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International Journal of Computer Discovered Mathematics


International Journal of Computer Discovered Mathematics
Published by the VUZF University of Finance, Business and Entrepreneurship, Sofia, Bulgaria


About this Journal   |   Editorial Board   |   Instructions for Authors   |   Review Process   |   Links
The first journal devoted to mathematics discovered by computers
ISSN 2367-7775

Editors-in-Chief:
Sava Grozdev, Professor, DSc,
VUZF University of Finance, Business and Entrepreneurship, Sofia, Bulgaria
e-mail: [email protected]
Hiroshi Okumura, Professor, Ph.D.
Maebashi Gunma, 371-0123, Japan
e-mail: [email protected]
Deko Dekov, Assoc. Professor, PhD,
Zahari Knjazheski 81, 6000 Stara Zagora, Bulgaria
e-mail: [email protected]


Volume 3 (2018)

Nguyen Chuong Chi, A Proof of Dao’s Generalization of the Sawayama Lemma, pp.1-4. Nguyen Ngoc Giang, Creation of new theorems from flanks, pp.5-36. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Triangles Homothetic with the Extouch Triangle, pp.37-43. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Intangents Triangle, pp.44-48. Nguyen Ngoc Giang, A New Proof and Some Generalizations of the Bottema Theorem, pp.49-54. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Problems for Students about Intouch Triangle, pp.55-61. Abdilkadir Altintas and Ercole Suppa, Extended Soddy Configurations, pp.62-68. Sava Grozdev, Hiroshi Okumura and Deko Dekov, A New Proof of the Feuerbach theorem, pp.69-70. Sava Grozdev, Hiroshi Okumura and Deko Dekov, The Paskalev-Tchobanov Distance Formula and Some of its Applications, pp.71-73. Nguyen Ngoc Giang, Using the affine and projective methods to prove and extend Dao's theorem, pp.74-81. Nguyen Ngoc Giang and Le Viet An, An Extension of the Steiner Line Theorem and Application, pp.82-87. Dao Thanh Oai, Some Equilateral Triangles Perspective to the Reference Triangle ABC, pp.88-96. Nguyen Ngoc Giang and Le Viet An, An Another Proof of Dao’s Theorem and its Converses, pp.97-103. Dao Thanh Oai, An Ellipse Through 12 Points and Golden Triangle, pp.104-109. Nguyen Ngoc Giang and Le Viet An, Three extentions of Kosnita's theorem, pp.110-117. Glenn C. Rhoads, Planar Tilings by Substitution Polykleins, pp.118-135. Nguyen Ngoc Giang and Dao Thanh Oai, Six Conics Theorem, pp.136-139. Sava Grozdev, Hiroshi Okumura and Deko Dekov, A Note on the Tangential Triangle, pp.140-142.
Volume 2 (2017)

Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Euler Anticevian Triangles, pp.1-29.
Supplementary Material. Euler Anticevian Triangles.zip Sava Grozdev, Hiroshi Okumura and Deko Dekov, A Note on the Leversha Point, pp.30-34. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Incentral Triangle, pp.35-45.
Supplementary Material. Incentral triangle.zip Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Triangles homothetic with the Orthic triangle, pp.46-54. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Half-Anticevian Triangle of the Incenter, pp.55-71.
Supplementary Material - Half-Anticevian Triangle of the Incenter.zip Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Excenters-Incenter Reflections Triangle, pp.72-80.
Supplementary Material - Excenters-Incenter Reflections Triangle Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Problems about Points on the Euler line, pp.81-85.
Supplementary Material - Points on the Euler line Sava Grozdev, Hiroshi Okumura and Deko Dekov, Triangles Homothetic with Triangle ABC, pp.86-89 Sava Grozdev, Hiroshi Okumura and Deko Dekov, Triangles Homothetic with Triangle ABC. Part 2, pp.90-96
Supplementary Material - HT2.zip Sava Grozdev, Hiroshi Okumura and Deko Dekov, Triangles Homothetic with Triangle ABC. Part 3, pp.97-105.
Supplementary Material - HT3.zip Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Triangles Associated with Triangulation Triangles, pp.106-110.
Supplementary Material - Triangulation Triangles.zip Sava Grozdev, Hiroshi Okumura and Deko Dekov, Leversha Triangles and Leversha Points, pp.111-116.
Supplementary Material - Leversha Points.zip Sava Grozdev, Hiroshi Okumura and Deko Dekov, Notable Circles, pp.117-134.
Supplementary Material - Notable Circles.zip Nguyen Ngoc Giang, Some properties of triangles or rectangles attached to sides of a triangle, pp.135-140. Nguyen Trung Kien, An Iterative Geometrical Approach for a Problem in the International Mathematical Olympiad 2017, pp.141-145. Nguyen Ngoc Giang, Flanks, new flanks, generalized flanks and their properties, pp.146-184. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Problems for Students about Excentral Triangle, pp.185-200.
Supplementary material - Excentral triangle Nguyen Ngoc Giang, The relation between three concurrent diagonals of a hexagon and rectangles attached to sides of a triangle, pp.201-207.

Volume 1 Number 1 (2016)

S. Grozdev and D. Dekov, Computer Discovered Mathematics: Euler Triangles, pp.1-10.
Supplementary Material: Euler_Triangles.zip S. Grozdev and D. Dekov, Computer Discovered Mathematics: Circles Containing the Parry Point, pp.11-14. S. Grozdev and D. Dekov, Computer Discovered Mathematics: Lester Circles, pp.15-25. S. Grozdev and D. Dekov, Computer Discovered Mathematics: The Incenter, pp.26-35. Francisco Javier García Capitán, Posing and Solving Problems with Barycentric Coordinates, pp.36-44. René Grothmann, The Geometry Program C.a.R., pp.45-61.
Supplementary Material: Grothmann-CaR.zip René Grothmann, Discover Euler Math Toolbox, pp.62-75. Dao Thanh Oai, A generalization of the Zeeman-Gossard perspector theorem, pp.76-79. S. Grozdev and D. Dekov, Computer Discovered Mathematics: Dividing Directed Segments, pp.80-88.
Supplementary Material: division.zip S. Grozdev and D. Dekov, Mathematics Discovered by Computers: Incenters of Triangles, pp.89-92. S. Grozdev and D. Dekov, Computer Discovered Mathematics: Circles through the Feuerbach Point, pp.93-96.

Volume 1 Number 2 (2016)

S. Grozdev and D. Dekov, Computer Discovered Mathematics: Half-Cevian Triangles, pp.1-8.
Supplementary Material: Half-Cevian-Triangles.zip S. Grozdev and D. Dekov, Computer Discovered Mathematics: The Mittenpunkt, pp.9-13 S. Grozdev and D. Dekov, Computer Discovered Mathematics: Gibert Triangles, pp.14-20.
Supplementary Material: Gibert-Triangles.zip Dao Thanh Oai, The Nine Circles Problem and the Sixteen Points Circle, pp.21-24. Ngo Quang Duong, Generalizations of some triangle geometry results associated with cubics, pp.25-39. Ngo Quang Duong, Some problems around the Dao's theorem on six circumcenters associated with a cyclic hexagon configuration, pp.40-47. S. Grozdev and D. Dekov, Computer Discovered Mathematics: Fuhrmann Triangles, pp.48-58. S. Grozdev and D. Dekov, Computer Discovered Mathematics: Harmonic Conjugates, pp.59-63.
Supplementary Material: Harmonic Conjugates.zip S. Grozdev and D. Dekov, Computer Discovered Mathematics: Inversion of Triangle ABC with respect to the Incircle, pp.64-74.
Supplementary Material: Inversion of ABC wrt the Incircle.zip S. Grozdev and D. Dekov, Barycentric Coordinates: Formula Sheet, pp.75-82. Mamut Sirazitdinov, Proofs of computer discovered theorems about Yiu Transform, pp.83-89. S. Grozdev and D. Dekov, Computer Discovered Mathematics: A Note on the Johnson Circles, pp.90-95.
Supplementary Material: Johnson Circles.zip S. Grozdev and D. Dekov, Computer Discovered Mathematics: Yff Triangles, pp.96-103.
Supplementary Material: Yff Triangles.zip S. Grozdev and D. Dekov, Computer Discovered Mathematics: A Note on the Gossard Triangles, pp.104-108.
Supplementary Material: Gossard Triangle.zip

Volume 1 Number 3 (2016)

Frank M. Jackson and Stalislav Takhaev, Heronian Triangles of Class J: Congruent Incircles Cevian Perspective, pp.1-8. Nguyen Trung Kien and Tran Thu Le, Problem of Twelve Circles, pp.9-12. Dao Thanh Oai, Generalizations of some famous classical Euclidean geometry theorems, pp.12-20. Nguyen Ngoc Giang, The extension from a circle to a conic having center: The creative method of new theorems, pp.21-32. Dao Thanh Oai, A Generalization of Sawayama and Thébault's Theorem, pp.33-35. Dao Thanh Oai, Another Generalization of the Sawayama and Thébault's Theorem, pp.36-39. Sava Grozdev and Deko Dekov, Computer Discovered Mathematics: Stanilov Triangles, pp.40-44.
Supplementary Material: Stanilov Triangles.zip Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: A Note on the Miquel Points, pp.45-49. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Orthopoles, pp.50-56 Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Haimov Triangle of the Incenter, pp.57-61

Volume 1 Number 4 (2016)

Alexander Skutin, Ways of Predicting Mathematics, pp.1-9. Alexander Skutin, Deformation of point on circle, pp.10-13. Sava Grozdev, Hiroshi Okumura and Deko Dekov, Computer Discovered Mathematics: Grebe Triangles, pp.14-23.
Supplementary Material Grebe triangles.zip.

Volume 0 (2015)

Welcome!, p.1. Advertisements, p.2. S. Grozdev and D. Dekov, A Survey of Mathematics Discovered by Computers, pp.3-20. Paul Yiu, Iterations of sum of powers of digits, pp.21-26. Paul Yiu, Collinearity of the reflections of the intercepts of a line in the angle bisectors of a triangle pp.27-31. Francisco Javier García Capitán, Barycentric Coordinates, pp.32-48. A. G. Koryanov, The computer program "Inverse Matrices", pp.49-53. Stefka Karakoleva, Make your first steps in the high-quality typesetting system LaTeX, pp.54-59. S. Grozdev and D. Dekov, Computer Discovered Mathematics: Hexyl-Anticevian Triangles, pp.60-69. S. Grozdev and D. Dekov, Computer Discovered Mathematics: Haimov Triangles, pp.70-79.
Supplementary Material: Haimov_Points.zip