Math 310 Section 11.1 Linear Measure

The English System (Length) There are four major units for measuring length in the English system: Inch Inch Foot Foot Yard Yard Mile Mile

The Metric System (Length) There are four major units used in the metric system for measuring length: Millimeter Millimeter Centimeter Centimeter Meter Meter Kilometer Kilometer

The Metric System Continued Although the four just mentioned are the most commonly used units, the metric system has several more: Hectometer Hectometer Dekameter Dekameter Decimeter Decimeter

Unit Conversions 1 mile 1760 yards 1 mile 5280 feet 1 yard 3 feet 1 foot 12 inches EnglishEnglish

Unit Conversions (Cont) 1 kilometer 1000 meters 1 meter 100 centimeters 1 centimeter 10 millimeters MetricMetric

Unit Conversions (Cont) Aprox centimeters 1 inch MetricEnglish

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.

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.

Metric (distance function) Def A metric (distance function) is a function d(a, b) that satisfies the following four criteria: 1. d(a, b) ≥ 0 2. d(a, b) = 0 means a = b 3. d(a, b) = d(b, a) 4. d(a, c) ≤ d(a, b) + d(b, c)

For Euclidean Geometry 1. AB ≥ 0 2. AB = 0 then A =B 3. AB = BA 4. AB + BC ≥ AC

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.

Ex

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

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.

Ex Find the perimeter of the following polygon. 20

Circumference Def A circumference is the perimeter of a circle.

Ex 3 Find the circumference of the following circle with the indicated radius. 6π6π

Arc Length The length of an arc on a circle can be found with the following formula: l = (π·r·θ)/180 Where does this formula come from?

Ex 2 85°

Additional HW Problems Covert 26 miles to kilometers. Covert 26 miles to kilometers. Pg 748 prblm 19 Pg 748 prblm 19