About This Chapter
Paths & Circuits - Chapter Summary
In this chapter, you can explore different theories of circuits and paths. You will start with the earliest theories by Euler that relating to paths and circuits. Move from these theories to the mathematical proofs he used to model them with. Next you can explore the contributions of William Rowan Hamilton and different methods to find the most efficient path of a circuit. When you have completed this chapter, you should be able to:
- Identify the contributions made by Euler
- Explain how Euler circuits and paths can be modeled mathematically
- Discuss the findings of William Rowan Hamilton
- Assess weighted and complete graphs using Hamilton circuits
- Identify different methods for finding the most efficient path for a circuit
All of our lessons were created by professional instructors and include an illustrated video. Video tags, available in your Timeline, allow you to quickly move between lessons and seek individual points within a lesson, making it easy to review confusing points. The Dashboard on your account page allows you to study whenever you find the time, using your phone, tablet or computer.
1. Euler Paths and Euler's Circuits
Watch this video lesson, and you will see how you can turn a math problem into a challenging brain game. Learn what it means for a graph to be Eulerian or semi-Eulerian.
2. Mathematical Models of Euler's Circuits & Euler's Paths
Watch this video lesson to see how Euler paths and circuits are used in the real world. Learn how to solve real-world problems by drawing a graph and finding Euler paths and circuits.
3. Hamilton Circuits and Hamilton Paths
After watching this video lesson, you will be able to determine how many Hamilton circuits a particular graph has, as well as find Hamilton circuits and paths in these graphs. Then, check out our quiz questions to test your new knowledge!
4. Assessing Weighted & Complete Graphs for Hamilton Circuits
Watch this video lesson and you will discover how to find a Hamilton circuit in a weighted graph. You'll also learn how to find the number of Hamilton circuits in a complete graph.
5. Methods of Finding the Most Efficient Circuit
After watching this video lesson, you will understand several ways in which you can solve the famous traveling salesman problem. You'll also learn the drawbacks to each solution method.
Earning College Credit
Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.
To learn more, visit our Earning Credit Page
Transferring credit to the school of your choice
Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.
Other chapters within the VCE Further Mathematics: Exam Prep & Study Guide course
- Population & Samples
- Categorical Data Representation
- Numerical Data Representation
- Data Distribution
- Correlation & Causation in Math
- Non-Causal Relationships in Statistics
- Linear Relationships
- Time Series Data
- Recursion & Financial Modeling
- Concepts of Financial Mathematics
- Matrices Overview
- Graphs & Networks
- Problem Solving With Networks
- Geometric Solids
- Measurement & Trigonometry
- Spherical Geometry
- Applications of Spherical Geometry
- Graphs & Relations
- Linear Programming Overview
- VCE Further Mathematics Flashcards