Graphs And Polyhedra
| Philosophy of Mathematics |
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Concept Map
Textbook
Additional Information
More on Networks
Extending Graph Theory
Useful websites
The document linked below gives few ideas in using story telling as a tool for understanding, interpreting and constructing graphs. Suggestions on how to assist students in making connections between graphs and the real world have also been given here.
Developing stories: Understanding graphs
Other useful websites
- Wikipedia page for Graph Theory
- For More Informations on Platonic Solids
- For interactive Platonic Solids
Reference Books
Click here for DSERT 10 th Text book chapter Graph Theory
Introduction to Graph Theory, By Douglas B.West/
Teaching Outlines
Concept #1 Representation of a Graph
Learning objectives
- To define what is node.
- to define what is arc
- To define what is Region
- To represent a Graph with node, Arc and Regions
Notes for teachers
Here we should remember in any Graph a point which is not represented by letter cannot be considered as NODE
Activities
Activity #1 Introduction to Graphs
Activity #2 Graph Theory
Concept #2 Types of Graphs
Learning objectives
- To identify Plane Graph
- To identify Non-Plane Graph
Notes for teachers
These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.
Activities
Activity No #1
Construction of regular polyhedrons
Activity No #2
Concept #3 Eulers formula for graph
Learning objectives
- Generalization of Euler's formula
- Verification of Euler's formula for Networks
Notes for teachers
These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.
Activities
Activity No #1
Verification of Euler's Formula for Graphs
Activity No #2 Activity on verification of eulers formula
Concept # 4 Traversibility of a graph
Learning objectives
- To Identify even order node
- To Identify Odd order node
- Condition for Traversibility
- Condition for Non- Traversibility of Graph
Notes for teachers
These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.
Activities
Activity No #1 Transversable_Networks
Activity No #2 Eulers formula verification
Concept # 5 Shapes of Polyhedrons
Learning objectives
- Recognize regular and irregular polyhedron
- Can write differences between regular and irregular polyhedron
Notes for teachers
there can only be 5 platonic polyhedrons.
Poly Hydrens
Definition
Activities
Activity No #1
Construction of regular octahedron and recognising th elements of Polyhedrons
Activity No #2
Polyhedra_Elements
[1]
Concept # 6 Elements of Polyhedrons
Learning objectives
- Recognizes vertexes faces and edges of a polyhedron
- Can count number of vertexes faces and edges of a polyhedron
Notes for teachers
These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.
Activities
Activity No #1
Construction of regular octahedron and recognising th elements of Polyhedrons
Activity No #2
Polyhedra_Elements
Concept # 7 Euler's Formula for Polyhedrons
Learning objectives
- Can count number of vertexes faces and edges of a polyhedron
- Verifies Euler's formula for a given polyhedron
Notes for teachers
These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.
Activities
Activity No #1 Activity on Eulers Theorem
Activity No #2 Work sheet on Verification of Eulers Formula for Ployhedrons
Assessment activities for CCE
Check your basic knowledge on Polyhedrons
| Why there are only 5 platonic solids?
Hints for difficult problems
Statement : The Königsberg bridge problem : if the seven bridges of the city of Königsberg (left figure; Kraitchik 1942), formerly in Germany but now known as Kaliningrad and part of Russia, over the river Preger can all be traversed in a single trip without doubling back, with the additional requirement that the trip ends in the same place it began.
Image Courtesy : http://mathworld.wolfram.com/KoenigsbergBridgeProblem.html
For solution click here
Project Ideas
Math Fun
Usage
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