Turkish Journal of Mathematics
Author ORCID Identifier
MIRCEA CRASMAREANU: 0000-0002-5230-2751
MARIUS MUNTEANU: 0009-0005-7542-2165
Abstract
This note introduces a sum for two interior points of an affine segment [AB] based on a trigonometric approach. Some properties of this operation, along with general examples (including squares of endpoints, the midpoint, and the centroid), are discussed. A main result is that the midpoint of a segment is the circular sum of the points dividing the segment with the ratios 4 and 9. In addition, we completely solve a Diophantine equation associated with the circular sum in order to identify all points with integer ratio whose circular sum is a point with integer ratio.
DOI
10.55730/1300-0098.3598
Keywords
affine segment, barycentric coordinates, circular sum
First Page
411
Last Page
420
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
CRASMAREANU, M, & MUNTEANU, M (2025). The circular sum of points of an affine segment. Turkish Journal of Mathematics 49 (4): 411-420. https://doi.org/10.55730/1300-0098.3598
