4.6 The Classification Theorem

In this subsection we state the Classification Theorem for surfaces, which classifies a surface in terms of its boundary number β, its orientability number ω and its Euler characteristic χ, each of which is a topological invariant – it is preserved under homeomorphisms.

Let us remind ourselves of these three numbers.

  • A surface may or may not have a boundary, and, if it does, then the boundary has finitely many disjoint pieces. The nu
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Akiane Kramarik
She started drawing at age 4, painting at 6, and writing poetry at 7. Now, Akiane Kramarik is one of the most sought after young artists of her time -- selling works for thousands, even tens of thousands of dollars. Akiane says she was taught by God. She's gained fame appearing on CNN and the Oprah Winfrey Show. In this Conversations, we talk with this gifted teenager about her art, her inspiration, and how she is using her craft to help others instead of just get rich.
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Teaching and learning in diverse university settings: analytic frameworks for integrating different
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This short film features ligers at a German Zoo. (Ligers are only bred and raised in captivity. Scientists are doubtful that a liger could exist in the wild.) Run time 01:22.
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The Frog Prince Part 4

This is part 4 of 11 of the very cute musical / movie, The Frog Prince, featuring many great actors and actresses from the 1980's.  If you enjoy musicals, you will enjoy this movie.

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1.3.10 Choosing The Right Tool For The Job

Before searching it is always a good idea to check what the source you have chosen covers to make sure it will unearth information that matches your search need (you will notice that all the resources we’ve covered in this guide have short descriptions to enable you to decide which to use). Some of the decision makers, depending on the context of your search might be:

  • Does it have full text?

  • Does it cover the right subject?


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The Fourth Revolution: the global race to reinvent the state [Audio]
Speaker(s): John Micklethwait, Adrian Wooldridge | Is Britain falling behind in the global race to reinvent the state? Britain has led previous attempts to reinvent the state, from the Hobbesian security revolution of the 17th century, to the liberal, meritocratic revolution of the 19th century, to the welfare revolution of the early 20th century. We are now embarked on a new revolution, driven by IT, unsustainable debts and the rise of emerging markets. But Britain is much less well placed to l
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Anna Birbraer, who was born in 1927 in Litin and lived there during the war years, tells about the monument erected at the site where children from Litin, the vast majority of whom were Jewish, were murdered in 1942. http://www.yadvashem.org//untoldstories/database/commemoration.asp?cid=752
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2.4 The atmosphere and polar ice

David A. Rothery Teach Yourself Planets, Chapter 6, pp. 66-75, Hodder Education, 2000, 2003.

Copyright © David Rothery

The Moon's atmosphere is almost as insubstantial as Mercury's, and probably has much the same origin. The Clementine mission returned our first clear views of the lunar poles, showing sites in particular near the south pole that are permanently in shadow, and which could therefore be places where ice might accumulate (Figure 1). Clementine's
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土曜市民セミナー「男らしさの神話と実話」の映像を公開しました。iTunes
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Acknowledgements

The material below is contained in chapter 3 of Economics and Economic Change Microeconomics (2006) (eds) Graham Dawson, Maureen Mackintosh and Paul Anand, which is published by Pearson Education Limited in association with The Open University. Copyright © The Open University.

The material acknowledged below is Proprietary, used under licence and not subject to Creative Commons Licence (see Author(s): The Open University

Virtual Maths, Density, Mass, Volume calculator
Interactive simulation, density, mass, and volume calculator
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Conclusion

This free course provided an introduction to studying education. It took you through a series of exercises designed to develop your approach to study and learning at a distance and helped to improve your confidence as an independent learner.


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4.7 Has telephone design changed over time?

As you can see from Figure 5 the design of the telephone has changed considerably over its lifetime, reflecting the improvements in technology, materials, components and manufacturing processes. Figures 1(a) to (f) show some of the early progress.
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History of Religions in America - Introduction
This video is the introduction and first part to the interview to Dr. Brekus. There is a list of all the topics to be treated in the interview, from the origins of religions in the colonies on and Dr. Brekus starts by describing what protestants in the colonies were like and what they did.  
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Alessandro Profumo: the need for transparency and new behaviours in finance
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Communicating India's Soft Power: Buddha to Bollywood
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In lesson 8 of One Minute Romanian you will learn to count from one to ten. Remember - even a few phrases of a language can help you make friends and enjoy travel more. Find out more about One Minute Romanian at our website - http://www.oneminutelanguages.com. One Minute Romanian is brought to you by the Radio Lingua Network and is ©Copyright 2008.Author(s): No creator set

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