3.1.1 Inserting half-twists

We can insert half-twists into a paper surface whenever a piece of the surface is homeomorphic to a rectangle ABCD with the following properties:

the edges AB and CD of the rectangle map to distinct parts of the boundary of the surface, and the edges BC and DA of the rectangle map to non-boundary points of the surface.

As illustrated in Author(s): The Open University

3 Graph sketching

In Section 2 we describe how the graphs of polynomial and rational functions may be sketched by analysing their behaviour – for example, by using techniques of calculus. We assume that you are familiar with basic calculus and that its use is valid. In particular, we assume that the graphs of the functions under consideration consist of smooth curves.

Click 'View document' below to open Section 2 (16 pages, 200KB).

7.3 Monitoring your progress

Use your records or logbook to provide a reflective commentary on:

  • what you did to help you set up and use information literacy methods and techniques to achieve your goals; for example, what you did to:

     

    • search for information and explore alternative lines of enquiry;

    • use different search strategies and tools effectively;

    • choose criteria and use them to critically ev
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3 Studying languages
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Computer crashes are often the result of viruses, worms or Trojans as unfortunately some internet users want to cause havoc or vandalise your computer. This unit provides a guide to the downsides of living with the Net. Advice on how to deal with these dangers is provided and security issues like spyware and adware are explained. The unit also deals with protecting children online, and provides links to various helpful websites which deal with the problems raised.
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