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
Between study group, debate, and chess tournaments there wasn’t much of a social scene around Winchester University in Omaha, Nebraska. The school year at this college was year round, but the students were given a 30 day summer vacation in July. The majority of the students went back home to visit their families during this time. But as juniors at the University Charles, Fredrick, and Stanley, all childhood buddies, decided it was time for a change and that they needed a little more spice in their
Stefanie is a former world’s best ranked female tennis player from Germany. She is considered to be one of the best tennis players of all time. Graf won 22 grand slams single titles, more than any other player has won since the era opened. In 1988, Graf became the only player, to win the "Golden Slam"- getting all four grand slam single titles and Olympic gold medal in the same year. She was the women’s tennis association’s No. 1 player for a record 377 weeks – the longest of any player, she is
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
0.1 abstract In a graph theory the shortest path problem is nding a minimum path and distance between two vertices.The ap- plication in many areas of shortest path algorithms are such as geographical rout- ing, transportation, computer vision and VLSI design involve solving optimiza- tion problems on large planar graphs. To calculate the shortest path we need to know some algorithms like Kruskal's algorithm,Prim's algorithm,Dijkstra's algorithm,BellmanFord's algorithm. These algorithms have some
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
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
States and southern Canada to earn points as well as completing routes designated on the destination tickets. The game itself is not only a fun way to spend hours playing but it is also a good tool to showcase various concepts in graph theory and combinatorics. Graph theory may also be useful in creating or enhancing game play strategies. Set Up and Game Play The original version of the game has a map of the United States and southern Canada with 30 destination tickets. An expansion to the original
Kelvin Silvester R. Calomarde LBYPH11 EB2 Individual Lab Report Title: Graphs and Equations Introduction: The study of physics involve a lot of data to be studied that is attained from experiments. To interpret these data would be important in order to predict a certain phenomenon and explain why and how things work. A model for the data to be interpreted is with the use of graphs and equations. Stewart (2012), states that a graph of an equation in x and y is the set of all points (x, y) in the coordinate
discussed in Physics is the study of free fall, or the effect of the force of gravity on any object. This experiments aimed to investigate the mechanics or the action of gravity an object by analyzing certain vectors related to free fall versus time graphs. These studies on free fall are important if further studies of projectile motion are being made. The objective of the study is to show that velocity, acceleration and distance are related such that one is actually the slope of the other. The
dice. Method: To use 600 dice and roll them up to the decided throw number of 14. This is going to be used as an example to show how the decaying of radioactive material works. Results: A results table for the number of dice remaining graph: Throw number Number of dice remaining Average 1 84 83 90 90 79 82 84.6 2 72 75 71 75 66 74 72.2 3 61 62 59 66 57 61 61.0 4 47 54 50 56 51 52 51.7
gauge wire (0.56mm diameter) and find its resistance when it is at 100cm, 80cm, 60cm, 40cm. Exactly how I will do this will be in my method. I will then plot a graph of resistance (Ω) against length (cm). From the graph I should be able to read off what length is needed to create 1.9Ω. Then finding and using the equation of the graph I will be able to find what length is need to create 28.5Ω. I will then be able at the end to say: " you need ….. cm of ……gauge constantan wire to
Hypothesis: Cars which are older and have got more mileage are generally cheaper, but if I have a vintage (antique) car it will change my graph so it would skew my data as an outlier. Also some cars will depreciate quicker than others in their first year. Plan: Using the data which has been given to me I will compare age to mileage on a scatter graph with price. If I did the investigation by hand I would have chosen a sample of 100 cars of about 20 being picked at random using every 5th
==== I’ve been given 60 pieces of data from pupils, about their height and foot size. I will be using a piece of software called Fathom where I will place this information into a scatter graph, to see whether or not my hypothesis is correct. Fathom will produce a line of best fit on my graph and tell me what my r-value is. The r-value shows the product moment correlation coefficient. I am expecting a positive correlation. To prove that my hypothesis is correct, I am looking for a product
33.5 60 38.5 70 43 80 47 Averaging= I=20 r=14+15 2 R=14.5 Analysing Graph The graph shows my averages of the angle of Incidence against the angle of Refraction. The graph shows a very slight curve. This suggests that my results are not quite accurate. This could be because the angles are not accurate, or in proportion. This means that at the start of the graph, the results are in proportion but as the angles increase, the angles become less proportionate.
Gradient Function Investigation Gradient Function In this investigation I am going to investigate the gradients of the graphs Y=AXN Where A and N are constants. I shall then use the information to find a formula for all curved graphs. To start the investigation I will draw the graphs where A=1 and N= a positive integer. Y=X2 X Height Width Gradient 1 1 0.5 2 2 4 1 4 3 9 1.5 6 4 16 2 8 Looking at the results above I can
length and the extensions are the same in both springs. So this means that T1 = k1x and T2 = k2x. So by knowing this, you get the formula: F = k1x + k2x = x (k1 +k2). So overall, the spring constant for the two springs is k1 + k2. For the graph, my prediction is the same as for a single spring as mentioned earlier but with a different constant. Springs In Series: In this diagram, T1 is the tension in spring 1, and T2 is the tension is spring 2. If I ignore the mass of the 2nd spring
point you are making no profit or loss, so it is when a businesses total revenue covers total costs so it is to show how much output you will have to produce to cover your total costs, within a business. Break even is usually shown in the form of a graph. To work out the break even point of a business you need 3 important components which are: 1. Fixed costs, which are not usually associated with production- these are costs that are at a set price and will not change if income is high or low e.g.
cross on white paper by the solid yellow sulphur precipitate at five different temperatures must be recorded. A graph showing time taken vs. temperature will produce a curve showing the effect of varying temperature on the rate of reaction. The Arrhenius equation ln k = ln A – (Ea / RT) can be shown graphically by plotting a graph of ln (t) against ln (1/T). The gradient of this graph = - (Ea / RT) which can be used to calculate activation energy. The y-intercept of the line = ln A where A is the
The Hertzsprung-Russell Diagram or, the H-R Diagram for short, is a graph which plots stars according to their temperature and absolute magnitude. This graph reveals a pattern, which in fact is quite interesting. The H-R Diagram is named for the two astronomers, Ejnar Hertzsprung and Henry Russell, who discovered this pattern of stars. These two astronomers independently discovered that comparing magnitudes and spectral class (color) of stars yielded a lot of information about them. One key purpose