Non-Euclidean Geometry is a concept that marvels scholars, mathematicians, and contemporary philosophers. This type of geometry diverges from Euclidean principles that are based on flat surfaces. Referring to Non-Euclidean Geometry, the terms Lobachevskian geometry and Riemannian geometry can be used interchangeably. These synonyms are named after the two mathematicians that developed different types of Non-Euclidean Geometry. Lobachevskian geometry emphasizes the concept of parallel lines, demonstrating that parallel lines can diverge or converge rather than running side by side as in Euclidean Geometry. Meanwhile, Riemannian geometry concerns the concept of curved surfaces. Both variations of Non-Euclidean Geometry contribute significantly to developing more profound encounters between mathematical and scientific constructs.