Euclid’s Fifth Postulate and Convergence of Non-Parallel Straight Lines  

作　　者：Kabenge Hamiss[1] 

出　　处：《Advances in Pure Mathematics》2019年第12期1059-1070,共12页理论数学进展（英文）

摘　　要：This paper proves Euclid’s fifth postulate and convergence of straight lines using the formula for the area of trapezoids and assuming straight lines, it derives a general formula for the area of trapezoids involving ratios and we assume that the straight lines determine the nature and area for all the rectilinear figures. Furthermore, this proof is essential in Geometric optics basically in proving and classifying beams of light (wave) that is to mathematically prove the presence of parallel, convergent and divergent beams of light assuming the ray of light is a straight line.This paper proves Euclid’s fifth postulate and convergence of straight lines using the formula for the area of trapezoids and assuming straight lines, it derives a general formula for the area of trapezoids involving ratios and we assume that the straight lines determine the nature and area for all the rectilinear figures. Furthermore, this proof is essential in Geometric optics basically in proving and classifying beams of light (wave) that is to mathematically prove the presence of parallel, convergent and divergent beams of light assuming the ray of light is a straight line.

关 键 词：INTERIOR ANGLE Intersect TRAPEZOID TRIANGLE CONVERGENCE 

分 类 号：O17[理学—数学]