Euler: Mathematician of the Real World Many people have convinced their selves that taking math seriously is not necessary or beneficial to them. Whether you grow up to be a teacher, photographer, or social worker, math will be with you when you carry out the rest of your life. Mathematics is an essential part of life and is woven through the very fabrics of the universe. In fact, a popular phrase that educators in this field like to say is, “math is used every day, in more ways than realized”. In correspondence with this course, college algebra is used in many careers and is in fact, part of the “real world”. To specify, Leonhard Euler is a terrific example of success in mathematics and how mathematics can contribute to other fields. Euler’s legendary skills have provided many achievements in numerous areas of mathematics such as, applying analytical methods to real world problems and geometry, as well as, other subjects such as music theory and astronomy. Leonhard Euler was born on April 15, 1707, right outside the city walls of Basel, Switzerland to Paulus Euler and Margaretha Brucker (Gautschi, 2008). However shortly after, he and his parents moved a short distance away to a town called Riehen (O'Connor & Robertson, 1998). There, his father, Paulus Euler was a minister and studied mathematics under the famous Jakob Bernoulli (Gautschi, 2008). Since Paulus had an interest in mathematics and was quite knowledgeable, he taught Leonhard his first schooling in the subject. From there, Leonhard was sent to a Latin school in Basel around the age of eight, where he lived with his grandmother (Gautschi, 2008). Unfortunately, he learned very little in the school so his father hired him a professional tutor, by the name of Johannes Burckhardt (Gautschi, 2008). Accordingly, Johannes was a young theologian who also expressed enthusiasm for mathematics (Gautschi, 2008). Even though, Leonhard displayed a fond interest in math, his father wanted him to follow his footsteps in the ministry. Therefore, he enrolled into the University of Basel where he took philosophy, at the age of thirteen. Also, taking classes under the mathematician Johann Bernoulli, Euler’s passion for mathematics caught the attention of the professor, and he encouraged him to study the texts on his own (Gautschi, 2008). Even so, “Euler completed his Master's degree in philosophy having compared and contrasted the philosophical ideas of Descartes and Newton” (O’Connor & Robertson, 1998). Euler began his study of theology later that year of 1723 (O’Connor & Robertson, 1998). However, Leonhard felt that he was destined for a career in mathematics rather than, theology. Therefore, with the help of Bernoulli who believed he had great potential, Euler was able to return to his passion in mathematics. Following this, by 1727, the young graduate had a paper in print, “a short article on isochronous curves in a resisting medium”, and had won second place in the Paris Academy contest for best arrangement of masts on a ship (O’Connor & Robertson, 1998). Accomplishing such great things at a young age, Euler applied himself to the Academy of Sciences in St. Petersburg, and expectantly, focused in mathematical science. There, he met the Secretary of the Academy named Christian Goldbach, who was best known for his hypothesis in number theory (Gautschi, 2008). Meeting Goldbach, proved to be a good thing for Euler as Finkel (1897) writes, “he carried the integral calculus to a higher degree of perfection, invented the calculation of sines, reduced analytical operations to greater simplicity, and threw new light on nearly all parts of pure or abstract mathematics” (p.298). Although unfortunately, after a series of health concerns, Euler lost sight in his right eye, ending his time in St. Petersburg. He then, set off to Berlin, accepting an invitation from the Prussian king Frederick II (Gautschi, 2008). Between the time of his invitation, and the time
The idea of swarm intelligence is consequent from the movement of the Ants that collect food from certain places and accumulate into the nest. The ant is selecting the shortest path from source to destination with the association in definite arrangement. The worker’s movement is much larger than the sum of separate activity. The idea of shortest path using swarm intelligence broadly used in circuit switching as well as wireless communication. It is distributed approach where efficiency via specific…
Being one the most astounding formulas in mathematics, Euler’s identity is popularly called God’s equation. Some people also go as far as calling it the mathematical equivalent of Da Vinci's Mona Lisa or Michaelangelo's David.
Named after Leonhard Euler, the formula establishes the deep relationship between trigonometric functions and complex exponential functions.
According to the formula, for any real number x,
In the above formula, e is the base of the natural logarithm…
shortest amount of time.
In order to figure out a logical way of maneuvering the New York City subway system, it is necessary to first understand a little background information on graph theory and different types of paths that can occur. “In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.” (Wikipedia, Graph Theory) Every graph has different aspects that make it unique, however, a graph in…
CLASS : 5 GAMMA
I/C NO :
SCHOOL : SMK DARUL EHSAN
TEACHER : PUAN ROSMAZARAH BT SULONG
Part 1 Question
Part 2 Question
Part 3 Question
As this Additional Mathematics Project Work for 2013 had been completed. I would…