International Journal of Computer Discovered Mathematics
Published by the Association for the Development of Education, Sofia, Bulgaria
About this Journal   |   Editorial Board   |   Instructions for Authors   |   Review Process   |   Links
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 11 (2026)

Stanley Rabinowitz, Francisco Javier Garcia Capitan. Some Geometric Properties of the Yff Points of a Triangle, pp. 1-19
Benjamin Cha, Dan Ismailescu, Yeon Woo (Amelia) Tae. Conics Determined by Triangle Centers in Ceva Configurations, pp. 20-36
Stanley Rabinowitz. Central Discs and Their Centers, pp. 37-59
Supplementary material


Volume 10 (2025)

Benjamin Warren. The Midpoint of the Incenter and the Circumcenter is the Center of a Conic Section, pp. 1-3
Benjamin Warren. The Incenter as a Homothetic Center of the Intouch Triangle, pp. 4-7
Benjamin Warren. The Centroid of a Triangle Lies on a Twin Circle, pp. 8-10
Benjamin Warren. Generalization of the Incenter, Gergonne Point, and X(104), pp. 11-14
Benjamin Warren. Generalizations of the Circumcenter, the Exeter Point, X(25), and the Euler Line, pp. 15-17
Benjamin Warren. The Diagonal Intersection of a Complete Tangential Quadrilateral Lies on the Radical Line of Two Certain Circles, pp. 18-19
Benjamin Warren. A Set of Coaxal Circles in Reference to a Triangle, pp. 20-28
Benjamin Warren. A Point in Reference to the Intouch Triangle, pp. 29-35
Benjamin Warren. Generalization of the Fuhrmann Circle, pp. 36-40
Benjamin Warren. Coaxal Circles that Arise from the Pedal and Circumcevian Triangles, pp. 41-44
Benjamin Warren. Generalization of the Perspectrix Formed by a Triangle and a Cevian Triangle, pp. 45-47
Benjamin Warren. The Bottema Point Lies on an Eight Point Circle, pp. 48-51
Benjamin Warren. The Centroid Lies on Another Circle, pp. 52-54
Benjamin Warren. A Line Associated With a Conic Section Passing Through the Sides of a Triangle, pp. 55-64
Benjamin Warren. Simple Generalization of Musselman’s Theorem, pp. 65-68. 05.02
Benjamin Warren. Generalization of the Isoperimetric Point and the Equal Detour Point, pp. 69-70
Benjamin Warren. A Circle Centered at the Nine Point Center, pp. 71-73
Benjamin Warren. Three Points on the Orthocentroidal Circle, pp. 74-76
Benjamin Warren. Coaxal Circles in the Context of the Circumcevian Triangle, pp. 77-80
Benjamin Warren. Two Circles That Concur on the Euler Line, pp. 81-85
Benjamin Warren. Three Concurrent Circles in the Context of a Certain Type of Hexagon, pp. 86-90
Stanley Rabinowitz, Ercole Suppa. More Relationships between a Central Quadrilateral and its Reference Quadrilateral, pp. 91-123
Supplementary material - proofs
Dan Ismailescu, Yunkyu James Lee, A Class of Special Tetrahedra, pp. 124-126
Ambuj Kumar, Bikash Kanti Sarkar. A new family of numbers to generate potentially infinite number of approximations of π, e and their combinations, pp. 127-138
Supplementary material - Lists of formulas
Benjamin Warren. Coaxal Circles and Triangles Homothetic to the Intouch Triangle about the Incenter, pp. 137-141
Benjamin Warren. A Circle of Triangle Centroids, pp. 142-148
Benjamin Warren. Three Euler Lines that Concur in X(20147) and a Circle Centered at the Midpoint of the Circumcenter and Nine-Point Center, pp. 149-152
Benjamin Warren. Euler Lines, Napoleon Points, and Equilateral Triangles, pp. 153-160
Benjamin Warren. Coaxal Circles in the Context of the Orthic and Circumcevian Triangles, pp. 161-163
Benjamin Warren. Three More Points on the Nine-Point Circle, pp. 164-166
Benjamin Warren. The Circle Centered at the Circumcenter Passing Through the Centroid, pp. 167-168
Benjamin Warren. A New Generalization of the Triangle Centroid, pp. 169-173
Benjamin Warren. A Result Related to a Generalization of the Triangle Centroid, pp. 174-179
Benjamin Warren. Euler Lines that Concur at a Point on a Circle, pp. 180-184
Benjamin Warren. Another Nine-Point Circle, pp. 185-187
Benjamin Warren. On a Certain Circle Which is Concentric with the Second Lozada Circle, pp. 188-192
Benjamin Warren. Tangents and a Parabola, pp. 193-194
Benjamin Warren. Coaxal Circles in the Context of Certain Parabolae, pp. 195-200
Benjamin Warren. A Circle in the Context of a Triangle and Parabola, pp. 201-203
Benjamin Warren. Generalization of Lambert’s Theorem, pp. 204-207
Benjamin Warren. A Line and Circle in the Context of a Parabola, pp. 208-211
Benjamin Warren. Another Generalization of the Fuhrmann Circle, pp. 212-214
Benjamin Warren. An Euler Line Generalization, pp. 215-218
Benjamin Warren. Proof of the Circle Centered at X(68325), pp. 219-221
Benjamin Warren. A Circle Whose Diameter Passes Through the Centroid, pp. 222-224
Benjamin Warren. A Circle That Emerges from A Quadric Curve in the Plane of a Triangle, pp. 225-234
Benjamin Warren. A Circle with the Centroid as a Fixed Point, pp. 235-240
Benjamin Warren. A Circle that Arises from the Pedal Triangle, pp. 241-244
Benjamin Warren. A Circle of Five Centroids that Arises from Two Pedal Triangles, pp. 245-247
Benjamin Warren. Two Pedal Triangles and a Circle, pp. 248-250
Benjamin Warren. The Circle Whose Diameter Connects the Orthocenters of a Triangle and its Orthic Triangle, pp. 251-254
Benjamin Warren. The Orthocenter Lies on the Circumcircle of the Circumcevian Triangle Reflected about the Pedal Triangle, pp. 255-259
Benjamin Warren. A Circle with an Euler Line Diameter, pp. 260-263
Benjamin Warren. An Equilateral Triangle Centered about the Centroid of a Triangle, pp. 264-276
Benjamin Warren. An Equilateral Triangle With a Special Circumdiameter, pp. 277-284
Benjamin Warren. A Point Related to Generalizations of the Isoperimetric and Equal Detour Points, pp. 285-286
Benjamin Warren. A Circle Related to Certain Projections Involving the Pedal Triangle, pp. 287-292
Benjamin Warren. The Euler Line as a Radical Axis of Coaxal Circles, pp. 293-296
Benjamin Warren. Generalization of a Circle in the Context of a Parabola and Triangle, pp. 297-301
Benjamin Warren. A Point on the Circumcircle Related to the Cevian Triangle, pp. 302-305
Benjamin Warren. A Circle Centered at the Midpoint of the Centroid and Circumcenter, pp. 306-309
Benjamin Warren. An Equilateral Triangle Centered at X(51), pp. 310-311
Benjamin Warren. Three Concurrent Circles, pp. 312-313
Stanley Rabinowitz. A Catalog of Properties of the Lemniscate of Bernoulli, pp. 314-324
Stanley Rabinowitz. Geometric Properties of a Cassini Oval, pp. 325-348
Stanley Rabinowitz, Ercole Suppa. More Shapes of Central Quadrilaterals, pp. 349-382
Supplementary material -BarycentricProofs-MoreShapes.
Stanley Rabinowitz. Ellipse Constructions, pp. 383-438
Stanley Rabinowitz. Catalog of Properties of the Ellipse - Part 1, pp. 439-488
TAKAAKI FUJITA. A Comprehensive Review of Hyper Geometry and Super Hypergeometry, pp. 489-499
TAKAAKI FUJITA. A Formal Framework for Fuzzy Hyper Geometry Extending Fuzzy Geometry through Hyperstructural Methods, pp. 500-511
Stanley Rabinowitz. Geometric Properties of a Hippopede, pp. 512-533
Ambuj Kumar, Bikash Kanti Sarkarb. 99.99_ accurate geometrical construction of all integer-valued angles from 1 to 90 using a marked ruler and compass, pp. 534-545
Ambuj Kumar, Bikash Kanti Sarkarb. Four high precision approximations of a regular heptagon using a marked ruler and compass, pp. 546-561
Ambuj Kumar, Bikash Kanti Sarkarb. A very precise approximation of 80◦ using a marked ruler and compass, pp. 562-571
TAKAAKI FUJITA. An Investigation into Fuzzy Wasan Geometry, pp. 572-580
TAKAAKI FUJITA. Rough Wasan Geometry A Set-Theoretic Approach to Traditional Japanese Geometry, pp. 581-589
Stanley Rabinowitz. Linear Relationships Between Lengths Associated with a Heptagonal Triangle, pp. 590-603
Supplementary material -BarycentricProofs-MoreShapes.
Volume10.1


Volume 9 (2024)

Samuel Porritt. On a pair of twin conics, pp. 1-8
Benjamin Warren. The Ellipses that Pass Through a Triangle Vertex Whose Foci are the Other Two Vertices, pp. 9-11
Benjamin Warren. The Midpoint of the Midpoints of the Diagonals of a Quadrilateral, pp. 12-15
Benjamin Warren. On a Certain Permutation Ellipse, pp. 16-19
Benjamin Warren. The Midpoints of the Vertices and the Midpoints Between the Vertices and the Circumcenter Lie on the Same Conic, pp. 20-22
Benjamin Warren. More on the Circles Which are Centered at Vertices of a Triangle and Passing Through the Rest of the Vertices, pp. 23-25
Benjamin Warren. The Diagonal Intersection Lies on the Radical Line of Two Certain Circles in a Quadrilateral, pp. 26-29
Nima Sarlak. Discovery of a property in 3-orthoschemes using computer, pp. 30-31
Benjamin Warren. Concurrence of Three Newton Lines, pp. 32-34
Benjamin Warren. The Newton Lines of the Quadrilaterals which Dissect a Regular n-gon by a Vertex and the Adjacent Vertex Midpoints are Concurrent, pp. 35-37
Benjamin Warren. The Newton Lines of Three Certain Quadrilaterals Formed from a Triangle are Concurrent, pp. 38-40
Benjamin Warren. Generalization of a Result about Concurrent Newton Lines Formed from Regular Polygons, pp. 41-43
Benjamin Warren. Generalization of the Triangle Centroid and the Van Lamoen Circle, pp. 44-53
Benjamin Warren. Further Generalization of a Result about Concurrent Newton Lines, pp. 54-77
Benjamin Warren. An Extension of the Van Lamoen Circle, pp. 78-81
Benjamin Warren. Generalization of a Result about a Certain Point on the Nine Point Circle, pp. 82-87
Benjamin Warren. A Generalization of Dao’s Theorem, pp. 88-154
Benjamin Warren. Certain Concurrent Lines in a Parallelogram, pp. 155-157
Benjamin Warren. Certain Concurrent Lines in a Regular Polygon, pp. 158-163
Benjamin Warren. The Midpoint of the Diagonal Intersection and the Midpoint Intersection in a Quadrilateral, pp. 164-166
Benjamin Warren. Generalization of the Euler and Nagel Lines, pp. 167-173
Benjamin Warren. Generalization of the Euler Line of a Quadrilateral, pp. 174-178
Benjamin Warren. Generalization of the Exeter Point, pp. 179-185
Benjamin Warren. On The Concurrency of Four Circles and a Conic Section, pp. 186-190
Benjamin Warren. Generalization of the Gergonne Point, pp. 191-196
Benjamin Warren. A Property of Certain Triangles Involving the Nine Point Circle, pp. 197-199
Benjamin Warren. Circles Centered at Vertices of Triangles, pp. 200-204
Benjamin Warren. Generalization of the Jha-Savaran Theorem, pp. 205-211
Benjamin Warren. Generalization of the Circumcenter, Exeter Point, and Euler Line, pp. 212-220
Benjamin Warren. A Seven Circumcenters Theorem, pp. 221-224
Benjamin Warren. On Certain Circles in Reference to a Triangle, pp. 225-229
Benjamin Warren. The Seven Circumcenters Theorem, pp. 230-233
Benjamin Warren. A Generalization of Commandino’s Theorem, pp. 234-237
Benjamin Warren. Three Lines Associated to Non-concurrent Cevians, pp. 238-241
Benjamin Warren. Generalization of Schiffler’s Theorem, pp. 242-248
Benjamin Warren. Generalization of the Mittenpunkt, pp. 249-254
Benjamin Warren. The Perspector of the Circumcevian and Antiorthocevian Triangles, pp. 255-258
Benjamin Warren. Generalization of the Nagel Point, pp. 259-263
Benjamin Warren. Five Concurrent Circles Formed from Two Cevians, pp. 264-270
Benjamin Warren. The Orthocenter is the Power Center of Three Certain Circles, pp. 271-273
Benjamin Warren. Certain Concurrent Circles in a Complete Quadrilateral, pp. 274-284
Benjamin Warren. Generalization of the Orthocenter, pp. 285-289
Benjamin Warren. Generalization of the Dao-Humenberger-Schuppar-De Villiers Theorem, pp. 290-331
Benjamin Warren. Three Concurrent Circles in Reference to Three Nonconcurrent Cevians, pp. 332-336
Benjamin Warren. Generalization of the Perspector of the Circumcevian and Antiorthocevian Triangles, pp. 337-345
Benjamin Warren. The Cevian Point as a Radical Center, pp. 346-350
Benjamin Warren. Short Proof of a Theorem of Rigby, pp. 351
Benjamin Warren. Equilateral Triangles Formed from Equilateral Triangles Erected on Triangles, pp. 352-362
Benjamin Warren. Twin Circles in a Complete Quadrilateral, pp. 363-365
Benjamin Warren. The Midpoint of the Circumcenter and the Cevian Point, pp. 366-369
Benjamin Warren. The Line Passing Through the Centroid and the Cevian Point, pp. 370-373
Benjamin Warren. A Fourth Point on a Certain Generalized Euler Line, pp. 374-380
Benjamin Warren. A Detail Regarding the Midpoint of the Midpoints of the Diagonals of a Quadrilateral, pp. 381-383
Benjamin Warren. A Circle Whose Center is the Circumcenter, pp. 384-386
Benjamin Warren. Concurrent Lines at an Altitude, pp. 387-388
Benjamin Warren. The Bottema Point Lies on a Circle, pp. 389-392
Benjamin Warren. A Circle Passing Through the Bottema Point and a Circle Centered at the Bottema Point, pp. 393-395
Benjamin Warren. A Third and Fourth Circle Passing Through the Bottema Point, pp. 396-398
Benjamin Warren. Another Perspector of the Antiorthocevian Triangle, pp. 399-402
Benjamin Warren. The Midpoints of the Centroids of the Six Triangles Dissected by Concurrent Cevians are in Perspective with the Triangle, pp. 403-406
Benjamin Warren. Another Perspector Regarding the Centroids of the Six Triangles Dissected by Concurrent Cevians, pp. 407-410
Benjamin Warren. Semicircles Erected on the sides of a Triangle, pp. 411-412
Benjamin Warren. A Perspector Involving Three Arbitrary Points on the Sides of a Triangle, pp. 413-414
Benjamin Warren. On The Line Connecting the Centroid of Three Points, a Fourth Point, and the Centroid of the Four Points, pp. 415-421
Benjamin Warren. The Circumcenters of the Two Triangles and Two Similar Rectangles Joined at a Vertex are Concyclic, pp. 422-424
Benjamin Warren. Tangents Through Four Points on a Conic Section, pp. 425-436
Benjamin Warren. Generalization of the Ellipse Formed by Six Circumcenters of a Triangle Vertex, the Cevian Point, and the Circumcevian triangle, pp. 437-440
Benjamin Warren. Three Congruent Circles, Six Parallel Lines, X(104), and a New Construction of the Intouch Triangle, pp. 441-451
Benjamin Warren. Simple Construction of a Splitter, pp. 452-453
Benjamin Warren. Simple Construction of a Cleaver, pp. 454-456
Benjamin Warren. Generalization of Van Aubel’s Theorem, pp. 457-460
Benjamin Warren. Three Circles That Concur at the Incenter, pp. 461-463
Benjamin Warren. Two More Circles in a Bottema-type Configuration, pp. 464-468
Benjamin Warren. Two Parallelograms and a Certain Circle in a Given Triangle, pp. 469-473
Benjamin Warren. Four Concentric Circles about the Incenter, pp. 474-477
Benjamin Warren. Generalization of a Result Regarding X(104) as a Perspector, pp. 478-483
Benjamin Warren. Three Circles that Concur at the Feuerbach Point, pp. 484-493
Benjamin Warren. The Incenter Lies on a Circle, pp. 494-497
Benjamin Warren. Three More Points on the Fuhrmann Circle, pp. 498-501
Benjamin Warren. A New Generalization of the Orthocenter, pp. 502-506
Benjamin Warren. A Result Related to a Generalization of the Orthocenter, pp. 507-511
Benjamin Warren. The Centroid of a Triangle Lies on a Circle Which is the Same Size as a Certain Circle Passing Through the Incenter of a Triangle, pp. 512-514
Benjamin Warren. The Circle Centered at the Incenter Which Passes Through the Circumcenter, pp. 515-517
Benjamin Warren. A Circle Theorem Corresponding to Two Distinct Chosen Points in the Plane of a Triangle, pp. 518-520
Benjamin Warren. The Points of Reflection of the Incenter about the Vertices Lie on the Bevan Circle, pp. 521-523
Nima Sarlak. An analytical proof of Nima_s theorem, pp. 524-526
Dan Ismailescu, Ganghun Kim and Kay Yeon Lee. On the Properties of Quadrilaterals determined by Triangle Centers, pp. 527-543
Stanislaw Majchrzak. On tangents to conic from triangle’s point of view, pp. 544-564
Volume 9.1
Volume 9.1


Volume 8 (2023)

Nguyen Ngoc Giang, Le Viet An, Nguyen Duy Phuoc. New Archimedean Circles in an Arbelos, pp. 1-8.
Antoine Mhanna. Trigonometric Identities and Urquhart’s Theorem, pp. 9-14.
Emmanuel A. J. Garcia. A Note on the Area of Triangles, pp. 16-18.
Stanley Rabinowitz. Location of the Vertices of the Self-Polar Triangle of Two Ellipse, pp. 19-21.
Stanley Rabinowitz. When Can a Triangle Center Coincide with a Vertex pp. 70-74
Supplementary Material
Stanley Rabinowitz. Proof of the Isogonal Disc Conjecture, pp. 75-77
Benjamin Warren. A Certain Set of Concyclic Points, pp. 78-84
Benjamin Warren. Generalization of a Triangle Type Criterion, pp. 85-90
Benjamin Warren. Another Point that Lies on the Newton Line, pp. 91-93
Benjamin Warren. A New Set of Collinear Points in a Quadrilateral, pp. 94-97
Benjamin Warren. Some Properties Regarding a Certain Circle Associated to a Cyclic Quadrilateral, pp. 98-102
Benjamin Warren. A Certain Point Associated to a Cyclic Hexagon, pp. 103-104
Benjamin Warren. The Miquel Point Lies on a Certain Line in a Quadrilateral, pp. 105-107
Benjamin Warren. The Power Center of Three Circles in a Cyclic Quadrilateral is the Diagonal Intersection Point, pp. 108-112
Sava Grozdev, Veselin Nenkov, Tatiana Madjarova. Radical Axes and Complex Numbers, pp. 113-121
Volume 8 - 1 - 2023
Volume 8 - 10 - 2023
Volume 8 - 2 - 2023
Volume 8 - 3 - 2023
Volume 8 - 4 - 2023
Volume 8 - 5 - 2023
Volume 8 - 6 - 2023
Volume 8 - 7 - 2023
Volume 8 - 8 - 2023
Volume 8 - 9 - 2023
Volume 8 - 9 - 2023


Volume 7 (2022)

Sava Grozdev, Veselin Nenkov. Generalizations of Some IMO Geometry Problems, pp. 1-24.
Stanley Rabinowitz. When Triangle Centers Lie Inside the Triangle, pp. 25-29.
Supplementary Material – Intriangle Relations.zip
Stanley Rabinowitz. A Computer Algorithm for Proving Symmetric Homogeneous Triangle Inequalities, pp. 30-62.
Supplementary Material – Blundon.zip
Stanley Rabinowitz. The Circumconics Among Us, pp. 63-76.
Supplementary Material – Circumconics.zip
Stanley Rabinowitz, Ercole Suppa. Exclusion of Trivial Angle Relationships in the Analysis of Geometrical Figures, pp. 77-130.
Stanley Rabinowitz, Ercole Suppa. The Shape of Central Quadrilaterals, pp. 131-180.
Supplementary Material – Quadrilateral Shapes.zip
Stanley Rabinowitz. Inequalities for Distances Between Triangle Centers, pp. 181-194.
Supplementary Material – Point Distances.zip
Stanley Rabinowitz. Inequalities Involving Central Cevians, pp. 195-213
Supplementary Material – Cevian Inequalities.zip
Stanley Rabinowitz, Ercole Suppa. Relationships between a Central Quadrilateral and its Reference Quadrilateral, pp. 214-287
Supplementary Material – Central Quadrilateral.zip
Kiminari Shinigawa, Clark Kimberling, Peter Moses. Euler Coordinates in the Plane of a Triangle, pp. 287-308
Sava Grozdev, Veselin Nenkov, Tatiana Madjarova, Eliseu Bessa, Mapaxe Luvunga. Systematization of a Type Symmetric Polynomials of Three Variables and Some Applications, pp. 309-323
Sava Grozdev, Veselin Nenkov, Tatiana Madjarova. Poncelet-Gergonne Circle of a Triangle, Moving Between Two Fixed Circles, pp. 324-337
Sava Grozdev, Veselin Nenkov, Tatiana Madjarova. Poncelet-Gergonne Circle, Symmetric polynomials and Baricentric Coordinates, pp. 338-343


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.
Stanley Rabinowitz. Catalog of Properties of the First Isodynamic Point of a Triangle, pp. 108-136.
Stanley Rabinowitz. Location of Triangle Centers Relative to the Incircle and Circumcircle, pp. 137-144.
Supplementary Material – Incircle Relations.zip
Sava Grozdev, Veselin Nenkov. Euler’s Line, Euler’s Curve and Thebault’s Point, pp. 145-156.


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