International Journal of Computer Discovered Mathematics
Published by the Association for the Development of Education, Sofia, Bulgaria
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IJCDM is the first journal devoted to mathematics discovered by computers

Editors-in-Chief:
Sava Grozdev, Professor, DSc,
Association for the Development of Education, Sofia, Bulgaria
Academician of Bulgarian Academy of Sciences and Arts
e-mail: sava.grozdev@gmail.com

Hiroshi Okumura, Professor, Ph.D.
Maebashi Gunma, 371-0123, Japan
e-mail: hokmr@yandex.com

Veselin Nenkov, Professor, PhD
“Nikola Vaptsarov” Naval Academy – Varna, Bulgaria.
e-mail: vnenkov@mail.bg




Volume 6 (2021)

Abdilkadir Altintaş, Leonard Giugiuc. Location of Some Kimberling Centers Respect to Orthocentroidal Circle, pp. 1-5
Stanley Rabinowitz, Ercole Suppa. Computer Investigation of Properties of the Gergonne Point of a Triangle, pp.6-42
Supplementary Material - Gergonne Properties.zip
Stanley Rabinowitz, Ercole Suppa. Equilateral Triangles formed by the Centers of Erected Triangles, pp. 43-67.
Tran Quang Hung, Floor van Lamoen. Odom’s Triangle, pp 68-77.
Stanley Rabinowitz.Inequalities Involving Gergonne and Nagel Cevians, pp. 78-83.
Supplementary Material - Gergonne Nagel Cevians.zip
Thanh Tung Vu. Median-orthologic Simplexes, pp. 84-86
Nguyen Chuong Chi. A Purely Synthetic Proof of the Dao’s Eight Circles Theorem, pp. 87-91.
Abdilkadir Altintaş. Congruent Circles on Locus Problems, pp. 92-96
Stanley Rabinowitz. Linear Relationships Between Squares of Cevian Lengths, pp. 97-103.


Volume 5 (2020)

Stanley Rabinowitz, Ercole Suppa, Abdilkadir Altintaș, Floor van Lamoen. Rabinowitz Conics Associated with a Triangle, pp. 1-12.
Supplementary Material - Rabinowitz Conic.zip
Stanley Rabinowitz, Arrangement of Central Points on the Faces of a Tetrahedron, pp. 13–41.
Supplementary Material - Tetrahedron Faces.zip
Abdilkadir Altintaş, On Some Properties of Neuberg Cubic, pp. 42–49.
Dao Thanh Oai, Another Generalization of the Simson Line, pp. 50–52.
Sava Grozdev, Veselin Nenkov, Several properties of the inscribed conic sections and a method for proofs with complex numbers, pp. 53-70.
Abdilkadir Altıntaş, On Concurrent Euler Lines, pp. 71-75.


Volume 4 (2019)

Dao Thanh Oai, Some Problems Around the Configuration of Eight Circles, pp.1-12.
Dao Thanh Oai, Four Proofs of the Generalization of the Simson Line, pp.13-17.
Todor Zaharinov, Inscribed Conics and the Darboux Cubic, pp.18-26.
Todor Zaharinov, Inscribed triangles with centroid in a given point, pp.27-35.
Todor Zaharinov, Sums With Square Distances Between a Point and Vertexes, pp.36-47.
Stanley Rabinowitz, Relationships Between Six Circles, pp.48-53.
Supplementary Material - Relationships Between Six Circles.zip
Martin At. Stanev, Locus of the centroid of the equilateral triangle inscribed in an ellipse, pp.54-65.

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 Altintaş 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.
Dao Thanh Oai, A Problem On Three Homothetic Centers Associated With A Convex Hexagon, pp.143-144.
Tran Minh Ngoc, A Purely Synthetic Proof of Dao’s Theorem On A Conic And Its Applications, pp.145-152.

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