# The A to Z of mathematics a basic guide - Sidebotham T.H.

ISBN 0-471-15045-2

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Acute-angled Right-angled Obtuse-angled

References: Axis of Symmetry, Equilateral Triangle, Isosceles Triangle, Rotational Symmetry. SCATTER DIAGRAM

A scatter diagram is used in statistics to see if two variables are related to each other. The two variables are the two coordinates of a point, and the points are plotted on a Cartesian graph. A scatter diagram is used when both sets of data are continuous and when one set of data does not seem to be dependent on the other. This means that there is not a formula connecting the two sets of data. If the two sets of data were related by a formula, then a line graph would be drawn, instead of a scatter diagram. The processes involved in drawing a scatter diagram are outlined in the following example.

Example. Bill is a math teacher and decided to measure the heights (H) in meters and weights (IT) in kilograms of 24 boys in his class to see if there was a correlation between the two variables. The results of his measurements were recorded in a table.

H w 1.30 50 1.34 1.36 1.36 50 50 52 1.38 53 1.40 54 1.42 54 1.42 55 1.44 1.46 1.48 56 55 56 1.48 58 1.50 57

H w 1.52 58 1.53 1.54 60 62 1.56 62 1.58 61 1.62 62 1.66 64 1.66 1.68 65 66 1.74 68 1.80 72

Using height on the horizontal axis and weight on the vertical axis, he plotted the 24 points. For example the first two points to be plotted on the graph are (1.30, 50) and (1.34, 50). See the figure. The broken axes indicate they do not start at (0, 0).

SECOND 403

If there is a good correlation between H and W, the points should roughly lie on, or near, a straight line. This has proved to be the case with Bill’s investigation. As a result of this investigation Bill can state that the heights of students in his class are related to their weights. In other words, there is a strong correlation between the heights and weights of students in his class. A straight line of “best fit” is drawn through, or near, as many points as possible, trying to get about the same number of points on either side of this line. If the points on the graph do not lie close to a line, but seem to be randomly scattered, then we assume there is not a correlation between the two variables H and W.

References: Cartesian Coordinates, Random Sample, Statistics.

SCIENTIFIC NOTATION

Reference: Standard Form.

SCORE

This is a set of 20. For example, a score of soldiers is a set of 20 soldiers.

SECANT

Reference: Chord.

SECOND

A unit of time.

References: CGS System of Units, Système International d’Unités.

404 SECTOR OF A CIRCLE

SECOND

A second is a very small unit of angle measure. The angle of 1 second is ^ of 1 minute, and the angle of 1 minute is ^ of 1 degree. There are 360 degrees in a full turn.

Reference: Degree, Minute.

SECTION

Reference: Cross Section.

SECTOR OF A CIRCLE

A sector is that part of a circle that lies between two radii OA and OB and the arc AB, as shown in figure a. The shaded region OAB is a sector of the circle that has its center at the point O. The remainder of the circle that is not shaded is also a sector of the same circle. To distinguish between the two sectors, the smaller sector is called the minor sector and the larger sector is called the major sector. The correct way to cut up a pizza is to cut it up into sectors, one sector for each person.

B

Example. Jo bought a family-size pizza. Her son Luke measures the diameter of the pizza to be 44 cm. Jo cuts the pizza into five equal pieces, one for each member of her family. What is the area of each piece?

Solution. If the diameter is 44 cm, then the radius of the pizza is R = 22 cm (see figure b). There are five equal pieces of pizza, so one piece has an area of | of the

SEMICIRCLE 405

area of the whole pizza. Write

A = 7tR2 Formula for the area of a circle

Therefore

Area of one piece = 5 x ttR2 There are five equal pieces in the pizza

= | x 7r x 222 Substitute R =22

= 304 to nearest whole number

The area of each piece of pizza is 304 cm2.

A word often confused with sector is segment. The chord of a circle divides the circle into a minor segment and a major segment (see figure c). The diameter divides the circle into two congruent half-circles called semicircles. The correct way to cut up a pizza is into sectors and not into segments!

(c)

References: Arc Length, Area, Chord, Circle, Geometry theorems, Perimeter, Radian, Radius, Semicircle.

SEGMENT OF A CIRCLE

Reference: Sector of a Circle.

SELECTION

Reference: Combinations.

SELLING PRICE

Reference: Cost Price.

SEMICIRCLE

A diameter of a circle divides the circle into two equal sectors, and each sector is called a semicircle.

406 SEPTAGON

Example. Pat loves fans and has a particular favorite. One day she opens out her favorite fan into the shape of a semicircle (see the figure). Her son David measures the diameter of the fan to be 27 cm. Calculate the area and perimeter of the fan.

Solution. The area of the fan will be half the area of the full circle of diameter 27 cm. Write

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