics: The Schroder Point, JCGEG, vol.4, 2009, no 6, PDF, 65 KB.
  7. Deko Dekov, Computer-Generated Mathematics: The Bevan-Schroder Point, JCGEG, vol.4, 2009, no 7, PDF, 48 KB.
  8. Deko Dekov, Computer-Generated Mathematics: Construction of the Inner Apollonius Circle of the Mixtilinear Incircles, JCGEG, vol.4, 2009, no 8, PDF, 42 KB.

    2008
  1. Deko Dekov, First Isodynamic Point, JCGEG, vol.3, 2008, no.1,   PDF, 103 KB.
  2. Deko Dekov, Second Isodynamic Point, JCGEG, vol.3, 2008, no.2,  PDF, 67 KB.
  3. Deko Dekov, Kenmotu Points, JCGEG, vol.3, 2008, no.3,    PDF, 136 KB.
  4. Deko Dekov, Napoleon Points, JCGEG, vol.3, 2008, no.4,   PDF, 57 KB.
  5. Deko Dekov, Gallatly-Kiepert Triangles, JCGEG, vol.3, 2008, no.5,   PDF, 127 KB.
  6. Deko Dekov, Construction of the Outer Gallatly-Kiepert Triangle, JCGEG, vol.3, 2008, no.6,   PDF, 132 KB.
  7. Deko Dekov, Gallatly-Kiepert Points, JCGEG, vol.3, 2008, no.7,   PDF, 111 KB.
  8. Deko Dekov, Lemoine-Kiepert Triangles, JCGEG, vol.3, 2008, no.8,   PDF, 162 KB.
  9. Deko Dekov, Lemoine-Kiepert Points, JCGEG, vol.3, 2008, no.9,   PDF, 84 KB.
  10. Hristo Milev, New Constructions of the Outer Gallatly-Kiepert Triangle, JCGEG, vol.3, 2008, no.10,   PDF, 55 KB.
  11. Deko Dekov, Fermat Triangles, JCGEG, vol.3, 2008, no.11,   PDF, 89 KB.
  12. Deko Dekov, Intangents Triangle, JCGEG, vol.3, 2008, no.12,   PDF, 99 KB.

  13. Problems about Feuerbach Point
  14. Deko Dekov, The Feuerbach Point lies on the Circle through the Symmedian Point, the Internal Center of Similitude of the Incircle and the Circumcircle and the Grinberg Point, JCGEG, vol.3, 2008,   PDF, 27 KB.
  15. Deko Dekov, The Feuerbach Point is the Centroid of the Hatzipolakis Triangle of the Feuerbach Point, JCGEG, vol.3, 2008,   PDF, 27 KB.
  16. Deko Dekov, The Feuerbach Point is the Circumcenter of the Desmic Mate the Outer Yff Triangle, JCGEG, vol.3, 2008,   PDF, 30 KB.
  17. Deko Dekov, The Feuerbach Point is the Perspector of the Euler Triangle and the Triangle of the Incenters of the Corner Triangles of the Orthocenter, JCGEG, vol.3, 2008,   PDF, 31 KB.
  18. Deko Dekov, The Feuerbach Point lies on the Parry Circle of the Intouch Triangle, JCGEG, vol.3, 2008,   PDF, 27 KB.
  19. Deko Dekov, The Feuerbach Point lies on the Nine-Point Circle of the Outer Yff Triangle, JCGEG, vol.3, 2008,   PDF, 30 KB.
  20. Deko Dekov, The Feuerbach Point lies on the Cevian Circle of the Mittenpunkt, JCGEG, vol.3, 2008,   PDF, 28 KB.
  21. Deko Dekov, The Feuerbach Point lies on the Pedal Circle of the Mittenpunkt, JCGEG, vol.3, 2008,   PDF, 27 KB.
  22. Deko Dekov, The Feuerbach Point is the External Center of Similitude of the Circumcircle and the Outer Johnson-Yff Circle, JCGEG, vol.3, 2008,   PDF, 27 KB.
  23. Deko Dekov, The Feuerbach Point lies on the Cevian Circle of the Schiffler Point, JCGEG, vol.3, 2008,   PDF, 33 KB.
  24. Deko Dekov, The Feuerbach Point lies on the Pedal Circle of the Schiffler Point, JCGEG, vol.3, 2008,   PDF, 34 KB.
  25. Deko Dekov, The Feuerbach Point lies on the Cevian Circle of the Yff Center of Conguence, JCGEG, vol.3, 2008,   PDF, 27 KB.
  26. Deko Dekov, The Feuerbach Point lies on the Pedal Circle of the Gergonne Point, JCGEG, vol.3, 2008,   PDF, 26 KB.
  27. Deko Dekov, The Feuerbach Point lies on the Pedal Circle of the Nagel Point, JCGEG, vol.3, 2008,   PDF, 26 KB.
  28. Deko Dekov, The Feuerbach Point lies on the Pedal Circle of the Moses Point, JCGEG, vol.3, 2008,   PDF, 26 KB.
  29. Deko Dekov, The Feuerbach Point lies on the Pedal Circle of the Weill Point, JCGEG, vol.3, 2008,   PDF, 29 KB.
  30. Deko Dekov, The Feuerbach Point lies on the Pedal Circle of the Evans Perspector, JCGEG, vol.3, 2008,   PDF, 30 KB.
  31. Deko Dekov, The Feuerbach Point is the Inverse of the Incenter in the Nine-Point, Circle of the Fuhrmann Triangle, JCGEG, vol.3, 2008,   PDF, 27 KB.
  32. Deko Dekov, The Feuerbach Point is the Perspector of the Incentral Triangle and the Feuerbach Triangle, JCGEG, vol.3, 2008,   PDF, 27 KB.
  33. Deko Dekov, The Feuerbach Point is the Homothetic Center of the Johnson Triangle and the Outer Yff Triangle, JCGEG, vol.3, 2008,   PDF, 28 KB.
  34. Deko Dekov, The Feuerbach Point is the Perspector of the Euler Triangle and the Triangle of the Moses Points of the Corner Triangles of the Orthocenter, JCGEG, vol.3, 2008,   PDF, 29 KB.
  35. Deko Dekov, The Feuerbach Point is the Perspector of the Euler Triangle and the Triangle of the Bevan Points of the Corner Triangles of the Orthocenter, JCGEG, vol.3, 2008,   PDF, 29 KB.
  36. Deko Dekov, The Feuerbach Point is the Perspector of the Euler Triangle and the Triangle of the Internal Centers of Similitude of the Incircles and the Circumcircles of the Corner Triangles of the Orthocenter, JCGEG, vol.3, 2008,   PDF, 30 KB.
  37. Deko Dekov, The Feuerbach Point is the Perspector of the Euler Triangle and the Triangle of the External Centers of Similitude of the Incircles and the Circumcircles of the Corner Triangles of the Orthocenter, JCGEG, vol.3, 2008,   PDF, 30 KB.
  38. Deko Dekov, The Feuerbach Point is the Perspector of the Euler Triangle and the Triangle of the Weill Points of the Corner Triangles of the Orthocenter, JCGEG, vol.3, 2008,   PDF, 29 KB.
  39. Deko Dekov, The Feuerbach Point is the Perspector of the Euler Triangle and the Triangle of the Evans Perspectors of the Corner Triangles of the Orthocenter, JCGEG, vol.3, 2008,   PDF, 29 KB.
  40. Deko Dekov, The Feuerbach Point is the Perspector of the Euler Triangle and the Triangle of the Orthocenters of the Corner Triangles of the Gergonne Point, JCGEG, vol.3, 2008,   PDF, 29 KB.
  41. Deko Dekov, The Feuerbach Point is the Perspector of the Euler Triangle and the Triangle of the Orthocenters of the Corner Triangles of the Nagel Point, JCGEG, vol.3, 2008,   PDF, 29 KB.
  42. Deko Dekov, The Feuerbach Point is the Homothetic Center of the Inner Yff Triangle and the Triangle of the Centers of the Orthocentroidal Circles of the Triangulation Triangles of the Orthocenter, JCGEG, vol.3, 2008,   PDF, 31 KB.
  43. Deko Dekov, The Feuerbach Point is the Homothetic Center of the Outer Yff Triangle and the Triangle of the Circumcenters of the Triangulation Triangles of the Orthocenter, JCGEG, vol.3, 2008,   PDF, 30 KB.
  44. Deko Dekov, The Feuerbach Point is the Homothetic Center of the Outer Yff Triangle and the Triangle of the Circumcenters of the Anticevian Corner Triangles of the Centroid, JCGEG, vol.3, 2008,   PDF, 32 KB.
  45. Deko Dekov, The Feuerbach Point is the Homothetic Center of the Outer Yff Triangle and the Triangle of the Orthocenters of the Anticevian Corner Triangles of the Symmedian Point, JCGEG, vol.3, 2008,   PDF, 28 KB.
  46. Deko Dekov, The Feuerbach Point is the Homothetic Center of the Outer Yff Triangle and the Triangle of reflections of the Circumcenter in the vertices of the Medial Triangle, JCGEG, vol.3, 2008,   PDF, 29 KB.
  47. Deko Dekov, The Feuerbach Point is the Inverse of the Incenter in the Second Droz-Farny Circle of the Fuhrmann Triangle, JCGEG, vol.3, 2008,   PDF, 27 KB.
  48. Deko Dekov, The Feuerbach Point is the External Center of Similitude of the Circumcircle of the Johnson Triangle and the Circumcircle of the Outer Yff Triangle, JCGEG, vol.3, 2008,   PDF, 29 KB.

    2007
  1. Deko Dekov, The Ambiguities of the Natural Language, JCGEG, vol.2, 2007, no 1,   PDF, 46 KB.
  2. Deko Dekov, Triangulation Triangles, JCGEG, vol.2, 2007, no 2,   PDF, 175 KB.
  3. Deko Dekov, Stevanovic Triangles, JCGEG, vol.2, 2007, no 3,  PDF, 125 KB.
  4. Deko Dekov, Corner Triangles, JCGEG, vol.2, 2007, no 4,   PDF, 91 KB.
  5. Deko Dekov, Anticevian Corner Triangles,   JCGEG, vol.2, 2007, no 5, PDF, 101 KB.
  6. Deko Dekov, Incenter, JCGEG, vol.2, 2007, no 6,  PDF, 68 KB.
  7. Deko Dekov, Grinberg Triangles, JCGEG, vol.2, 2007, no 7,   PDF, 102 KB.
  8. Deko Dekov, Hatzipolakis Triangles, JCGEG, vol.2, 2007, no 8,   PDF, 46 KB.
  9. Deko Dekov, Malfatti Squares Triangle, JCGEG, vol.2, 2007, no 9,   PDF, 57 KB.
  10. Deko Dekov, Construction of the Malfatti Squares Triangle, JCGEG, vol.2, 2007, no 10,   PDF, 143 KB.
  11. Deko Dekov, Symmedian Point, JCGEG, vol.2, 2007, no 11,   PDF, 70 KB.
  12. Deko Dekov, Triangles of Reflections. Part 1, JCGEG, vol.2, 2007, no 12,   PDF, 74 KB.
  13. Deko Dekov, Triangles of Reflections. Part 2, JCGEG, vol.2, 2007, no 13,   PDF, 102 KB.
  14. Deko Dekov, Triangles of Reflections. Part 3, JCGEG, vol.2, 2007, no 14,   PDF, 146 KB.
  15. Deko Dekov, Euler Triangles, JCGEG, vol.2, 2007, no 15,   PDF, 139 KB.
  16. Deko Dekov, Orthocenter, JCGEG, vol.2, 2007, no 16,   PDF, 69 KB.
  17. Deko Dekov, Half-Cevian Triangles, JCGEG, vol.2, 2007, no 17,   PDF, 105 KB.
  18. Deko Dekov, Half-Anticevian Triangles, JCGEG, vol.2, 2007, no 18,   PDF, 63 KB.
  19. Deko Dekov, Centroid, JCGEG, vol.2, 2007, no 19,   PDF, 105 KB.
  20. Deko Dekov, Circumcenter, JCGEG, vol.2, 2007, no 20,   PDF, 129 KB.
  21. Deko Dekov, Nine-Point Center, JCGEG, vol.2, 2007, no 21,   PDF, 63 KB.
  22. Deko Dekov, Gergonne Point, JCGEG, vol.2, 2007, no 22,   PDF, 44 KB.
  23. Deko Dekov, Nagel Point, JCGEG, vol.2, 2007, no 23,   PDF, 46 KB.
  24. Deko Dekov, Mittenpunkt, JCGEG, vol.2, 2007, no 24,   PDF, 38 KB.
  25. Deko Dekov, Spieker Center, JCGEG, vol.2, 2007, no 25,   PDF, 46 KB.
  26. Deko Dekov, Grinberg Point, JCGEG, vol.2, 2007, no 26,   PDF, 85 KB.
  27. Deko Dekov, Gibert Point, IJCDEG, vol.2, 2007, no 27,   PDF, 97 KB.
  28. Deko Dekov, Side Triangles, JCGEG, vol.2, 2007, no 28,   PDF, 81 KB.
  29. Deko Dekov, Moses Point, JCGEG, vol.2, 2007, no 29,   PDF, 77 KB.
  30. Deko Dekov, Skordev Point, JCGEG, vol.2, 2007, no 30,   PDF, 94 KB.
  31. Deko Dekov, Inner Johnson Triangles, JCGEG, vol.2, 2007, no 31,   PDF, 133 KB.
  32. Deko Dekov, Apollonius Triangles, JCGEG, vol.2, 2007, no 32,   PDF, 166 KB.
  33. Deko Dekov, Moses Triangles, JCGEG, vol.2, 2007, no 33,   PDF, 220 KB.
  34. Deko Dekov, de Longchamps Point, JCGEG, vol.2, 2007, no 34,   PDF, 96 KB.
  35. Deko Dekov, Weill Point, JCGEG, vol.2, 2007, no 35,   PDF, 61 KB.
  36. Deko Dekov, Congruent Isoscelizers Point, JCGEG, vol.2, 2007, no 36,   PDF, 38 KB.
  37. Deko Dekov, Yff Center of Conguence, JCGEG, vol.2, 2007, no 37,   PDF, 51 KB.
  38. Deko Dekov, Equal Parallelians Point, JCGEG, vol.2, 2007, no 38,   PDF, 47 KB.
  39. Deko Dekov, Fuhrmann Center, JCGEG, vol.2, 2007, no 39,   PDF, 64 KB.
  40. Deko Dekov, Grebe Triangles, JCGEG, vol.2, 2007, no 40,   PDF, 225 KB.
  41. Deko Dekov, Equilateral Triangles, JCGEG, vol.2, 2007, no 41,   PDF, 90 KB.
  42. Deko Dekov, Outer Fermat Point, JCGEG, vol.2, 2007, no 42,   PDF, 62 KB.
  43. Deko Dekov, Inner Fermat Point, JCGEG, vol.2, 2007, no 43,   PDF, 38 KB.
  44. Deko Dekov, Outer Vecten Point, JCGEG, vol.2, 2007, no 44,   PDF, 66 KB.
  45. Deko Dekov, Inner Vecten Point, JCGEG, vol.2, 2007, no 45,   PDF, 41 KB.

    2006
  1. Deko Dekov, Apollonius Circle, JCGEG, vol 1, 2006, no 1,  PDF, 134 KB.
  2. Deko Dekov, Apollonius Problem, JCGEG, vol 1, 2006, no 2,   PDF, 139 KB.
  3. Deko Dekov, Compositions of Transformations in Triangle Geometry, JCGEG, vol 1, 2006, no 3,   PDF, 36 KB.

    Encyclopedia, first edition
  1. Deko Dekov, Computer-Generated Encyclopedia of Euclidean Geometry, 2006. (Russian edition, 2008).
    The first encyclopedia discovered by a computer.

    2003
  1. Deko Dekov, The use of the computer program "Abacus" for numerical integration of differential equations, Conference at the Union of Scientis in Bulgaria in Stara Zagora, 2003.
    The computer program "Abacus" finds an essential error in the 12th edition of the famous book by Piskunov.

    1991-2001 Selected papers
  1. Deko Dekov, Finite complete rewriting systems for semigroups and groups, Mathematika Balkanica. vol.15, 2001, no 1-2, pp.125-138.
  2. Deko Dekov, Deciding Embeddability of Partial Groupoids into Semigroups, Semigroup Forum (Springer), 1999, vol.58, 395-414.
    Impact Factor: 0.372.
    DOI: 10.1007/BF03325437
    Quoted in:
    1. L. Poinsot, G. Duchamp, C. Tollu, Partial monoids: associativity and confluence, 2010.
    2. S.H. Gensemer, Partial groupoid embeddings in semigroups, Associahedra, Tamari Lattices and Related Structures, 2012, Springer.
  3. Deko Dekov, Free products with amalgamation of monoids, Journal of Pure and Applied Algebra (Elsevier), 1998, vol.125, 129-133.
    Impact Factor: 0.567.
    DOI: 10.1016/S0022-4049(96)00145-4
    Quoted in
    1. M.V. Lawson, A.R. Wallis, A correspondence between a class of monoids and self-similar group actions II, International Journal of Algebra and Computation, 2015.
    2. J.M. Corson, L.L. Ross, Automata with Counters that Recognize Word Problems of Free Products, Journal of Foundations of Computer Science, 2015.
  4. Deko Dekov, The class of all embeddable semigroup amalgams is not finitely axiomatizable, Journal of Pure and Applied Algebra (Elsevier), 1998, vol.125, 135-139.
    Impact Factor: 0.567. DOI: 10.1016/S0022-4049(96)00146-6
    Quoted in:
    1. M.V. Sapir, Algorithmic problems for amalgams of finite semigroups, Journal of Algebra, 2000.
  5. Deko Dekov, Finite Complete Rewriting Systems for Groups, Communications in Algebra (Taylor & Francis), 1997, vol.25, 4023-4028.
    Impact Factor: 0.388.
    Quoted in:
    1. M. Brittenham, S. Hermiller, A uniform model for almost convexity and rewriting systems, Journal of Group Theory, 2014.
  6. Deko Dekov, Embeddability and the word problem, Journal of Symbolic Logic, 1995, vol.60, 1194-1198.
    Impact Factor: 0.541.
    DOI: 10.2307/2275882
    Quoted in:
    1. L. Poinsot, G. Duchamp, C. Tollu, Partial monoids: associativity and confluence, 2010.
    2. C.J. van Alten, Partial algebras and complexity of satisfiability and universal theory for distributive lattices, boolean algebras and Heyting algebras, Theoretical Computer Science, 2013.
    3. A. Mani, Constrained abstract representation problems in semigroups and partial groupoids, Glasnik matemati?ki, 2004.
  7. Deko Dekov, HNN Extensions of Semigroups, Semigroup Forum (Springer), 1994, vol.49, 83-87.
    Impact Factor: 0.372.
    Quoted in:
    1. J.M. Howie, Fundamentals of Semigroup Theory, Oxford University Press, Oxford, 1996.
    2. A. Yamamura, HNN extensions of inverse semigroups and applications, International Journal of Algebra and Computation, 1997.
    3. J. Fountain, J.E. Pin, P. Weil, Covers for monoids, Journal of Algebra, Volume 271, Issue 2, 15 January 2004, Pages 529?586.
    4. A. Yamamura, HNN extensions of semilattices, International Journal of Algebra and Computation, 1999.
    5. I.M. Araujo, Finite presentability of semigroup constructions, International Journal of Algebra and Computation, 2002.
    6. A Yamamura, Embedding theorems for HNN extensions of inverse semigroups, Journal of Pure and Applied Algebra, 2007.
  8. Deko Dekov, Free Products with Amalgamation of Semigroups, Semigroup Forum (Springer), 1993, vol.46, 54-61.
    Impact Factor: 0.372.
    Quoted in:
    1. J.M. Howie, Fundamentals of Semigroup Theory, Oxford University Press, Oxford, 1996.
    2. J.C. Birget, S.W. Margolis, J. Meakin, On the word problem for tensor products and amalgams of monoids, International Journal of Algebra and Comutation, 1999.
  9. Deko Dekov, The class of all S-pregroups is not finitely axiomatizable, Proceedings of the American Mathematical Society, 1992, vol.115, no.4, 895-897.
    Impact Factor: 0.627.
    Quoted in:
    1. S Lipschutz, On Pregroups and Generalizations, Proceedings of the 1996 Beijing International Conference, 1998, Springer Verlag.
  10. Deko Dekov, The Embedding of Semigroup Amalgams, Journal of Algebra (Elsevier), 1991, vol.141, 158-161.
    Impact Factor: 0.599.
    Quoted in:
    1. J.M. Howie, Fundamentals of Semigroup Theory, Oxford University Press, Oxford, 1996.
    2. E.S. Ljapin, A.E. Evseev, The Theory of Partial Algebraic Operations (Mathematics and Its Applications), 1997, Springer.
    3. J.C. Birget, S.W. Margolis, J. Meakin, On the word problem for tensor products and amalgams of monoids, International Journal of Algebra and Comutation, 1999.

    Ph.D.Thesis.
    Selected papers published from 1977 to 1990.

  1. Deko Dekov, Problemes universels relatifs aux classes polaires des relations, Serdica Mathematical Journal, vol.16, 1990, no. 1-2, 14-18.
  2. Deko Dekov, Existence de structures quotient, Serdica Mathematical Journal, vol.14, 1988, no. 4, 343-349.
  3. Deko Dekov, Problemes universels relatifs aux classes polaires, Serdica Mathematical Journal. vol.14, 1988, no.3, 223-233.
  4. Deko Dekov, Sur l?existence de structures quotient, Proceedings of the Bulgarian Academy of Sciences, vol.40, 1987, no. 7, 17-19.
  5. Deko Dekov, On the analog of Post theorem for poyadic monoids, Proc. Symp. n-ary Structures, Skopje, 1982, 171-173.
  6. Deko Dekov, Sur les structures algebriques des relations, Revue Roum. Math. Pures et Appl., vol.27, 1982, no 1, 15-24.
  7. Deko Dekov, Clases polaires quotient, Proceedings of the Bulgarian Academy of Sciences, vol.33, 1980, no 1, 11-14.
  8. Deko Dekov, Precategories quotient, Proceedings of the Bulgarian Academy of Sciences, vol.32, 1979, no. 12, 1619-1622.
  9. Deko Dekov, Projections des clases n-polaires, Proceedings of the Bulgarian Academy of Sciences, vol.30, 1977, no.8, 801-804.