4.3 The Euler characteristic

Subdivisions of surfaces lead to the third number used to classify surfaces, the Euler characteristic.

Definition

The Euler characteristic χ of a subdivision of a surface is

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The world is becoming more and more interconnected. Globalization changes how people consume, work and live almost everywhere on the world. Today, many economic, political, cultural or ecological relationships are not explainable from a national perspective. At the same time, a controversial debate about the consequences of globalization has begun. But what are the main causes for globalization? In what areas it is most prominent? And who are the winners and looser of globalization?
Author(s): Barkemeyer,Künzl

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Rights not set

3.2 Io

Io is one of the most marvellous bodies in the Solar System, but the intense radiation bathing its surface (Figure 2) makes it unlikely that anyone will ever be able to visit. Even robotic spacecraft cannot survive this close to Jupiter for very long, so the Galileo Jupiter orbiter made very few close fly-bys of Io.
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2.2 Population screening for genetic disease: the precedents

Knowing about particular genes, or their effects, also permits screening – the search in a population for persons with certain genotypes that are associated with a particular disease. Thus the test may be offered to one and all. Until now, screening programmes have focused on one gene at a time, or one disease at a time, in cases where a mutated gene poses serious health problems and something can be done for those who are found to carry the mutation. What that something is varies with the
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This free course, Teaching secondary science, will identify and explore some of the key issues around science pedagogy in secondary schools. Through coming to understand these issues and debates, you will reflect on your practice as a science teacher and develop a greater awareness of the wider context of science education and how this affects science in the secondary school curriculumAuthor(s): Creator not set

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July 12 - China's export machine is slowing down, so where are the consumers who were supposed to ride to the rescue of the world's second-largest economy?
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This video shows many different incidents of ball lightning. Ball lightning may be an atmospheric electrical phenomenon, the physical nature of which is still controversial. The term refers to reports of luminous, usually spherical objects which vary from pea-sized to several meters in diameter. It is sometimes associated with thunderstorms, but unlike lightning flashes, which last only a fraction of a second, ball lightning reportedly lasts many seconds. Video is set to music and no words are s
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Define entropy and calculate the increase of entropy in a system with reversible and irreversible processes. Explain the expected fate of the universe in entropic […]

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On this day in 1895, the world's first commercial movie screening takes place at the Grand Cafe in Paris. The film was made by Louis and Auguste Lumiere, two French brothers who developed a camera-projector called the Cinematographe. The Lumiere brothers unveiled their invention to the public in March 1895 with a brief film showing workers leaving the Lumiere factory. On December 28, the entrepreneurial siblings screened a series of short scenes from everyday French life and charged admission fo
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Acknowledgements

This free course was written by Ms Candida Clark

Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence.

The material acknowledged be
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POL335 Session 8 Spring 2012
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Subject Special: Science

In this subject special on science, we focus on a range of podcasts from astronomy to biology, physics to medicine. We feature a few of the podcasts that are listed in the mathematics and science category of our Podcast Directory for Educators. We illustrate some of the wide range of topics that are listed. In
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UPDATE: "Houston, we have a problem!" Moving feeds in Feedburner.
UPDATE: to cut the long story short iTunes /Mac app support basically told me I was 'out of luck'. I did a bit more thinking. My head must have been exceptionally clear today, because I came up with a solution! Now all 'A Spoonful of Russian' media should show up in your podcatcher app. Now I got my podcast tied to the right gmail address, all the dear old subscribers are kept, and iTunes Store reviews/ratings are intact. That reminds me - I can always use a review or two;)
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Acknowledgements

The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.

Grateful acknowledgement is made to the following sources for permission to reproduce material in this course:

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Students learn that two fractions are equivalent if the fractions are the same when they are written in lowest terms. For example, 4/7 and 8/14 are equivalent fractions, because they are both equal to 4/7 when written in lowest terms. Students also learn to find fractions that are equivalent to a given fraction by multiplying the numerator and denominator of the given fraction by the same number. For example, to find fractions that are equivalent to 1/8, multiply the numerator and denominator by
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A group of students at Penn Alexander are hacking parents’ classic warning that video games turn brains to mush. In a course developed by Yasmin Kafai, a professor of teaching, learning, and leadership at the Graduate School of Education (GSE), a group of 12 sixth to eighth graders are working not only to understand how video games work, but to actually create the games themselves. “The goal of the [coding] program is not to turn everyone into a programmer. It’s the same as teaching stud
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