Sets of points that are a certain distance apart

The article continues the cycle ([1] – [15]) of methodological developments by the authors. The article discusses problems related to sets of points whose distances are rational numbers (let's call these sets rational). The study of such sets is related to the solution of Diophantine equations. The relevant tasks can be used when choosing topics for students' research work. The authors draw on their work experience at the Faculty of Information Technology of the MSUPE.

1. KulaninD.,NurkaevaI.M.Ontwogeometricproblemson an extra-mumm.Mathematicsatschool.2019.No.4.pp.35-40.
2. KulaninD.,NurkaevaI.M.Onceagainabout the Mavlo task.Mathematicsatschool.2020.No.2.pp.76-79.
3. KulaninD.,StepanovM.E.,NurkaevaI.M.Propaedeutics of solving extreme problemsin a schoolmathematicscourse.Datamodelingandanalysis.2019.No.4.pp.127-144.
4. KulaninD.,NguyenWuQuang,StepanovM.E.Tangibleobjectivitywithcomputersupport.Datamodelingandanalysis.Scientificjournal.2019.No.4.pp.145-156.
5. KulaninD.,StepanovM.E.,NurkaevaI.M. The role of imaginativethinkinginscientificthinking.Datamodelingandanalysis.2020.Vol.10.No.2Pp.110-128.
6. KulaninD.,StepanovM.E.,NurkaevaI.M.Onvariousapproachestosolvingextremeproblems.Datamodelingandanalysis.2020.Vol.11.No.1.pp.40-60.
7. LunguN.,NorinV.P.,WrittenD.T.,ShevchenkoYu.A.,KulaninE.D.Collection of problemsinhighermathematicswithcontrolpapers.Moscow,2013.Volume2(8thedition).
8. StepanovE.Somequestions of teachingmethods of higher education mathematics.Datamodelingandanalysis.2017.No.1.pp.54-94.
9. KulaninD.,StepanovM.E.From the experience of workinginremotemodeLearningModelinganddataanalysis.2022.Vol. 12.No.3.pp.58-70.
10. KulaninD.,StepanovM.E.Comprehensiveconsideration of mathematicalconceptsas a methodologicaltechnique.Datamodelingandanalysis.2022.vol. 12.No.4.Pp .67-84.
11. KulaninD.,StepanovM.E.Onvisualization of solutions to someextremetasks.Datamodelingandanalysis.2022.vol. 12.No.4.pp.94-104.
12. KulaninD.,StepanovM.E.,Panfilov A.D.,PotonyshevI.S. A systematicapproachto the method of typhlopedagogyon the exampleofmathematicalanalysis problems.Datamodelingandanalysis.2022.vol. 12.No.2.pp.34-82.
13. KulaninD.,StepanovM.E.Computationalexperimentinteachinghighermathematicson the example of numbertheory.Datamodelingandanalysis.2024.Vol.14.No.1.pp.170-195.
14. KulaninD.,StepanovM.E. The use of imagesinteachinghigher education mathematics.Datamodelingandanalysis.2024.vol.14.No.2.C.192-225.
15. KulaninD.,StepanovM.E.Computationalexperimentinteachinghighermathematics.Combinatoricsanditsapplications.Modelingandanalysisdata.2024.vol.14.No.3.C.174-202.
16. SerpinskyPythagoreantriangles.Moscow,StateEducational and PedagogicalPublishing House of the Ministry of Education of the RSFSR,1959.
17. ZyuzkovM.Experimentsinnumbertheory.TomskNTLPublishing House,2019.
18. OreGraphTheory.Moscow,Nauka,1980.
19. AlexandrovS.Introduction to thegeneraltheory of setsandfunctions.Moscow–L.StatePublishing House of Technical and TheoreticalLiterature.1948.
20. PrasolovV.Elements of combinatorialanddifferentialtopology.Moscow,ICNMO,2004.
21. BakelmanYa. Inversion.Moscow,Nauka,1966.
22. MikhelovichSh. Kh. Theory of Moscow,HigherSchool,1962.