Graphs And Polyhedra

 ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

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= Concept Map = Flash

= Textbook =
 * 1) Karnataka text book for Class 10, Chapter 17 - Graphs And Polyhedra


 * 1) NCERT book on Graphs

=Additional Information= | More on Networks | Extending Graph Theory

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 =

Learning objectives

 * 1) To define what is node.
 * 2) to define what is arc
 * 3) To define what is Region
 * 4) 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

Learning objectives

 * 1) To identify Plane Graph
 * 2) 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

Learning objectives

 * 1) Generalization of Euler's formula
 * 2) 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

Learning objectives

 * 1) To Identify even order node
 * 2) To Identify Odd order node
 * 3) Condition for Traversibility
 * 4) 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

Learning objectives

 * 1) Recognize regular and irregular polyhedron
 * 2) Can write differences between regular and irregular polyhedron

Notes for teachers
there can only be 5 platonic polyhedrons.

Activities
Activity No #1 Construction of regular octahedron and recognising th elements of Polyhedrons Activity No #2 Polyhedra_Elements

Learning objectives

 * 1) Recognizes vertexes faces and edges of a polyhedron
 * 2) 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

Learning objectives

 * 1) Can count number of vertexes faces and edges of a polyhedron
 * 2) 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.

http://photonics.cusat.edu/images/koning4.jpg

Image Courtesy : http://mathworld.wolfram.com/KoenigsbergBridgeProblem.html

For solution click here

= Project Ideas =

= Math Fun =

Usage

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