Problem statement:The interior angles sum of a number of Euclidean triangles was transformed into quadratic equations. The analysis of those quadratic equations yielded the following proposition: There exists Euclidean triangle whose interior angle sum is a straight angle. Approach: In this study, the researchers introduced a new hypothesis for quadratic equations and derived an entirely new result. Results: The result of the study was controversial, but mathematically consistent. Conclusion/Recommendations: The researchers politely requested the research community to establish the quadratic equation's hypothesis.
The fifth Euclidean postulate problem in geometry is 2300 years old. This postulate is also known as Euclids parallel postulate. The great mathematicians tried their best to deduce the fifth postulate from the other four postulates. But unfortunately nobody could succeed in this geometrical battle. The studies devoted to this problem led to the origin of two non-Euclidean geometries. The authors resurveyed and established and gave a proof for this problem
Abstract:The origin of geometry dates back 30000(Thirty thousand years) B.C [3] . Euclid of Alexandria (2300 B.C.) complied the Elements which is the first scientific text book. Euclid assumed five postulates. There is no proof for the fifth postulate. Almost all the celebrated mathematicians tried their best to deduce this from the first four postulates. But unfortunately, nobody was successful. Saccheri and Lambert worked on this problem for more than 50 years. The authors start where Saccheri and Lambert failed to obtain the following result/theorem. In a Lambert quadrilateral the fourth angel is the right angle or the lateral sides of a Lambert quadrilateral are equal. This proposition was proved by proof by contradiction.
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