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 8 (2023)
Volume 7 (2022)
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Sava Grozdev, Veselin Nenkov. Generalizations of Some IMO Geometry
Problems, pp.
1-24.
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Stanley Rabinowitz. When Triangle Centers Lie Inside the Triangle, pp.
25-29.
Supplementary Material – Intriangle Relations.zip
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Stanley Rabinowitz. A Computer Algorithm for Proving Symmetric
Homogeneous
Triangle Inequalities, pp. 30-62.
Supplementary Material – Blundon.zip
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Stanley Rabinowitz. The Circumconics Among Us, pp. 63-76.
Supplementary Material – Circumconics.zip
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Stanley Rabinowitz, Ercole Suppa. Exclusion of Trivial Angle
Relationships in
the Analysis of Geometrical Figures, pp. 77-130.
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Stanley Rabinowitz, Ercole Suppa. The Shape of Central Quadrilaterals,
pp.
131-180.
Supplementary Material – Quadrilateral Shapes.zip
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Stanley Rabinowitz. Inequalities for Distances Between Triangle
Centers, pp. 181-194.
Supplementary Material – Point Distances.zip
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Stanley Rabinowitz. Inequalities Involving Central Cevians, pp. 195-213
Supplementary Material – Cevian Inequalities.zip
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Stanley Rabinowitz, Ercole Suppa. Relationships between a Central
Quadrilateral and its Reference Quadrilateral, pp. 214-287
Supplementary Material – Central Quadrilateral.zip
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Kiminari Shinigawa, Clark Kimberling, Peter Moses. Euler Coordinates in
the Plane of a Triangle, pp. 287-308
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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
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Sava Grozdev, Veselin Nenkov, Tatiana Madjarova. Poncelet-Gergonne
Circle of a Triangle, Moving Between Two Fixed Circles, pp. 324-337
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Sava Grozdev, Veselin Nenkov, Tatiana Madjarova. Poncelet-Gergonne
Circle, Symmetric polynomials and Baricentric Coordinates, pp. 338-343
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Volume 6 (2021)
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Abdilkadir Altintaş, Leonard Giugiuc. Location of Some Kimberling
Centers
Respect to Orthocentroidal Circle, pp. 1-5.
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Stanley Rabinowitz, Ercole Suppa. Computer Investigation of
Properties of the
Gergonne Point of a Triangle, pp.6-42.
Supplementary Material - Gergonne Properties.zip
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Stanley Rabinowitz, Ercole Suppa. Equilateral Triangles formed by
the Centers of
Erected Triangles, pp. 43-67.
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Tran Quang Hung, Floor van Lamoen. Odom’s Triangle, pp 68-77.
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Stanley Rabinowitz.Inequalities Involving Gergonne and Nagel
Cevians, pp.
78-83.
Supplementary Material - Gergonne Nagel Cevians.zip
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Thanh Tung Vu. Median-orthologic Simplexes, pp. 84-86.
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Nguyen Chuong Chi. A Purely Synthetic Proof of the Dao’s Eight
Circles Theorem,
pp. 87-91.
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Abdilkadir Altintaş. Congruent Circles on Locus Problems, pp. 92-96.
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Stanley Rabinowitz. Linear Relationships Between Squares of Cevian
Lengths, pp.
97-103.
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Stanley Rabinowitz. Catalog of Properties of the First Isodynamic
Point of a
Triangle, pp. 108-136.
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Stanley Rabinowitz. Location of Triangle Centers Relative to the
Incircle and
Circumcircle, pp. 137-144.
Supplementary Material – Incircle Relations.zip
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Sava Grozdev, Veselin Nenkov. Euler’s Line, Euler’s Curve and
Thebault’s Point,
pp. 145-156.
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Volume 5 (2020)
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Stanley Rabinowitz, Ercole Suppa, Abdilkadir Altintaș, Floor van
Lamoen.
Rabinowitz Conics Associated with a Triangle, pp. 1-12.
Supplementary Material - Rabinowitz Conic.zip
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Stanley Rabinowitz, Arrangement of Central Points on the Faces
of a Tetrahedron,
pp. 13–41.
Supplementary Material - Tetrahedron Faces.zip
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Abdilkadir Altintaş, On Some Properties of Neuberg Cubic, pp.
42–49.
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Dao Thanh Oai, Another Generalization of the Simson Line, pp.
50–52.
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Sava Grozdev, Veselin Nenkov, Several properties of the
inscribed conic sections
and a method for proofs with complex numbers, pp. 53-70.
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Abdilkadir Altıntaş, On Concurrent Euler Lines, pp. 71-75.
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Volume 4 (2019)
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Dao Thanh Oai,
Some Problems Around the Configuration
of Eight Circles, pp.1-12.
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Dao Thanh Oai,
Four Proofs of the Generalization of the Simson
Line, pp.13-17.
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Todor Zaharinov,
Inscribed Conics and the Darboux Cubic,
pp.18-26.
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Todor Zaharinov,
Inscribed triangles with centroid in a given
point, pp.27-35.
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Todor Zaharinov,
Sums With Square Distances Between a Point
and Vertexes, pp.36-47.
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Stanley Rabinowitz,
Relationships Between Six Circles,
pp.48-53.
Supplementary
Material - Relationships Between Six
Circles.zip
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Martin At. Stanev,
Locus of the centroid of the
equilateral triangle inscribed in an
ellipse,
pp.54-65.
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Volume 3 (2018)
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Nguyen Chuong Chi,
A Proof of Dao’s Generalization of the Sawayama
Lemma, pp.1-4.
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Nguyen Ngoc Giang,
Creation of new theorems from flanks,
pp.5-36.
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Sava Grozdev, Hiroshi Okumura and Deko
Dekov,
Triangles Homothetic with the Extouch
Triangle, pp.37-43.
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Sava Grozdev, Hiroshi Okumura and Deko
Dekov,
Intangents Triangle, pp.44-48.
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Nguyen Ngoc Giang,
A New Proof and Some Generalizations
of the Bottema Theorem,
pp.49-54.
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Sava Grozdev, Hiroshi Okumura
and Deko Dekov,
Problems for Students about
Intouch Triangle, pp.55-61.
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Abdilkadir Altintaş and
Ercole Suppa,
Extended Soddy
Configurations,
pp.62-68.
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Sava Grozdev, Hiroshi
Okumura and Deko Dekov,
A New Proof of the
Feuerbach theorem,
pp.69-70.
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Sava Grozdev,
Hiroshi Okumura and
Deko Dekov,
The
Paskalev-Tchobanov
Distance Formula and
Some of its
Applications,
pp.71-73.
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Nguyen Ngoc
Giang,
Using the affine
and projective
methods to prove
and extend Dao's
theorem,
pp.74-81.
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Nguyen Ngoc
Giang and Le
Viet An,
An Extension
of the
Steiner Line
Theorem and
Application,
pp.82-87.
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Dao
Thanh
Oai,
Some
Equilateral
Triangles
Perspective
to the
Reference
Triangle
ABC,
pp.88-96.
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Nguyen
Ngoc
Giang
and
Le
Viet
An,
An
Another
Proof
of
Dao’s
Theorem
and
its
Converses,
pp.97-103.
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Dao
Thanh
Oai,
An
Ellipse
Through
12
Points
and
Golden
Triangle,
pp.104-109.
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Nguyen
Ngoc
Giang
and
Le
Viet
An,
Three
extentions
of
Kosnita's
theorem,
pp.110-117.
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Glenn
C.
Rhoads,
Planar
Tilings
by
Substitution
Polykleins,
pp.118-135.
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Nguyen
Ngoc
Giang
and
Dao
Thanh
Oai,
Six
Conics
Theorem,
pp.136-139.
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Sava
Grozdev,
Hiroshi
Okumura
and
Deko
Dekov,
A
Note
on
the
Tangential
triangle,
pp.140-142.
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Dao
Thanh
Oai,
A
Problem
On
Three
Homothetic
Centers
Associated
With
A
Convex
Hexagon,
pp.143-144.
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Tran
Minh
Ngoc,
A
Purely
Synthetic
Proof
of
Dao’s
Theorem
On
A
Conic
And
Its
Applications,
pp.145-152.
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Volume 2 (2017)
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Sava Grozdev, Hiroshi Okumura and Deko Dekov,
Computer Discovered Mathematics: Euler
Anticevian Triangles, pp.1-29.
Supplementary Material. Euler Anticevian
Triangles.zip
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Sava Grozdev, Hiroshi Okumura and Deko
Dekov,
A Note on the Leversha Point, pp.30-34.
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Sava Grozdev, Hiroshi Okumura and Deko
Dekov,
Computer Discovered Mathematics:
Incentral Triangle, pp.35-45.
Supplementary Material. Incentral
triangle.zip
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Sava Grozdev, Hiroshi Okumura and
Deko Dekov,
Computer Discovered Mathematics:
Triangles homothetic with the Orthic
triangle,
pp.46-54.
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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
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Sava Grozdev, Hiroshi
Okumura and Deko Dekov,
Computer Discovered
Mathematics:
Excenters-Incenter
Reflections Triangle,
pp.72-80.
Supplementary Material -
Excenters-Incenter
Reflections Triangle
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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
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Sava Grozdev,
Hiroshi Okumura and
Deko Dekov,
Triangles Homothetic
with Triangle ABC,
pp.86-89
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Sava Grozdev,
Hiroshi Okumura
and Deko Dekov,
Triangles
Homothetic with
Triangle ABC.
Part 2,
pp.90-96
Supplementary
Material -
HT2.zip
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Sava
Grozdev,
Hiroshi
Okumura and
Deko Dekov,
Triangles
Homothetic
with
Triangle
ABC. Part 3,
pp.97-105.
Supplementary
Material -
HT3.zip
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Sava
Grozdev,
Hiroshi
Okumura
and Deko
Dekov,
Computer
Discovered
Mathematics:
Triangles
Associated
with
Triangulation
Triangles,
pp.106-110.
Supplementary
Material
-
Triangulation
Triangles.zip
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Sava
Grozdev,
Hiroshi
Okumura
and
Deko
Dekov,
Leversha
Triangles
and
Leversha
Points,
pp.111-116.
Supplementary
Material
-
Leversha
Points.zip
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Sava
Grozdev,
Hiroshi
Okumura
and
Deko
Dekov,
Notable
Circles,
pp.117-134.
Supplementary
Material
-
Notable
Circles.zip
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Nguyen
Ngoc
Giang,
Some
properties
of
triangles
or
rectangles
attached
to
sides
of
a
triangle,
pp.135-140.
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Nguyen
Trung
Kien,
An
Iterative
Geometrical
Approach
for
a
Problem
in
the
International
Mathematical
Olympiad
2017,
pp.141-145.
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Nguyen
Ngoc
Giang,
Flanks,
new
flanks,
generalized
flanks
and
their
properties,
pp.146-184.
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Sava
Grozdev,
Hiroshi
Okumura
and
Deko
Dekov,
Computer
Discovered
Mathematics:
Problems
for
Students
about
Excentral
Triangle,
pp.185-200.
Supplementary
material
-
Excentral
triangle
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Nguyen
Ngoc
Giang,
The
relation
between
three
concurrent
diagonals
of
a
hexagon
and
rectangles
attached
to
sides
of
a
triangle,
pp.201-207.
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Volume 1 Number 1 (2016)
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S. Grozdev and D. Dekov,
Computer Discovered Mathematics: Euler
Triangles, pp.1-10.
Supplementary
Material:
Euler_Triangles.zip
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S. Grozdev and D. Dekov,
Computer Discovered Mathematics: Circles
Containing the Parry Point,
pp.11-14.
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S. Grozdev and D. Dekov,
Computer Discovered Mathematics:
Lester Circles, pp.15-25.
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S. Grozdev and D. Dekov,
Computer Discovered Mathematics:
The Incenter, pp.26-35.
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Francisco Javier García
Capitán,
Posing and Solving Problems
with Barycentric
Coordinates, pp.36-44.
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René Grothmann,
The Geometry Program
C.a.R., pp.45-61.
Supplementary
Material:
Grothmann-CaR.zip
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René Grothmann,
Discover Euler Math
Toolbox,
pp.62-75.
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Dao Thanh Oai,
A generalization
of the
Zeeman-Gossard
perspector
theorem,
pp.76-79.
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S. Grozdev
and D.
Dekov,
Computer
Discovered
Mathematics:
Dividing
Directed
Segments,
pp.80-88.
Supplementary
Material:
division.zip
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S.
Grozdev
and D.
Dekov,
Mathematics
Discovered
by
Computers:
Incenters
of
Triangles,
pp.89-92.
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S.
Grozdev
and
D.
Dekov,
Computer
Discovered
Mathematics:
Circles
through
the
Feuerbach
Point,
pp.93-96.
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Volume 1 Number 2 (2016)
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S. Grozdev and D. Dekov,
Computer Discovered Mathematics:
Half-Cevian Triangles, pp.1-8.
Supplementary
Material:
Half-Cevian-Triangles.zip
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S. Grozdev and D. Dekov,
Computer Discovered Mathematics: The
Mittenpunkt, pp.9-13
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S. Grozdev and D. Dekov,
Computer Discovered Mathematics:
Gibert Triangles, pp.14-20.
Supplementary
Material:
Gibert-Triangles.zip
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Dao Thanh Oai, The Nine
Circles Problem and the
Sixteen Points Circle,
pp.21-24.
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Ngo Quang Duong,
Generalizations of some
triangle geometry
results associated
with cubics,
pp.25-39.
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Ngo Quang Duong,
Some problems around
the Dao's theorem on
six circumcenters
associated with a
cyclic hexagon
configuration,
pp.40-47.
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S. Grozdev and
D. Dekov,
Computer
Discovered
Mathematics:
Fuhrmann
Triangles,
pp.48-58.
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S. Grozdev
and D.
Dekov,
Computer
Discovered
Mathematics:
Harmonic
Conjugates,
pp.59-63.
Supplementary
Material:
Harmonic
Conjugates.zip
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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
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S.
Grozdev
and
D.
Dekov,
Barycentric
Coordinates:
Formula
Sheet,
pp.75-82.
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Mamut
Sirazitdinov,
Proofs
of
computer
discovered
theorems
about
Yiu
Transform,
pp.83-89.
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S.
Grozdev
and
D.
Dekov,
Computer
Discovered
Mathematics:
A
Note
on
the
Johnson
Circles,
pp.90-95.
Supplementary
Material:
Johnson
Circles.zip
|
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S.
Grozdev
and
D.
Dekov,
Computer
Discovered
Mathematics:
Yff
Triangles,
pp.96-103.
Supplementary
Material:
Yff
Triangles.zip
|
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S.
Grozdev
and
D.
Dekov,
Computer
Discovered
Mathematics:
A
Note
on
the
Gossard
Triangles,
pp.104-108.
Supplementary
Material:
Gossard
Triangle.zip
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Volume 1 Number 3 (2016)
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Frank M. Jackson and Stalislav
Takhaev,
Heronian Triangles of Class J:
Congruent Incircles Cevian
Perspective,
pp.1-8.
|
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Nguyen Trung Kien and Tran Thu
Le,
Problem of Twelve Circles,
pp.9-12.
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Dao Thanh Oai,
Generalizations of some
famous classical Euclidean
geometry theorems,
pp.12-20.
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Nguyen Ngoc Giang,
The extension from a
circle to a conic having
center: The creative
method of new
theorems, pp.21-32.
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Dao Thanh Oai,
A Generalization of
Sawayama and
Thébault's Theorem,
pp.33-35.
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Dao Thanh Oai,
Another
Generalization
of the Sawayama
and Thébault's
Theorem,
pp.36-39.
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Sava Grozdev
and Deko
Dekov,
Computer
Discovered
Mathematics:
Stanilov
Triangles,
pp.40-44.
Supplementary
Material:
Stanilov
Triangles.zip
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|
Sava
Grozdev,
Hiroshi
Okumura
and Deko
Dekov,
Computer
Discovered
Mathematics:
A Note
on the
Miquel
Points,
pp.45-49.
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Sava
Grozdev,
Hiroshi
Okumura
and
Deko
Dekov,
Computer
Discovered
Mathematics:
Orthopoles,
pp.50-56
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Sava
Grozdev,
Hiroshi
Okumura
and
Deko
Dekov,
Computer
Discovered
Mathematics:
Haimov
Triangle
of
the
Incenter,
pp.57-61
|
Volume 1 Number 4 (2016)
Volume 0 (2015)
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Welcome!, p.1.
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Advertisements, p.2.
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S. Grozdev and D.
Dekov,
A Survey of
Mathematics
Discovered by
Computers,
pp.3-20.
|
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|
Paul Yiu,
Iterations of
sum of powers of
digits,
pp.21-26.
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Paul Yiu,
Collinearity
of the
reflections
of the
intercepts
of
a line in
the angle
bisectors of
a triangle
pp.27-31.
|
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|
Francisco
Javier
García
Capitán,
Barycentric
Coordinates,
pp.32-48.
|
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|
A.
G.
Koryanov,
The
computer
program
"Inverse
Matrices",
pp.49-53.
|
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Stefka
Karakoleva,
Make
your
first
steps
in
the
high-quality
typesetting
system
LaTeX,
pp.54-59.
|
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S.
Grozdev
and
D.
Dekov,
Computer
Discovered
Mathematics:
Hexyl-Anticevian
Triangles,
pp.60-69.
|
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|
S.
Grozdev
and
D.
Dekov,
Computer
Discovered
Mathematics:
Haimov
Triangles,
pp.70-79.
Supplementary
Material:
Haimov_Points.zip
|
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