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

ISBN 0-471-15045-2

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(d)

The perpendicular bisector of the line segment joining two points A and B is the locus of points that are equidistant from the points A and B. This locus is the arrowed line in figure d, and four points of the locus showing the equal distances are marked on the bisector. If there are fires of equal intensity at the points A and B and you wish to walk between the fires with the least chance of getting burnt, then the route you would take would be the perpendicular bisector of the line segment AB.

References: Angle Bisector, Circle, Perpendicular Bisector.

LOGARITHMIC CURVE Reference: Exponential Curve.

LOWER QUARTILE

References: Cumulative Frequency Graph, Interquartile Range.

LOWEST COMMON DENOMINATOR

Reference: Fractions.

LOWEST COMMON MULTIPLE

Abbreviation LCM. Also known as the least common multiple.

References: Factor, Fractions.

M

MAGIC SQUARE

A magic square is a square grid of counting numbers that is arranged in such a way that the sum of the numbers in each row, or column, or diagonal in the grid is the same total. A 4 by 4 square grid is shown in figure a. If we add up the numbers in each row, or each column, or in each diagonal, we get the same answer, 34. The numbers used in the grid are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16, since it is a 4 by 4 magic square.

16 3 2 13

5 10 11 8

9 6 7 12

4 15 14 1

10 1 16 7

15 8 9 2

3 12 5 14

6 13 4 11

(a) (b)

There is more than one way of arranging the numbers 1-16 in a 4 by 4 grid to form a magic square. Another possible arrangement is shown in figure b.

MAGNIFICATION

This is another name for enlargement. Reference: Enlargement.

MAGNITUDE OF A VECTOR

Reference: Vector.

281

282 MAXIMUM VALUE

MAJOR ARC

Reference: Arc.

MAJOR SECTOR

Reference: Sector of a Circle.

MAJOR SEGMENT

Reference: Segment of a Circle.

MANY-MANY CORRESPONDENCE

Reference: Correspondence.

MANY-ONE CORRESPONDENCE

Reference: Correspondence.

MAPPING

Reference: Correspondence.

MAPS ONTO

Reference: Correspondence.

MAXIMUM VALUE

Suppose you are in a car and your speed is increasing to a high speed at point A as shown in the figure, until you approach a bend. Looking ahead, you see the comer and start to slow down from this high speed. As you travel around the comer your speed drops to a minimum, at point B. You accelerate out of the comer, picking up speed as you go. At point C you are traveling fast again. The figure shows a map of the corner, and below that is a velocity-time graph showing how your car speed changes as you travel around the comer. There are three points on the graph corresponding to the three points A, B, and C on the map.

MEASUREMENT

283

At point A the car has a local maximum speed. It is not the overall greatest speed of the car, because further on, after point C, it is going faster. That is why we say that at point A the car has a local maximum speed. Similarly, at point B the car has a local minimum speed, because it could be traveling at a lower speed some other time.

The local maximum and local minimum points on a graph are often simply called maximum and minimum points, respectively.

References: Concave, Turning Points.

MEAN

The mean of a set of data can be found using a scientific calculator. Since calculators vary from one manufacturer to another and may require different instructions, refer to the handbook for instructions. The explanation of mean is found under the entries Arithmetic Mean and Central Tendency.

References: Arithmetic Mean, Central Tendency.

MEAN SQUARE DEVIATION

Reference: Standard Deviation.

MEASUREMENT

A measurement is the size or quantity of something. Here are some examples of measurements and the units used:

♦ The mass of a car is 850 kilograms.

♦ The length of a garden is 40 meters.

284 MEDIATOR

♦ The area of a farm is 2450 hectares.

♦ My lunch break is 50 minutes in duration.

♦ The temperature of the swimming pool is 21°C.

♦ The milk jug has a capacity of 800 milliliters.

Reference: Metric Units.

MEDIAN OF A SET OF DATA

References: Central Tendency, Cumulative Frequency Graph, Interquartile Range.

MEDIAN OF A TRIANGLE

The median of a triangle is the line drawn from a vertex of the triangle to the midpoint of the side that is opposite to that vertex. A triangle has three medians, which intersect in a point called the centroid of the triangle, marked G in the figure. The centroid G divides each median of the triangle in the ratio 2:1. In the drawing the line VM is the mediator of the triangle VAB, where M is the midpoint of the side AB which is opposite the vertex V.

One of the properties of the median of a triangle is that it divides the triangle VAB into two triangles VAM and VBM that are of equal area. If you were asked to divide a triangle into two “equal” parts using a straight line, then the median would be a good way of achieving it.

Reference: Ratio.

MEDIATOR

The mediator of a line segment is the line that bisects the line segment at right angles. In the figure, the mediator of the line segment AS is also the line that is called the axis of symmetry of the line segment AS. The mediator is also known as the perpendicular bisector of the line segment AS.

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