Imagine that a line on a Cartesian graph is approximately the distance y in feet a person walks in x hours. What does the slope of this line represent? How is this graph useful? Provide another example for your colleagues to explain. The slope of the line represents the speed of the person in feet per hour. This graph is useful because it provides a visual representation of the continuous motion of the person walking, something that could not provided by something like a bar graph. In a bar graph, the sheer number of columns and their shape makes representation of a temporal action cumbersome, whereas in a line graph, the information is represented fluidly, as it is reality. (See Figure 1 for another example.) What is the difference between a scatterplot and a line graph? Provide an example of each. Does one seem better than the other? In what ways is it better? A scatter plot consists of several data points placed on a Cartesian graph that are not connected to each other, where the data is shown as a collection of points. A line graph is an extension of the scatter plot in which the data is connected by straight segments of lines. A scatter plot might be used to analyze the relationship between achievement test scores and income (Figure 2), while a line graph might be used to analyze the distance traveled by a car in minutes (Figure 3). For certain purposes, especially those that involve relating two variables that related by some kind of formula, a line graph is better because it shows the definitive relationship between the two variables, a relationship that, due to the formulaic nature of the relationship, will not change. Scatter plots are best used for other relationships.

Figure 1. Cost of an object (y) and the Year (x) (http://www.westegg.com/inflation/)

Figure 2. Test Scores (y) and Income (x) (Hypothetical)

Figure 3. Distance traveled by a car in meters (y) and Time in minutes (x) (Hypothetical)

...connected graph G, a spanning graph of G that is a tree is called a spanning tree. A spanning tree for an undirected graph G = (V,E) is a graph G’ = (V,E’) such that G’ is a tree. In other words, G’ has the same set of vertices, but edges have been removed from E so that the resulting graph is a tree. This amounts to saying that G’ is acyclic. If G is directed, it means that cycles have been removed. Since a tree with |V|...

...V. Adamchik
1
Graph Theory
Victor Adamchik Fall of 2005
Plan
1. Basic Vocabulary 2. Regular graph 3. Connectivity 4. Representing Graphs
Introduction
A.Aho and J.Ulman acknowledge that “Fundamentally, computer science is a science of abstraction.” Computer scientists must create abstractions of real-world problems that can be represented and manipulated in a computer. Sometimes the process of abstraction is simple. For example, we use a logic to...

..."Cartesian" is named after the French mathematician and philosopher Rene Descartes, who lived from 1596 until 1650. Cartesian diver lab is used commonly in scientific experiments to illustrate principle of buoyancy. The objective of this Cartesian diver lab is to demonstrate Pascal's law and Archimedes' principles.
Observation is the key to conduct this experimental study of the Cartesian diver. First a 2-liter bottle is filled with...

...had its roots in the work of two mathematicians, Paul Erdos and Alfred Renyi. Their work suggested that systems such as communications could be effectively modelled by connecting nodes with randomly placed links. Their simple approach revitalised graph theory and led to the emergence of the field of random networks.
An important prediction of random network theory is regardless of the random placement of links most nodes will still have approximately the same number of...

...LAB # 1
Graph Matching
Principles of Physics I Laboratory
Breanna Wilhite
Introduction
In this lab motion will be represented by graphs that plots distance and velocity vs. time. A motion detector will be used to measure the time it takes for a high frequency sound pulse to travel from the detector to an object and back. By using this method sound can determine the distance to the object, or its position. This device will determine in what direction the...

...Graphs and Function
What is the relation between the graphs and function and how was it applied in the real world?
Graphs are frequently used in national magazines and newspaper to present information about things such as the world’s busiest airports (O’Hare in China is first, Heathrow in London is sixth), about the advertising-dollar receivers in the United States (newspaper are first, radio is fourth) and about NCAA men’s golf team title...

...Baker Machine Company
Layout
Problem 3.4. (Summary)
Baker Machine is considering two alternative layouts. We will compare the Weighted-Distance Scores using rectilinear distance* of the two block plans to determine which alternative layout is better.
Alternative Layout 1 Alternative Layout 2
3 | 6 | 4 |
5 | 1 | 2 |
3 | 1 | 4 |
5 | 6 | 2 |
* rectilinear distance – the distance between two points with a series 90-degree turns, as along city blocks
Data
Baker Machine...