Triangulated Polygons Essay -- Mathematics

From the beginning of time there have been many anomalies in humanity. With the advancement of techniques, tools, and knowledge, our understanding of the world aspires to clarify our curiosities. The most beneficial to factors throughout our history would include our knowledge of numbers. Numbers hold great possibilities and bring forth answers to the most complex systems of life. Our mathematics is incorporated into basic aspects of our daily lives, allowing us to unlock our potentials and give keys to uncover the hidden secrets in the universe. There are many applications to mathematics such as triangulating polygons. Triangulation is a surveying technique in which a region is divided into a series of triangular elements based on a line of known length so that accurate measurements of distances and directions may be made by the application of trigonometry. (Company, 2009) Since its discovery, triangulation has lent the world many beneficial advantages. Polygons exist as multi-sided shapes. These shapes can be subdivided into many non-overlapping triangles. These triangles connect corners to corners, creating diagonals that section it off. These sections are called convex hulls. The many uses of algorithms allow anyone to calculate these triangular hulls. The mathematics behind triangulating polygons was originated in Alexandria by the man, Euclides. Euclides was a Greek mathematician who was highly revered as the â€Å"Father of Geometry.† Euclides possessed a mysterious personal life, because his life was not documented and often confused with others. He taught many children mathematics during the reign of Ptolemy. His father and grandfather were thought to be Greek, but this is not certain considering the confusion between him... ...'s Formula. Retrieved from ENRICH: http://nrich.maths.org/1384 Company, H. M. (2009). Triangulation. Retrieved from TheFreeDictionary by Farlex: http://www.thefreedictionary.com/triangulation csunplugged. (2010, October 30). Santa's Dirty Socks (Divide and Conquer Algorithms). Retrieved from Youtube: http://www.youtube.com/watch?v=wVPCT1VjySA lecture, P. T. (1993). Triangulations and Arrangements. McGill University. Math Open Reference. (2009). Euclid. Retrieved from Math Open Reference: http://www.mathopenref.com/euclid.html Suksak, P. S. (2010, November 30). Catalan Numbers Presentation 2. Retrieved from Slide Share: http://www.slideshare.net/PaiSukanyaSuksak/catalan-number-presentation2 Teter, M. (2000, March 15). Sonar a way of seeing sound. Retrieved from Cornell Center for Material Research: http://www.ccmr.cornell.edu/education/ask/index.html?quid=260 Triangulated Polygons Essay -- Mathematics From the beginning of time there have been many anomalies in humanity. With the advancement of techniques, tools, and knowledge, our understanding of the world aspires to clarify our curiosities. The most beneficial to factors throughout our history would include our knowledge of numbers. Numbers hold great possibilities and bring forth answers to the most complex systems of life. Our mathematics is incorporated into basic aspects of our daily lives, allowing us to unlock our potentials and give keys to uncover the hidden secrets in the universe. There are many applications to mathematics such as triangulating polygons. Triangulation is a surveying technique in which a region is divided into a series of triangular elements based on a line of known length so that accurate measurements of distances and directions may be made by the application of trigonometry. (Company, 2009) Since its discovery, triangulation has lent the world many beneficial advantages. Polygons exist as multi-sided shapes. These shapes can be subdivided into many non-overlapping triangles. These triangles connect corners to corners, creating diagonals that section it off. These sections are called convex hulls. The many uses of algorithms allow anyone to calculate these triangular hulls. The mathematics behind triangulating polygons was originated in Alexandria by the man, Euclides. Euclides was a Greek mathematician who was highly revered as the â€Å"Father of Geometry.† Euclides possessed a mysterious personal life, because his life was not documented and often confused with others. He taught many children mathematics during the reign of Ptolemy. His father and grandfather were thought to be Greek, but this is not certain considering the confusion between him... ...'s Formula. Retrieved from ENRICH: http://nrich.maths.org/1384 Company, H. M. (2009). Triangulation. Retrieved from TheFreeDictionary by Farlex: http://www.thefreedictionary.com/triangulation csunplugged. (2010, October 30). Santa's Dirty Socks (Divide and Conquer Algorithms). Retrieved from Youtube: http://www.youtube.com/watch?v=wVPCT1VjySA lecture, P. T. (1993). Triangulations and Arrangements. McGill University. Math Open Reference. (2009). Euclid. Retrieved from Math Open Reference: http://www.mathopenref.com/euclid.html Suksak, P. S. (2010, November 30). Catalan Numbers Presentation 2. Retrieved from Slide Share: http://www.slideshare.net/PaiSukanyaSuksak/catalan-number-presentation2 Teter, M. (2000, March 15). Sonar a way of seeing sound. Retrieved from Cornell Center for Material Research: http://www.ccmr.cornell.edu/education/ask/index.html?quid=260