International Journal of Computer-Generated Mathematics



Contents


Volume 10 (2015)
  1. Sava Grozdev & Deko Dekov, The Simon and Newell prediction is realized by the "Discoverer",   PDF, 65 KB.

      Problems
      Stevanovic Circle
  1. Sava Grozdev & Deko Dekov, Five Problems about Circles Orthogonal to the Stevanovic circle.   PDF, 52 KB.
      Prasolov Products
  1. Sava Grozdev & Deko Dekov, Prasolv Cevian Products, Problem 97, published in the MathProblems, vol.4, no 2, 263-264. Solution to the Problem.   PDF, 97 KB.
    Enclosed File: Supplementary Material.   zip, 396 KB.
  2. Sava Grozdev & Deko Dekov, Prasolov Anticevian Products   PDF, 24 KB.
    Enclosed File: Solution to the problem.
  3. Sava Grozdev & Deko Dekov, Prasolov Pedal Products.   PDF, 24 KB.
    Enclosed File: Solution to the problem.
  4. Sava Grozdev & Deko Dekov, Prasolov Cirumcevian Products   PDF, 24 KB.
    Enclosed File: Solution to the problem.

Volume 9 (2014)
  1. Sava Grozdev & Deko Dekov, Learning through Discoveries,   PDF, 58 KB.
    Enclosed File: 2014-1.zip, 11 KB.
  2. Sava Grozdev & Deko Dekov, The Computer Program "Discoverer" and the Encyclopedia of Computer-Generated Mathematics" (Bulgarian),   PDF, 190 KB.
  3. Sava Grozdev & Deko Dekov, Investigation of circumconics by using the computer program "Discoverer" (Bulgarian),   PDF, 182 KB.
    Enclosed File: 2014-3.zip, 10 KB.
  4. Sava Grozdev & Deko Dekov, A New Relation between the Steiner Circumellipse and the Kiepert Hyperbola,   PDF, 42 KB.
  5. Sava Grozdev & Deko Dekov, The computer program "Discoverer" as a tool of mathematical investigation,   PDF, 69 KB.
    Enclosed File: 2014-5.zip, 14 KB.
  6. Sava Grozdev & Deko Dekov, Supplementary Material to the Note by Grozdev and Dekov, published in Mathematical Gazette in November 2014,   PDF, 68 KB.
    Enclosed File: 2014-6.zip, 45 KB.
      Problems
      Lester Circle
  1. Sava Grozdev & Deko Dekov, The Centroid of the Triangle of Reflections of the Kiepert Center in the Sidelines of Triangle ABC lies on the Lester circle   PDF, 22 KB.
  2. Sava Grozdev & 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   PDF, 23 KB.
  3. Sava Grozdev & 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   PDF, 23 KB.
  4. Sava Grozdev & Deko Dekov, The Lester Circle is orthogonal to the Orthocentroidal Circle of the Outer Fermat Triangle of the Johnson Triangle   PDF, 23 KB.
  5. Sava Grozdev & Deko Dekov, The Lester Circle is orthogonal to the Orthocentroidal Circle of the Inner Fermat Triangle of the Johnson Triangle   PDF, 25 KB.
  6. Sava Grozdev & 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   PDF, 28 KB.
  7. Sava Grozdev & 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   PDF, 22 KB.
  8. Sava Grozdev & Deko Dekov, The Lester Circle is orthogonal to the Brocard Circle of the Fourth Brocard Triangle   PDF, 18 KB.
  9. Sava Grozdev & Deko Dekov, The Lester Circle is orthogonal to the Brocard Circle of the Second Brocard Triangle of the Fourth Brocard Triangle   PDF, 20 KB.
  10. Sava Grozdev & 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   PDF, 22 KB.

Volume 8 (2013)
  1. Sava Grozdev & Deko Dekov, Computer-Generated Mathematics: Stevanovic Products,   PDF, 49 KB.
    Enclosed File: 2013-1.zip, 79 KB.
  2. Sava Grozdev & Deko Dekov, Points on the Kiepert Hyperbola,   PDF, 27 KB.
    Enclosed File: 2013-2.zip, 53 KB.
  3. Sava Grozdev & Deko Dekov, Points on the Steiner Circumellipse,   PDF, 25 KB.
    Enclosed File: 2013-3.zip, 57 KB.
      Volume 8 (2013) All Articles, PDF, 274 KB.


Volume 7 (2012)

      Teacher's Corner
  1. Deko Dekov, A new simple root-finding method,   PDF, 10 KB.
    Supplementary material: JCGM201201_Supplementary_Material.zip, 2.59 MB.
  2. Deko Dekov, The use of the brute-force method for finding the roots of an equation,   PDF, 39 KB.
    Supplementary material: JCGM201202_Examples_brute-force.pdf, 10 KB.
  3. Deko Dekov, A new approach for finding the extrema of a function without use of derivatives,   PDF, 34 KB.
    Supplementary material: JCGM201203_Supplementary_Material.zip, 54 KB.
  4. Deko Dekov, The use of the brute-force method for finding the extrema of a function,   PDF, 19 KB.
    Supplementary material: JCGM201204_Examples_brute-force.pdf, 80 KB.
  5. Deko Dekov, A new simple numerical method for solving nonlinear systems,   PDF, 37 KB.
    Supplementary material: JCGM201205_Example.pdf, 11 KB.
  6. Deko Dekov, The use of the brute-force method for solving nonlinear systems,   PDF, 37 KB.
    Supplementary material: JCGM201206_Example_brute-force.pdf, 8 KB.
  7. Deko Dekov, A new approach to the approximation of a data set by a continuous function,   PDF, 56 KB.
    Supplementary material: JCGM201207_Supplementray_Material.zip, 23 KB.
  8. Deko Dekov, The use of the brute-force method for finding the least squares approximation of a data set by a continuous function,   PDF, 60 KB.
    Supplementary material: JCGM201208_Examples.pdf, 15 KB.
  9. Deko Dekov, A new simple numerical method for least squares approximation of a sample by a continuous probability distribution,   PDF, 34 KB.
    Supplementary material: JCGM201209_Example.pdf, 9 KB.
  10. Deko Dekov, The least squares normal approximation to the binomial distribution,   PDF, 28 KB.
    Supplementary material: JCGM201210_Binomial_Distribution.pdf, 6 KB.
  11. Deko Dekov, A new approach for solving 2 and 3-dimensional linear optimization problems,   PDF, 30 KB.
    Supplementary material: JCGM201211_Supplementary_Material.zip, 12 KB.
  12. Deko Dekov, The use of the brute-force method for solving 2 and 3-dimensional linear optimization problems,   PDF, 29 KB.
    Supplementary material: JCGM201212_Supplementary_Material.zip, 161 KB.
  13. Deko Dekov, The use of the brute-force method for solving the traveling salesman problem,   PDF, 46 KB.
    Supplementary material: JCGM201213_Supplementary_Material.zip, 857 KB.
  14. Deko Dekov, The use of the brute-force method for solving the knapsack problem,   PDF, 20 KB.
    Supplementary material: JCGM201214_Supplementary_Material.zip, 2.38 MB.
  15. Deko Dekov, The use of the brute-force method for solving the money-exchanging problem,   PDF, 18 KB.
    Supplementary material: JCGM201215_Supplementary_Material.zip, 98 KB.
  16. Deko Dekov, The use of the brute-force method for solving the set covering problem,   PDF, 63 KB.
    Supplementary material: JCGM201216_Supplementary_Material.zip, 49 KB.
  17. Deko Dekov, The least squares normal approximation to the Poisson distribution,   PDF, 50 KB.
    Supplementary material: JCGM201217_Supplementary_Material.zip, 32 KB.
  18. Deko Dekov, A new approach to the Pareto interpolation,   PDF, 29 KB.
    Supplementary material: JCGM201218_Supplementary_Material.pdf, 8 KB.
  19. Deko Dekov, Number of calculations in a numerical method,   PDF, 61 KB.
      Volume 7 (2012) All Articles, PDF, 6.88 MB.

Volume 6 (2011)
  1. Deko Dekov, Towards the first computer-generated encyclopedia ,   PDF, 41 KB.

Volume 5 (2010)

  1. Deko Dekov, Computer-Generated Mathematics: The Stanilov Triangle,   PDF, 68 KB.
  2. Deko Dekov, Computer-Generated Mathematics: Construction of the Stanilov Triangle,   PDF, 174 KB.
      Volume 5 (2010) All Articles, PDF, 192 KB.


Volume 4 (2009)

  1. Deko Dekov, Computer-Generated Mathematics: The Gergonne Point,   PDF, 91 KB.
  2. Deko Dekov, Computer-Generated Mathematics: Eleven Circles passing through the Parry Point,   PDF, 31 KB.
  3. Deko Dekov, Computer-Generated Mathematics: The Feuerbach Point,   PDF, 37 KB.
  4. Deko Dekov, Computer-Generated Mathematics: The Kiepert-Parry Point, PDF, 132 KB.
  5. Deko Dekov, Computer-Generated Mathematics: The Pohoata Point, PDF, 54 KB.
  6. Deko Dekov, Computer-Generated Mathematics: The Schroder Point, PDF, 65 KB.
  7. Deko Dekov, Computer-Generated Mathematics: The Bevan-Schroder Point, PDF, 48 KB.
  8. Deko Dekov, Computer-Generated Mathematics: Construction of the Inner Apollonius Circle of the Mixtilinear Incircles, PDF, 42 KB.

      Volume 4 (2009) All Articles, PDF, 437 KB.


Volume 3 (2008) All Articles

  1. Deko Dekov, First Isodynamic Point   PDF, 103 KB.
  2. Deko Dekov, Second Isodynamic Point   PDF, 67 KB.
  3. Deko Dekov, Kenmotu Points   PDF, 136 KB.
  4. Deko Dekov, Napoleon Points   PDF, 57 KB.
  5. Deko Dekov, Gallatly-Kiepert Triangles   PDF, 127 KB.
  6. Deko Dekov, Construction of the Outer Gallatly-Kiepert Triangle   PDF, 132 KB.
  7. Deko Dekov, Gallatly-Kiepert Points   PDF, 111 KB.
  8. Deko Dekov, Lemoine-Kiepert Triangles   PDF, 162 KB.
  9. Deko Dekov, Lemoine-Kiepert Points   PDF, 84 KB.
  10. Hristo Milev, New Constructions of the Outer Gallatly-Kiepert Triangle   PDF, 55 KB.
  11. Deko Dekov, Fermat Triangles   PDF, 89 KB.
  12. Deko Dekov, Intangents Triangle   PDF, 99 KB.

      Problems
      Feuerbach Point

  1. 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   PDF, 27 KB.
  2. Deko Dekov, The Feuerbach Point is the Centroid of the Hatzipolakis Triangle of the Feuerbach Point   PDF, 27 KB.
  3. Deko Dekov, The Feuerbach Point is the Circumcenter of the Desmic Mate the Outer Yff Triangle   PDF, 30 KB.
  4. 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   PDF, 31 KB.
  5. Deko Dekov, The Feuerbach Point lies on the Parry Circle of the Intouch Triangle   PDF, 27 KB.
  6. Deko Dekov, The Feuerbach Point lies on the Nine-Point Circle of the Outer Yff Triangle   PDF, 30 KB.
  7. Deko Dekov, The Feuerbach Point lies on the Cevian Circle of the Mittenpunkt   PDF, 28 KB.
  8. Deko Dekov, The Feuerbach Point lies on the Pedal Circle of the Mittenpunkt   PDF, 27 KB.
  9. Deko Dekov, The Feuerbach Point is the External Center of Similitude of the Circumcircle and the Outer Johnson-Yff Circle   PDF, 27 KB.
  10. Deko Dekov, The Feuerbach Point lies on the Cevian Circle of the Schiffler Point   PDF, 33 KB.
  11. Deko Dekov, The Feuerbach Point lies on the Pedal Circle of the Schiffler Point   PDF, 34 KB.
  12. Deko Dekov, The Feuerbach Point lies on the Cevian Circle of the Yff Center of Conguence   PDF, 27 KB.
  13. Deko Dekov, The Feuerbach Point lies on the Pedal Circle of the Gergonne Point   PDF, 26 KB.
  14. Deko Dekov, The Feuerbach Point lies on the Pedal Circle of the Nagel Point   PDF, 26 KB.
  15. Deko Dekov, The Feuerbach Point lies on the Pedal Circle of the Moses Point   PDF, 26 KB.
  16. Deko Dekov, The Feuerbach Point lies on the Pedal Circle of the Weill Point   PDF, 29 KB.
  17. Deko Dekov, The Feuerbach Point lies on the Pedal Circle of the Evans Perspector   PDF, 30 KB.
  18. Deko Dekov, The Feuerbach Point is the Inverse of the Incenter in the Nine-Point Circle of the Fuhrmann Triangle   PDF, 27 KB.
  19. Deko Dekov, The Feuerbach Point is the Perspector of the Incentral Triangle and the Feuerbach Triangle   PDF, 27 KB.
  20. Deko Dekov, The Feuerbach Point is the Homothetic Center of the Johnson Triangle and the Outer Yff Triangle   PDF, 28 KB.
  21. 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   PDF, 29 KB.
  22. 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   PDF, 29 KB.
  23. 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   PDF, 30 KB.
  24. 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   PDF, 30 KB.
  25. 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   PDF, 29 KB.
  26. 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   PDF, 29 KB.
  27. 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   PDF, 29 KB.
  28. 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   PDF, 29 KB.
  29. 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   PDF, 31 KB.
  30. 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   PDF, 30 KB.
  31. 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   PDF, 32 KB.
  32. 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   PDF, 28 KB.
  33. 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   PDF, 29 KB.
  34. Deko Dekov, The Feuerbach Point is the Inverse of the Incenter in the Second Droz-Farny Circle of the Fuhrmann Triangle   PDF, 27 KB.
  35. 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   PDF, 29 KB.

      Letters to the Editor
      Dimiter Skordev, Letter to the Editor  PDF, 20 KB.

      Volume 3 (2008) All Articles, PDF, 798 KB.
      Volume 3 (2008) All Problems for school students and teachers, PDF, 715 KB.

Volume 2 (2007)

  1. Deko Dekov, The Ambiguities of the Natural Language   PDF, 46 KB.
  2. Deko Dekov, Triangulation Triangles   PDF, 175 KB.
  3. Deko Dekov, Stevanovic Triangles  PDF, 125 KB.
  4. Deko Dekov, Corner Triangles   PDF, 91 KB.
  5. Deko Dekov, Anticevian Corner Triangles   PDF, 101 KB.
  6. Deko Dekov, Incenter   PDF, 68 KB.
  7. Deko Dekov, Grinberg Triangles   PDF, 102 KB.
  8. Deko Dekov, Hatzipolakis Triangles   PDF, 46 KB.
  9. Deko Dekov, Malfatti Squares Triangle   PDF, 57 KB.
  10. Deko Dekov, Construction of the Malfatti Squares Triangle   PDF, 143 KB.
  11. Deko Dekov, Symmedian Point   PDF, 70 KB.
  12. Deko Dekov, Triangles of Reflections. Part 1   PDF, 74 KB.
  13. Deko Dekov, Triangles of Reflections. Part 2   PDF, 102 KB.
  14. Deko Dekov, Triangles of Reflections. Part 3   PDF, 146 KB.
  15. Deko Dekov, Euler Triangles   PDF, 139 KB.
  16. Deko Dekov, Orthocenter   PDF, 69 KB.
  17. Deko Dekov, Half-Cevian Triangles   PDF, 105 KB.
  18. Deko Dekov, Half-Anticevian Triangles   PDF, 63 KB.
  19. Deko Dekov, Centroid   PDF, 105 KB.
  20. Deko Dekov, Circumcenter   PDF, 129 KB.
  21. Deko Dekov, Nine-Point Center   PDF, 63 KB.
  22. Deko Dekov, Gergonne Point   PDF, 44 KB.
  23. Deko Dekov, Nagel Point   PDF, 46 KB.
  24. Deko Dekov, Mittenpunkt   PDF, 38 KB.
  25. Deko Dekov, Spieker Center   PDF, 46 KB.
  26. Deko Dekov, Grinberg Point   PDF, 85 KB.
  27. Deko Dekov, Gibert Point   PDF, 97 KB.
  28. Deko Dekov, Side Triangles   PDF, 81 KB.
  29. Deko Dekov, Moses Point   PDF, 77 KB.
  30. Deko Dekov, Skordev Point   PDF, 94 KB.
  31. Deko Dekov, Inner Johnson Triangles   PDF, 133 KB.
  32. Deko Dekov, Apollonius Triangles   PDF, 166 KB.
  33. Deko Dekov, Moses Triangles   PDF, 220 KB.
  34. Deko Dekov, de Longchamps Point   PDF, 96 KB.
  35. Deko Dekov, Weill Point   PDF, 61 KB.
  36. Deko Dekov, Congruent Isoscelizers Point   PDF, 38 KB.
  37. Deko Dekov, Yff Center of Conguence   PDF, 51 KB.
  38. Deko Dekov, Equal Parallelians Point   PDF, 47 KB.
  39. Deko Dekov, Fuhrmann Center   PDF, 64 KB.
  40. Deko Dekov, Grebe Triangles   PDF, 225 KB.
  41. Deko Dekov, Equilateral Triangles   PDF, 90 KB.
  42. Deko Dekov, Outer Fermat Point   PDF, 62 KB.
  43. Deko Dekov, Inner Fermat Point   PDF, 38 KB.
  44. Deko Dekov, Outer Vecten Point   PDF, 66 KB.
  45. Deko Dekov, Inner Vecten Point   PDF, 41 KB.
      Volume 2 (2007) All Articles, PDF, 2.61 MB.

Volume 1 (2006)

  1. Deko Dekov, Apollonius Circle,   PDF, 134 KB.
  2. Deko Dekov, Apollonius Problem   PDF, 139 KB.
  3. Deko Dekov, Compositions of Transformations in Triangle Geometry   PDF, 36 KB.

      Volume 1 (2006) All Articles, PDF, 240 KB.