Introduction to vertex-edge graphs tutoring: Vertex-edge graph is a very interesting and important part of discrete mathematics. The graphs have group of shapes or objects called as vertices and other group whose elements are called as nodes or edges. The node or edge having the same vertex it’s starting and ending both vertices is known as self-loop or simply a loop. If there is one or more than one edge is connecting a given pairs of vertices then they are called as parallel type edges. Let
Orly Katz Mrs.White IB Pre-Calculus SL 18 November 2013 Softball vs. Math The sport of softball has been played since the 1800’s, when it was first invented by George Hancock. As the game developed through the years, it became evident to not only the players, but the spectators as well, that mathematics was a crucial aspect of the beloved sport. As a softball player for many years, one begins to see the connections between the two very clearly. When investigating the degree of importance math has
Graph Theory: The Four Coloring Theorem "Every planar map is four colorable," seems like a pretty basic and easily provable statement. However, this simple concept took over one hundred years and involved more than a dozen mathematicians to finally prove it. Throughout the century that many men pondered this idea, many other problems, solutions, and mathematical concepts were created. I find the Four Coloring Theorem to be very interesting because of it's apparent simplicity paired with it's
In order to define and establish what graph theory is, we must first make note of its origin and its basis within the broad subject of mathematics. Graph theory, a smaller branch in a large class of mathematics known as combinatorics, which defined by Jacob Fox as, “is the study of finite or countable discrete structures.” Areas of study in combinatorics include enumerative combinatorics, combinatorial design, extremal combinatorics, and algebraic combinatorics. These subfields consist of the counting
The Mathematics of Map Coloring The four-color conjecture has been one of several unsolved mathematical problems. From 1852 to this day, practically every mathematician has studied the problem long and hard, but to no avail. The conjecture looks as though it has been solved by Wolfgang Haken and Kenneth Appel, both of the University of Illinois. They have used computer technology to prove the conjecture. The calculation itself goes on for about 1200 hours. The staggering length of the computation
CHAPTER 1 INTRODUCTION 1.1 Motivation The performance of the single core processor has hit the wall because of power requirements and heat dissipations. Then Hardware industry started creating multicore CPUs. Although, they can compute millions of instructions per second, there are some computational problems that are so complex that a powerful microprocessor needs years to solve them. To build more powerful microprocessors requires an expensive and intense production process. Some computations
Art And Mathematics:Escher And Tessellations On first thought, mathematics and art seem to be totally opposite fields of study with absolutely no connections. However, after careful consideration, the great degree of relation between these two subjects is amazing. Mathematics is the central ingredient in many artworks. Through the exploration of many artists and their works, common mathematical themes can be discovered. For instance, the art of tessellations, or tilings, relies on geometry
Tree definitions If you already know what a binary tree is, but not a general tree, then pay close attention, because binary trees are not just the special case of general trees with degree two. I use the definition of a tree from the textbook, but bear in mind that other definitions are possible. Definition. A tree consists of a (possible empty) set of nodes. If it is not empty, it consists of a distinguished node r called the root and zero or more non-empty subtrees T1, T2, …, Tk such that
12 vertices, 30 edges Many people wonder why there should be exactly five Platonic solids, and whether there is one that has not been found yet. However, it is easy show that there must be five and that there cannot be more than five. At each vertex, at least three faces must come together, because if only two came together they would collapse against o... ... middle of paper ... ...ere derived strictly from careful observation and had no theoretical basis. However, about 30 years after Kepler
is equal to 0, there is 1 real solution. The vertex of a quadratic function is lowest or highest point on a parabola. The x-coordinate can be found using -b/2a then used to find the other variable in the original equation. I also learned that the axis of symmetry is the x-value of the vertex or midpoint of the two x-intercepts. I have also revisited similar word problems where I have to determine the variables, create a function, solve for the vertex using -b/2a, and using that to solve for the other
3.6 The Viterbi Algorithm (HMM) The Viterbi algorithm analyzes English text. Probabilities are assigned to each word in the context of the sentence. A Hidden Markov Model for English syntax is used in which the probability of the word is dependent on the previous word or words. The probability of word or words followed by a word in the sentence the probability is calculated for bi-gram, tri-gram and 4-gram.Depending on the length of the sentence the probability is calculated for n-grams [1]. 3
The bridges of the ancient city of Königsberg posed a famous and almost problematic challenge a few centuries ago. But this isn’t just about the math problem; it’s also a story about a famous Swiss mathematician named Leonhard Euler who founded the study of topology and graph theory by solving this problem. The effects of this problem have lasted centuries, and have helped develop several parts of our understanding of mathematics. We don’t hear too much about Euler, but he is one of the most important
Introduction In Yorba Buena high school, English Language Learning (ELL) student face obstacles connecting with the textbooks and comprehending the academic content. Section 10.1 of the Algebra 1 textbook (Larson, Boswell, Kanold & Stiff, 2007) is analyzed for comprehensibility and strategies to support students to connect with the text at intellectual level (Vacca, Vacca & Mraz, 2011). The chapter ten of the textbook will be thought at a tenth grade class during the week of March 11, 2012. Most
linear function. Thus by determining my slope I’m able to find my average rate of change for a linear function. Next I learned how to find the vertex of a quadratic function with the formula of vertex=-b/2a and from there I’m able to identify the axis of symmetry. From that point I was able to build quadratic functions from verbal math problems including the vertex formula, which is useful to solve parts of word problems. When it comes to solving inequalities, I need two points to pick a point in between
option to get promotion earlier. The only way to get the promotion to the secretary is the regular promotion process on the basis of seniority in the job experience in the post of jo... ... middle of paper ... ...eight of a single tree before. The Vertex provides both the tree height and location of the tree in just two clicks. This instrument is new for all the foresters who have been working here. Once, my director general called me in his cabin and asked me whether I could operate the LINTAB, a
Projectile motion: mathematics SL IA Dhruv Chavan Rationale: This idea was chosen due to my background in sports. I have played basketball for the past 6 years 2 of which have been in Raha. Basketball is a sport which involves many aspects of mathematics, the main one being trigonometry. I have found that many times during the game I am required to shoot the ball from distances that exceed the three-point line and therefore require more power in order for the ball to reach the rim. In most games
straight line and a circle, and the straight line is moved around the circumference of the circle while also always passing through a fixed point at a distance away from the circle. The parts formed are labeled the upper nappe, the lower nappe, and the vertex, (Prime, 1) as described in the diagram below in diagram 1: The cone is then used with the help of a right plane to form the different circles, parabolas, ellipses, and hyperbolas, as shown below in diagram 2 on the next page. Taking a flat plane
Conic sections are used all over the world. Conic sections are used in things such as bridges, roller coasters, stadiums, and other objects. A conic section is the intersection of a plane with a cone. The changes in the angle of the intersection produce a circle, ellipse, parabola, and hyperbola. All the types of conic sections can be identified using the general form equation. The general form equation is x2+Bxy+Cy2+Dx+Ey+F=0. Using the general form equation can help identify each type of conic
The Sierpinski Triangle Deep within the realm of fractal math lies a fascinating triangle filled with unique properties and intriguing patterns. This is the Sierpinski Triangle, a fractal of triangles with an area of zero and an infinitely long perimeter. There are many ways to create this triangle and many areas of study in which it appears. Named after the Polish mathematician, Waclaw Sierpinski, the Sierpinski Triangle has been the topic of much study since Sierpinski first discovered it in
produced. The definition of a cone includes the surface generated by a straight line that moves so that it always intersects the circumfrence of a given circle and passes through a given point not on the plane of the circle. The point, called the vertex of the cone, divides th... ... middle of paper ... ...t a polar equation for the ellipse. In defining the quality , our polar equation then becomes ; since , we have  and thus  Because a , b , and f must be positive lengths, the quantity