I have tried to link some topics in mathematics which included the word " Rational" , I have got many references which used " Rational" in Group theory and Probability and number theory and algebraic geometry and Topology,Chaos theory and so on , Now I'm confused and I have asked my self many times why that "Rational" occurs so much in all topics of mathematics probably informatic and physics ? Why this word interesting in mathematics ? According to the below linked reference I ask why always we investigate to get things in mathematics to be rational ?What is the special of that word rational in mathematics ?
**List of Linked reference include word " Rational"**:
[Regularization of Rational Group Actions](https://arxiv.org/abs/1808.08729)
[Rational Points on Rational Curves](https://arxiv.org/abs/1911.12551)
[Automatic sets of rational numbers](https://arxiv.org/abs/1110.2382)
[Rational homology 3-spheres and simply connected definite bounding](https://arxiv.org/abs/1808.09135)
[Rational Homotopy Theory](https://link.springer.com/book/10.1007/978-1-4613-0105-9)
[A Rational Informatics-enabled approach to the Standardised Naming of Contours and Volumes in Radiation Oncology Planning](https://www.academia.edu/7430350/A_Rational_Informatics-enabled_approach_to_the_Standardised_Naming_of_Contours_and_Volumes_in_Radiation_Oncology_Planning)
[Is Science Rational?](https://link.springer.com/chapter/10.1007/978-94-010-2115-9_36)
[A note on p-rational fields and the abc-conjecture](https://arxiv.org/abs/1903.11271)
[Remarks on rational vector fields on CP1](https://arxiv.org/abs/1909.09439)
[Rational Analysis](https://www.sciencedirect.com/topics/computer-science/rational-analysis)
[Rational probability measures](https://www.sciencedirect.com/science/article/pii/030439758990042X)
[A trace formula for the distribution of rational G-orbits in ramified covers, adapted to representation stability](https://arxiv.org/abs/1703.01710)
[Rational cobordisms and integral homology](https://arxiv.org/abs/1811.01433)
[Conditioned invariant subspaces, disturbance decoupling and solutions of rational matrix equations](https://www.tandfonline.com/doi/abs/10.1080/00207178608933450)
[Why study unirational and rational varieties?](https://mathoverflow.net/q/287364/51189)
[Degree of rational maps via specialization](https://arxiv.org/abs/1901.06599)
[Minimum rational entropy fault tolerant control for non-Gaussian singular stochastic distribution control systems using T-S fuzzy modelling](https://www.tandfonline.com/doi/abs/10.1080/00207721.2018.1526984)
[On the generic nonexistence of rational geodesic foliations in the torus, Mather sets and Gromov hyperbolic spaces](https://link.springer.com/article/10.1007/BF01377597)
[Irrationality Measure of Pi](https://arxiv.org/abs/1902.08817)
[Rational Unified Process](https://arxiv.org/abs/1609.07350)
[Rational Computations of the Topological K-Theory of Classifying Spaces of Discrete Groups](https://arxiv.org/abs/math/0507237)
[On Periodic and Chaotic Orbits in a Rational Planar System](https://arxiv.org/abs/1405.3124)
**Note** I do not investigate about the meaning of the word "Rational" in each topic but I want to know why its were dominated why it is interesting whatever the kind of its meaning ?
In elliptic curves theory Rational is derived from the firleld which the curve is built over
It is very impotant to study the rational points (rational coordinates) since the rational field has many algebraic extensions and this is an important property
In elliptic curves theory Rational is derived from the firleld which the curve is built over
It is very impotant to study the rational points (rational coordinates) since the rational field has many algebraic extensions and this is an important property
Rational in all topics is not different from the one in the theory of numbers.
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