Measures of TimeMeasures of LengthMeasures of Weight/MassMeasures of VolumeMeasures of Temperature and AnglesError and Precision in MeasurementConclusionMeasures of Time Measures of Length Measures of Weight/Mass Measures of Volume Measures of Temperature and Angles Error and Precision in Measurement ConclusionMATH 113Section 10.1: Systems of MeasurementProf. Jonathan DuncanWalla Walla CollegeWinter Quarter, 2007Measures of Time Measures of Length Measures of Weight/Mass Measures of Volume Measures of Temperature and Angles Error and Precision in Measurement ConclusionOutline1Measures of Time2Measures of Length3Measures of Weight/Mass4Measures of Volume5Measures of Temperature and Angles6Error and Precision in Measurement7ConclusionMeasures of Time Measures of Length Measures of Weight/Mass Measures of Volume Measures of Temperature and Angles Error and Precision in Measurement ConclusionSystems of MeasurementIn chapter 10 we will examine measurements as they relate togeometry. There are many different systems and types ofmeasurement to consider.Types of MeasurementsThere are many different types of me asurements. The types wewill consider include:TimeLengthWeightVolumeTemperatureMeasures of Time Measures of Length Measures of Weight/Mass Measures of Volume Measures of Temperature and Angles Error and Precision in Measurement ConclusionMeasuring TimeSome of the first systems of measurements developed may havebeen meant to measure time.Ancient Measures of TimeSumerianThe Sumerians had only two division points in t he day.Midday, when the sun was overhead, and sunset.BabyloniansBabylonians divided the day into 12 equal “hours” and thennight. However, the lengths of these hours differed accordingto the season. They also divided the year into 360 days.(why?)GreeksThe ancient Greeks divided the day into 24 hours withstandard length.Measures of Time Measures of Length Measures of Weight/Mass Measures of Volume Measures of Temperature and Angles Error and Precision in Measurement ConclusionAccuracy and Time MeasurementNot only the measures of time, but the technology used hasbecome more useful and accurate over time.Technology and Time MeasurementSundialsSundials in the form of obelisk date from as early as 3500 B.C. and were developed by many culturesincluding the Egyptians, Chinese, Greeks, and Romans. Most sundials were worked only in a given location.Water ClockNext to sundials, water clocks are possibly the oldest time-measuring device. Water clocks were thought tohave existed in India and China as early as 3000 B.C. While the principles of the water clock are still usedtoday, the use of water flow to power a clock is rare and more decorative than for functional accuracy.HourglassThe earliest evidence of the use of an hourglass is from the 14th century. Hourglasses were the firstdependable, reusable, and reasonably accurate measure of time. They are functional at sea and not liableto freeze or affected by the weather.Mechanical ClocksWhile no clocks survive from medieval Europe, mentions in church records reveal that between 1280 and1320 a new type of clock mechanism using weights and some oscil la ting mechanism was developed. Thismarks the beginning of the true mechanical clock.Atomic ClockThe atomic clock uses an atomic resonance frequency to keep extremely accurate time. These clocksmaintain a continuous and stable time scale. The first atomic clock was built in 1949 by the US Nati onalBureau of Standards. Currently, one second is defined to be the duration of 9,192,631,770 periods of acesium-133 atom.Measures of Time Measures of Length Measures of Weight/Mass Measures of Volume Measures of Temperature and Angles Error and Precision in Measurement ConclusionAncient Measures of LengthAncient units of length were often based on lengths from the body.Ancient Units of LengthThe following ancient units of length were based on various measurements taken from the body.CubitThe cubit is defined to be the distance from the tip of one’s elbow to the tip of the middle finger.FootThe foot was defined by the ancient Romans to be the actual length of Hercules’ Foot.YardA yard is the distance from the tip of British king Edgar I nose to the tip of his middle finger on anoutstretched arm.SpanA span is the width of an open handHandA hand is the width of a clos ed handFathomThe width of an outstretched arm is a fathom.Measures of Time Measures of Length Measures of Weight/Mass Measures of Volume Measures of Temperature and Angles Error and Precision in Measurement ConclusionRoman Measurements of LengthThe Romans under Alexander the Great developed a cohesivesystem of measurements of length.Roman Measurements of LengthThe Roman measurements of length are based on the foot seen inthe previous slide.The foot was divided into 12 unciae.Five feet made a pace.A mile was 1000 paces.Historical NoteAlexander the Great employed professional pacers to measure thedistance his army traveled.Measures of Time Measures of Length Measures of Weight/Mass Measures of Volume Measures of Temperature and Angles Error and Precision in Measurement ConclusionModern Measures of Length - English SystemThere are two widely used systems of measurement for lengthemployed today.English Measures of LengthThe English system of measurements for length is based on theinch.1 inch (in) is the basic unit of me asurement1 foot (ft) is 12 inches1 yard (yd) is three feet1 mile (mi) is 1760 yards, or 5280 feetExampleConvert 14 feet to inches and 48 inches to yards.Measures of Time Measures of Length Measures of Weight/Mass Measures of Volume Measures of Temperature and Angles Error and Precision in Measurement ConclusionModern Measures of Length - Metric SystemThe metric system of measurement was first proposed in 1670. It wasadopted by the French in 1789 to help standardize measurements afterthe the revolution and prevent the rich from cheating the poor.The MeterThe basic unit of measurement in the metric system is the meter (m). Itis defined to be one ten-millionth the distance from the line from theequator to the north pole passing through Barcelona, Paris, and Dunkirk.Metric PrefixesOther metric measures of length are powers of ten times a meter.11000110011010 100 1000milli- centi- deci- deca- hecto- kilo-Conversions Between SystemsTo convert between systems, use 1 inch ≈ 2.5 centimeters.Measures of Time Measures of Length Measures of Weight/Mass Measures of Volume Measures of Temperature and Angles Error and Precision