3 Pie charts and bar charts The data set in Table 7 (section 1.8) comprised non-numerical or categorical data. Such data often appear in newspaper reports and are usually represented as one or other of two types of graphical display, one type is called a pie chart and the other a bar chart; these are arguably the graphical displays most familiar to the general public, and are certainly ones that you will have seen before. Pie charts are discussed in section 2.2 and bar charts in section 2.4. Some problems
2.2 Geometric shapes – quadrilaterals 1.3.2 Angles on a line If several angles make up a half turn, then the sum of those angles must be 1.3.1 Angles at a point Another useful property to remember is that one complete turn is 360°. This means that when there are several angles making up a complete turn, the sum of those angles must be 360°. For instance, if the angles turned by a Big Wheel at a fairground as it picks up passengers were α, β, γ and δ as shown in the diagram below, then α + β + γ + δ = 360°. 1.3 Angles, points and lines Very often, angles in a shape are determined by the geometric properties of that shape. For example, a square has four right angles. So, when you know a shape is a square, you do not need to measure its angles to know that they are 90°. The rest of this section will look at the properties of shapes that enable you to deduce and calculate angles rather than measure them. You may like to add these properties to your notes. Try some yourself 1.2 How to measure an angle To measure an angle you need a protractor. The protractor shown here is a semicircle that is graduated to measure angles from 0° to 180°. It is also possible to buy circular protractors that measure angles from 0° to 360°. Try some yourself What angles do the hour hand and the minute hand of a clock turn through in five hours? Every hour the minute hand turns th 1.1 Angles, notation and measurement In everyday language, the word ‘angle’ is often used to mean the space between two lines (‘The two roads met at a sharp angle’) or a rotation (‘Turn the wheel through a large angle’). Both of these senses are used in mathematics, but it is probably easier to start by thinking of an angle in terms of the second of these – as a rotation. The diagram below shows a fixed arm and a rotating arm (with the arrow), which are joined together at O, forming an angle between th Learning outcomes After studying this course, you should be able to: understand geometrical terminology for angles, triangles, quadrilaterals and circles measure angles using a protractor use geometrical results to determine unknown angles recognise line and rotational symmetries find the areas of triangles, quadrilaterals and circles and shapes based on these. Acknowledgements All written material contained within this course originated at the Open University Course image: HÃ¥kan Dahlström in Flickr made available under Creative Commons Attribution 2.0 Licence. Don't miss out: If reading this text has inspired you to learn more, Keep on learning   There are more than 800 courses on OpenLearn for you to Conclusion This free course provided an introduction to studying Mathematics. 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. 4.4 Self-assessment questions and problems Find the distance between the numbers 2 − i and 1 + 3i. 2.1 Introduction In this section we shall define the complex number system as the set R × R (the Cartesian product of the set of reals, R, with itself) with suitable addition and multiplication operations. We shall define the real and imaginary parts of a complex number and compare the properties of the complex number system with those of the real number system, particularly from the point of view of analysis. 3.5.1 Try some yourself Answer the following questions (a) What is 40% as a fraction? (b) What is  2.2.1 Try some yourself A recipe for four people calls for 2.1 Introduction Proportion is another way of expressing notions of part and whole. You might say that the proportion of village inhabitants who are children is a quarter, or that the proportion of fruit juice in the punch is two thirds, or that the proportion of sand in the concrete is three quarters. All these examples involve the fractions 1.5.1 Try some yourself Which is greater, 1.2 minutes or 70 seconds? There are at least three ways of answering this: 1.5 Speeds Speed is the ratio of distance travelled to time taken. A runner's speed may be quoted in metres per second, miles per hour or kilometres per hour. The units are given as:    unit of distance per unit of time. When you have a distance covered (such as a mile) and a time taken (such as four minutes) the average speed is defined as
× 360° = 180°. Therefore, in the following diagram, α + β + γ + δ = 180°.
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