The taxicab radian and investigations into taxicab geometry
Jalen Ball Mentor: Manouchehr Misaghian Department of Mathematics Introduction: I was tasked with investigating two topics and writing the results as a paper with the help of my professor. The two topics are: the taxicab radian and investigations into taxicab geometry Materials and Methods; The entirety of the materials used have been scholarly articles related to Euclidian and taxicab geometry and trigonometry. Although our research is related to Taxicab geometry, comparisons to Euclidian geometry is where much of our progress is made and finding new questions to answer. The established methods for researching mathematics used in this project are straightforward. I have referenced a paper published by the University of Hawaii titled "How does one do mathematical research" by E. Lee Lady. He notes that there are two types of questions to answer: Open-ended and closed-ended. During this project, we have broken the open-ended questions down into closed-ended questions. For instance, before we can write an introduction into the Taxicab radian (open-ended), we must first confirm previously theorized concepts of the taxicab angle, asking ourselves and proving if they are true (closed-ended). Results and Discussion: At this point in our research, we are focusing on confirmation of previously theorized concepts in the area of Taxicab trigonometry to write an introduction, such as confirming that and understanding why the taxicab unit circle has a circumference of 8 units, that the value of pi in taxicab trigonometry is 4, and the value of cosine and sine. Summary: After confirming previously theorized concepts related to the taxicab radian, we will use the information from which we have confirmed the validity to write an introduction into taxicab radian (typically denoted t-radian) and investigate related theories to taxicab trigonometry such as Taxicab Butterfly Theory. Dr. Manouchehr Misaghian is an Associate Professor of Mathematics with research interests in algebraic number theory, geometry, and topology. Jalen Ball is a junior majoring in mechanical engineering with a minor in mathematics. References: 1. Goland, L. (1990) "Karl Menger and Taxicab Geometry", Mathematics Magazine, 63 (5), pp 326327. 2. Greenberg, Marvin Jay, (2008) "Euclidean and Non-Euclidean Geometries", 4th, edition, Freeman and Company, New York. 3. Krause, E.F. (1986), "Taxicab Geometry, An adventure in Non-Euclidean Geometry", Dover Publications, New York. 4. Graham R., Yao F.; A Whirlwind of Computational Geometry, The American Mathematical Monthly, Vol. 97, No. 8, Oct (1990), pp. 687-702.
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