Math 310

1
Math 310

• Section 11.1
• Linear Measure

2
The English System (Length)

• There are four major units for measuring length
  in the English system
  
• Inch
• Foot
• Yard
• Mile

3
The Metric System (Length)

• There are four major units used in the metric
  system for measuring length
  
• Millimeter
• Centimeter
• Meter
• Kilometer

4
The Metric System Continued

• Although the four just mentioned are the most
  commonly used units, the metric system has
  several more
  
• Hectometer
• Dekameter
• Decimeter

5
Unit Conversions
English
English
1 foot
12 inches
1 yard
3 feet
1 mile
5280 feet
1 mile
1760 yards
6
Unit Conversions (Cont)
Metric
Metric
1 centimeter
10 millimeters
1 meter
100 centimeters
1 kilometer
1000 meters
7
Unit Conversions (Cont)
Metric
English
Aprox. 2.54 centimeters
1 inch
8
Dimensional Analysis

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

9
Ex

• Convert 2 feet to inches.
• Convert 12 yards to inches.
• Convert 4 miles to inches.
• Convert 1 inch to miles.
• Convert 3 kilometers to millimeters
• Convert 1 foot to centimeters.
• Convert 1 mile to kilometers.

10
Metric (distance function)

• Def
• A metric (distance function) is a function d(a,
  b) that satisfies the following four criteria
  
• d(a, b) 0
• d(a, b) 0 means a b
• d(a, b) d(b, a)
• d(a, c) d(a, b) d(b, c)

11
For Euclidean Geometry

• AB 0
• AB 0 then A B
• AB BA
• AB BC AC

12
Triangle Inequality

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

13
Ex
14
Ex

• The perimeter of an isosceles triangle is 40,
  which of the following could not be the base?
  
• 1
• 8
• 15
• 24

15
Perimeter

• Def
• The perimeter of a simple closed curve is the
  length of the curve. For a polygon this is
  simple the sum of the sides of the polygon.

16
Ex
Find the perimeter of the following polygon.
20
17
Circumference

• Def
• A circumference is the perimeter of a circle.

18
Ex
Find the circumference of the following circle
with the indicated radius.
3
6p
19
Arc Length

• The length of an arc on a circle can be found
  with the following formula
  
• l (pr?)/180
• Where does this formula come from?

20
Ex
21
Additional HW Problems

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