Math 310Math 310

Section 11.1Section 11.1

Linear MeasureLinear Measure

The English System The English System (Length)(Length)

There are four major units for There are four major units for measuring length in the English measuring length in the English system:system:

InchInch FootFoot YardYard MileMile

The Metric System The Metric System (Length)(Length)

There are four major units used in the There are four major units used in the metric system for measuring length:metric system for measuring length:

MillimeterMillimeter CentimeterCentimeter MeterMeter KilometerKilometer

The Metric System The Metric System ContinuedContinued

Although the four just mentioned are Although the four just mentioned are the most commonly used units, the the most commonly used units, the metric system has several more:metric system has several more:

HectometerHectometer DekameterDekameter DecimeterDecimeter

Unit ConversionsUnit Conversions

1 mile1 mile1760 yards1760 yards

1 mile1 mile5280 feet5280 feet

1 yard1 yard3 feet3 feet

1 foot1 foot12 inches12 inches

EnglishEnglishEnglishEnglish

Unit Conversions (Cont)Unit Conversions (Cont)

1 kilometer1 kilometer1000 meters1000 meters

1 meter1 meter100 centimeters100 centimeters

1 centimeter1 centimeter10 millimeters10 millimeters

MetricMetricMetricMetric

Unit Conversions (Cont)Unit Conversions (Cont)

Aprox. 2.54 Aprox. 2.54 centimeterscentimeters1 inch1 inch

MetricMetricEnglishEnglish

Dimensional AnalysisDimensional Analysis

Dimensional analysis is a process for Dimensional analysis is a process for converting between units. Similar to converting between units. Similar to converting fractions, the idea is that converting fractions, the idea is that you multiply you starting value by a you multiply you starting value by a fraction equal to one, thereby never fraction equal to one, thereby never actually changing the value, just the actually changing the value, just the representation.representation.

ExEx

Convert 2 feet to inches.Convert 2 feet to inches.

Convert 12 yards to inches.Convert 12 yards to inches.

Convert 4 miles to inches.Convert 4 miles to inches.

Convert 1 inch to miles.Convert 1 inch to miles.

Convert 3 kilometers to millimetersConvert 3 kilometers to millimeters

Convert 1 foot to centimeters.Convert 1 foot to centimeters.

Convert 1 mile to kilometers.Convert 1 mile to kilometers.

Metric (distance Metric (distance function)function)

DefDef

A metric (distance function) is a A metric (distance function) is a function d(a, b) that satisfies the function d(a, b) that satisfies the following four criteria:following four criteria:

1.1. d(a, b) ≥ 0d(a, b) ≥ 0

2.2. d(a, b) = 0 means a = bd(a, b) = 0 means a = b

3.3. d(a, b) = d(b, a)d(a, b) = d(b, a)

4.4. d(a, c) ≤ d(a, b) + d(b, c)d(a, c) ≤ d(a, b) + d(b, c)

For Euclidean GeometryFor Euclidean Geometry

1.1. AB ≥ 0 AB ≥ 0

2.2. AB = 0 then A =BAB = 0 then A =B

3.3. AB = BAAB = BA

4.4. AB + BC ≥ ACAB + BC ≥ AC

Triangle InequalityTriangle Inequality

DefDef

The triangle inequality states that the The triangle inequality states that the sum of any two sides of a triangle (3 sum of any two sides of a triangle (3 pts in a plane) is greater than the pts in a plane) is greater than the third side.third side.

ExEx

ExEx

The perimeter of an isosceles triangle The perimeter of an isosceles triangle is 40, which of the following could is 40, which of the following could not be the base?not be the base?

11 88 1515 2424

PerimeterPerimeter

DefDef

The The perimeterperimeter of a simple closed of a simple closed curve is the length of the curve. For curve is the length of the curve. For a polygon this is simple the sum of a polygon this is simple the sum of the sides of the polygon.the sides of the polygon.

ExEx

4

53

1

4

12

Find the perimeter of the following polygon.

20

CircumferenceCircumference

DefDef

A A circumferencecircumference is the perimeter of is the perimeter of a circle.a circle.

ExEx

3

Find the circumference of the following circle with the indicated radius.

6π

Arc LengthArc Length

The length of an arc on a circle can be The length of an arc on a circle can be found with the following formula:found with the following formula:

ll = ( = (ππ··rr··θθ)/180)/180

Where does this formula come from?Where does this formula come from?

ExEx

2

85°

Additional HW ProblemsAdditional HW Problems

Covert 26 miles to kilometers.Covert 26 miles to kilometers. Pg 748 prblm 19Pg 748 prblm 19