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

ISBN 0-471-15045-2

**Download**(direct link)

**:**

**47**> 48 49 50 51 52 53 .. 126 >> Next

DOMAIN

References: Cartesian Coordinates, Correspondence.

DOMINO

Reference: Polyominoes.

DOT PLOT

This is a graph that is used in statistics and consists of vertical lines of dots to show the frequencies instead of columns, as in the bar graph. An example of a dot plot is included in the following example.

Example. The following frequency table shows how 20 people in Jacob’s office travel to work. Draw a dot plot graph to display these data.

Dodecahedron

Net for dodecahedron

Method of travel Frequency

Car

7

Cycle

2

Train

5

Walk

6

Solution. In the figure each of the methods of travel has a column of dots, and each dot in this example represents one student. This scale needs to be included. The horizontal axis must be labeled and the graph given a title.

166

DUODECIMAL

Types of Transport to Work

Scale: • = 1 person

Car Cycle Train Walk Type of transport

References: Bar Graph, Frequency Table, Statistics.

DUODECIMAL

Sometime called duodenary. Duodecimal is a number system based on 12 and powers of 12. It uses 12 digits for counting, whereas the decimal (denary) system of counting uses 10 digits, because it is based on 10. The digits used in base 12 are {0, 1, 2, 3,4, 5, 6,7, 8, 9, t, e}, where t is ten and e is eleven. Special symbols for ten and eleven are needed, because the units column goes up to eleven, and 10 and 11 cannot be used, because they occupy two columns.

The column headings for the duodecimal system are powers of 12 (compared with the decimal system, which has powers of 10); five of the column headings, expressed in base 10 numbers, look as follows:

124 = 20,736 123 = 1728 1 22 = 144 1 21 = 12 Units, 1-e

There are present-day applications of the duodecimal system:

♦ 12 eggs in one dozen, 12 dozen in one gross

♦ 12 months in 1 year

♦ 12 inches in 1 foot

♦ 12 hours before noon and 12 hours after noon

References: Binary Numbers, Decimal System, Denary Numbers, Digit.

E

EAST

References: Angle, Bearings.

EDGE

An edge is a straight line where two planes of a three-dimensional polyhedron meet. A plane of a solid is a flat surface, and a vertex is a point where three or more planes meet. The side of a polyhedron is sometimes called an edge. The polyhedron shown in figure a is a square-based pyramid. It has eight edges, five planes, and five vertices.

There is a formula connecting the number of edges (E), the number of faces (F), and the number of vertices (V) of three-dimensional polyhedra. This formula is called Euler’s formula, named after the man who discovered it. The formula is

Example. Verify that Euler’s formula is true for a three-dimensional triangular

♦An edge, which is where two planes meet

(a)

A vertex, which is a point where three planes meet

F + V = E + 2

prism.

167

168 ELEVATION

Solution. Figure b is a sketch of the prism. The formula to verify is F+V=£ +2

F + V =5 + 6 There are 5 faces and 6 vertices

£ + V = 11

£ + 2 = 9 + 2 There are 9 edges

£ + 2 = 11

.-.£ + + = £ + 2 Each side of the formula is equal to 11

(the symbol denotes “therefore”)

References: Euler’s Formula Plane, Polyhedron, Prism, Pyramid, Vertex.

ELEVATION

An elevation is a view, drawn accurately to scale, from the front, side, or back of an object.

Example. Draw the front, side, and back elevations of the nine blocks in figure a. The blocks are drawn on an isometric grid.

Solution

1

1 2

1 3

1

2 1

2 1 1

1

2 1

3 1

Front

elevation

(a)

Side

elevation

Back

elevation

In the solution the squares are numbered to indicate how many blocks are positioned in that particular row. A plan view from above can also be drawn. To draw this view imagine you are positioned at the front of the blocks, looking down on them (see figure b).

ENDECAGON

169

2

3 2

(b)

References: Angle of Elevation, Isometric, Plan.

ELIMINATION

This is a method of solving simultaneous equations.

Reference: Simultaneous Equations.

ELLIPSE

An ellipse looks like a “flattened circle” (see figure a). A common name for an ellipse is an oval, but this is not a word used in mathematics. An ellipse has two axes of symmetry, and the order of rotational symmetry is two. The ellipse is important in science and mathematics because planets move in elliptical orbits around the sun.

One method of drawing an ellipse is to get a length of string and join its ends together to form a loop (see figure b). Place a piece of paper on a drawing board and insert in the paper two thumb tacks placed sufficiently far apart so that when the string is looped around them it is slack. Place a pencil in the loop and with it pull the string taut. Now move the pencil, keeping the string taut, and the shape traced out by the pencil will be an ellipse.

Reference: Conic Sections.

ENDECAGON

This is an 11-sided polygon, which may also be called a hendecagon. The angle sum of the endecagon is given under the entry Polygon.

(b)

170 ENLARGEMENT

ENLARGEMENT

This is sometimes called a dilation, or a magnification. An enlargement is one of the geometrical transformations that occurs in everyday life at the movie theater when the film is projected, and enlarged, onto a screen by passing light rays through the film. Using this example, we can say that the source of light in the projector is the center of enlargement, the film is the object, the picture on the screen is the image, and the number of times the image is bigger than the object is the scale factor (k) of the enlargement. The rays of light in this example correspond to rays we can draw with a pencil.

**47**> 48 49 50 51 52 53 .. 126 >> Next