aspg-24-1130-1791482518 20261008180158 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6430 2771-6449 2022 3 1 Prem Kumar Singh Department of Computer Science and Engineering, Gandhi Institute of Technology and Management Visakhapatnam, Andhra Pradesh 530045, India There are several mathematical theorem and other equation which is used frequently. However many researchers or scholar unable to prove them mathematically. One of the famous example is Pythagrous theorem, Budhayana, Pingala, Fibonacci series or even (a+b)2=a2+b2+2ab. It is indeed requirement to understand the basic proof of thiese mathematical theorem and its contradictory. This paper tried to provide some basic proof for these famous theorem and its relations with existing approaches for various applications. 2022 39 53 1130 https://creativecommons.org/licenses/by/4.0/ 10.54216/JNFS.030105 https://www.americaspg.com/journal/24/article/1130 https://www.americaspg.com/storage/1482.pdf