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Abstract
In this work, a generalization of the existing classical subject Geometry is done by, introducing a new geometry called by “Region Geometry”. It is observed that the classical subject Geometry is R-Geometry, a special case of the subject “Region Geometry” corresponding to the trivial region R. Every region A generates its own region geometry called by ‘A-Region Geometry’ subject to fulfilment of few conditions. Although this is a purely theoretical work, but this theory is expected to cater to Mathematics and all branches of STEM including AI, Data Science, modern Statistics etc in a new direction.
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References
- Bashmakova, I.G. and G. S. Smirnova, G.S. (2000). Geometry : the First Universal Language of Mathematics, Kluwer Academic Publishers.
- Biswas, Ranjit. (2026a). The existing huge volume of algebraic structures in the subject “ALGEBRA” has few serious hidden gaps and needs fixing in order to validate many of the elementary and important frequently practiced algebraic computations, Indonesian Journal of Mathematics and Analysis, 2026, Vol.1, pp 35–69 (Open Access) (https://doi.org/10.21776/ub.ijma.2026.004.01.4)
- Biswas, Ranjit. (2026b). “Object Theory” : the classical “Number Theory” is a special case, Turkish Journal of Analysis and Number Theory, (accepted) to appear in Vol.14(1), 2026 (Open Access).
- Boyer, Carl B. (2004). History of Analytic Geometry. Dover Publications, Inc., Mineola, New York.
- Chahal, J. S. (2025). Number Theory and Geometry through History,
- CRC Press.
- Dani, S.G. and Papadopoulos,A. (2019). Geometry in History, Springer Nature Switzerland, (ISBN: 978-3-030-13608-6)
- Dillon, Meighan I. (2018). Geometry Through History : Euclidean, Hyperbolic, and Projective Geometries, Springer Cham.
- https://doi.org/10.1007/978-3-319-74135-2
- Edward T Walsh, Edward.T. (2014). A First Course in Geometry,
- Dover Publications.
- Hamilton, J. G. Kettle, F. (1900). A First Geometry Book, Edward Arnold (London).
- Loney, S. L. (1895). The Elements of Coordinate Geometry, Macmillan & Co..
- Loney, S. L. (1975). The Elements of Coordinate Geometry. Part-I, Macmillan Student Edition, Macmillan India Limited, Madras.
- Loney, S. L. (1923). The Elements of Coordinate Geometry. Part-II, Modern Publishers
- Ostermann, A and Wanner, G., Geometry by Its History, Springer Undergraduate Texts in Mathematics (ISBN: 978-3-642-29162-3).
- Robbins, Herbert. and Courant, Richard. (1996). What is Mathematics?: An Elementary Approach to Ideas and Methods. Second edition, Oxford University Press, New York.
- Shult, Ernest E. (2011), Points and Lines: Characterizing the Classical Geometries, Universitext Series, Springer-Verlag Berlin Heidelberg.
References
Bashmakova, I.G. and G. S. Smirnova, G.S. (2000). Geometry : the First Universal Language of Mathematics, Kluwer Academic Publishers.
Biswas, Ranjit. (2026a). The existing huge volume of algebraic structures in the subject “ALGEBRA” has few serious hidden gaps and needs fixing in order to validate many of the elementary and important frequently practiced algebraic computations, Indonesian Journal of Mathematics and Analysis, 2026, Vol.1, pp 35–69 (Open Access) (https://doi.org/10.21776/ub.ijma.2026.004.01.4)
Biswas, Ranjit. (2026b). “Object Theory” : the classical “Number Theory” is a special case, Turkish Journal of Analysis and Number Theory, (accepted) to appear in Vol.14(1), 2026 (Open Access).
Boyer, Carl B. (2004). History of Analytic Geometry. Dover Publications, Inc., Mineola, New York.
Chahal, J. S. (2025). Number Theory and Geometry through History,
CRC Press.
Dani, S.G. and Papadopoulos,A. (2019). Geometry in History, Springer Nature Switzerland, (ISBN: 978-3-030-13608-6)
Dillon, Meighan I. (2018). Geometry Through History : Euclidean, Hyperbolic, and Projective Geometries, Springer Cham.
https://doi.org/10.1007/978-3-319-74135-2
Edward T Walsh, Edward.T. (2014). A First Course in Geometry,
Dover Publications.
Hamilton, J. G. Kettle, F. (1900). A First Geometry Book, Edward Arnold (London).
Loney, S. L. (1895). The Elements of Coordinate Geometry, Macmillan & Co..
Loney, S. L. (1975). The Elements of Coordinate Geometry. Part-I, Macmillan Student Edition, Macmillan India Limited, Madras.
Loney, S. L. (1923). The Elements of Coordinate Geometry. Part-II, Modern Publishers
Ostermann, A and Wanner, G., Geometry by Its History, Springer Undergraduate Texts in Mathematics (ISBN: 978-3-642-29162-3).
Robbins, Herbert. and Courant, Richard. (1996). What is Mathematics?: An Elementary Approach to Ideas and Methods. Second edition, Oxford University Press, New York.
Shult, Ernest E. (2011), Points and Lines: Characterizing the Classical Geometries, Universitext Series, Springer-Verlag Berlin Heidelberg.