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Surfaces
Science, Maths & Technology

Surfaces

...careful how we count the vertices, edges and faces. The following worked problem provides further illustration. Worked problem 3 Find the Euler characteristic of the subdivision of the projective plane given by Figure 90. [Figure 90] Figure 90Solution We label all the vertices, edges and faces, using the same labels for any that are identified, as in Figure 91. [Figure...
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Level 3: Advanced 20 hrs
Exploring Ovid’s big ideas
History & The Arts

Exploring Ovid’s big ideas

...careful attention to the differences between McCarter and Golding’s translations. Which one do you like best? Write down your answer to this question, and the reason why, in the box below. He strayned oftentymes to speake, and was about to say, “I am Actaeon! Know your Lorde and Master sirs, I pray.” But use of wordes and speech did want to utter forth his mind....
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Level 1: Introductory 6 hrs
Environment: understanding atmospheric and ocean flows
Nature & Environment

Environment: understanding atmospheric and ocean flows

...adult, there are more organisms to produce young in the next generation, who produce more young in the next, and so on. This leads to a population explosion. Economic growth is supposed to work the same way – increased wealth this year allows us to spend and invest to produce more wealth next year, with this continuing year after year. Of course, the sound from the...
View course Environment: understanding atmospheric and ocean flows
Level 1: Introductory 10 hrs
What is Europe?
Society, Politics & Law

What is Europe?

...adult was at least seventy by the end of the century and war, if not organised violence more generally, was a personal experience only for a very small minority of contemporary Europeans. There were clearly different conceptions of Europe and the association it now formed among the different countries of Europe, and differing levels of commitment to the European idea...
View course What is Europe?
Level 1: Introductory 10 hrs
The search for water on Mars
Science, Maths & Technology

The search for water on Mars

...Careful investigation of the size, rounding and distribution of the pebbles led the mission team to conclude that they were deposited by a stream that was knee to hip deep and probably flowed at an average velocity of 0.20 to 0.75 m s−1. In addition to these conglomerates, sandstones and mudstones were found. The fine-grained nature of the mudstones showed that they...
View course The search for water on Mars
Level 1: Introductory 5 hrs
From Brexit to the break-up of Britain?
Society, Politics & Law

From Brexit to the break-up of Britain?

...careful listening. (You may like to make notes in the box below.) Questions to bear in mind while considering the points she makes include: What is the ‘regional’ problem and how should it be understood? Why is it not enough simply to map the economic and social differences between areas of the UK? Can prosperity in one place be understood without recognising its...
View course From Brexit to the break-up of Britain?
Level 1: Introductory 12 hrs
Working with our environment: an introduction
Nature & Environment

Working with our environment: an introduction

...careful definitions, which can always be challenged. Without access to that background information the safest approach is to accept the figures as a reliable guide, but not necessarily to the accuracy given. Since human settlement approximately 700–800 years ago, the indigenous forests, which once covered about 85 percent of the land area, have been reduced from some 23...
View course Working with our environment: an introduction
Level 1: Introductory 11 hrs
Introducing vectors for engineering applications
Science, Maths & Technology

Introducing vectors for engineering applications

...care must be taken to ensure that the answer given by a calculator is correct. Activity 11 Find the magnitude to two decimal places and direction to one decimal place of the following vectors. a. negative three times i plus j b. vector element 1 negative two element 2 zero c. vector element 1 two element 2 four...Introducing vectors for engineering applications: 2.4...
View course Introducing vectors for engineering applications
Level 1: Introductory 5 hrs