Born in Skopje, Macedonia. After a while I got my bachelors degree in (both Pure and Applied) Mathematics (equivalent of Honours Degree). All that at the Cyril and Methodius University in Skopje. I had my Masters degree there too. My Ph.D. studies were done at the University of Toronto.


My first research area was Universal Algebra. The following articles are from that period.

1. Subalgebras of Commutative Distributive Semigroups, God.Zbornik 32, Mat. Fak.Univ.Kiril i Metodij, Skopje, Macedonia (1981), 53-57

2. Subalgebras of Distributive Semigroups, Proceedings of the First International Symposium n-ary Structures, Skopje 1981, Mak. Akad. na Nauk. i Umetn., Skopje, Macedonia (1982), 223-228

3. Embedding Unoids in Semigroups Belonging to Some Varieties of Semigroups, God.Zbor.33/34, Mat.Fak. Univ.Kiril i Metodij, Skopje, Macedonia (1982/83), 77-83

4. Embedding Algebras in Distributive Semigroups, Third Yugoslavian Algebraic Conference, Belgrad, Yugoslavia 1982, 77-83

5. Some Proper Quasivarietiesof Subalgebras of Semigroups, Proceedings of the Second International Symposium nary Structures, Center Appl.Math. Sofia, Bulgaria, (1985),171-175

Then I made a shift to Infinite Group Theory.

6. Topographs and Groups, Journal of Pure and Applied Algebra, (1992), 47-57

7. The Automorphism Group of a Free Group: Centralizers and Stabilizers, Journal of Algebra, (1992), 435-502


Then, whatever came my way.

8. Some Evident Summation Formulas, The Mathematical Intelligencer, Volume 22, Number 3 (2000), 47-49

9. Integration by Parts: a Visual Proof, Visual Mathematics, Vol. 3, No. 1, 2001.


Even things that do not look like math:

10. Crystals and Quasicrystals: Construction of 2D Lattices and Demonstrations Using a Laser Pointer, (joint with Petrusevski and Najdovski), some chemical journal, 2003.


Visiting the no-no land: a small dosage of mathematics and metaphysics:

11. Knots, Bands and Miracles: Regarding the Zöllner-Slade Phenomena, Journal of the Society of Psychical Research, January 2010


Back to regular fun: it is amazing what has been overlooked for 2500 years:

12. One Pythagoras for All Dimensions, Mathematical Intelligencer, 2014


A couple of books:

1. Math and Art: An Introduction to Visual Mathematics; CRC (Taylor and Frances), June 2008 (in collaboration with R. Padmanabhan)

2. An Illustrated Introduction to Topology and Homotopy; CRC (Taylor and Frances), March 2015


I have done math-related cartoons: there is one in the Winter 2001 issue of The Mathematical Intelligencer, another in the Summer 2001 issue of the same magazine. The Fall 2007 issue of the Mathematical Intelligincer has a cartoon of mine on the front cover.

A Mathematica program for generating Ammann tilings can be found here (Wolfram's site).

A couple of manuals for Calculus I and II, 146 + 125 pages, 1996. (I do not know if the manuals are still in use).


Various hobbies. I have played chess long enough to feel like devoting a small page to it - right here. (Recreational) soccer is currently my primary sport. Once, being somewhat bored, I bounced a ball 2100 times (no hands) before it fell to the ground. I prefer playing. :-).



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