2017 AAPT Summer Meeting Cincinnati, OH. AC03: Using History to Take the Mystery Out of Units
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1 2017 AAPT Summer Meeting Cincinnati, OH AC03: Using History to Take the Mystery Out of Units Robert A. Morse Emeritus, St. Albans School
2 Why use history in teaching units? Physics units - tricky for US students. Different from homely and familiar units. Early assignment review of units & conversions history of units in context of practice with unit conversion History practical origin of traditional units, PLUS attraction of the arcane! Student difficulty in unit conversion revealed math issues google-ization of knowledge changed that, but history still interesting. Start with units in US system convert within US system & between US and SI systems develop sense of scale from personal values of units
3 Length: foot, cubit, yard, fathom, hand, inch Foot measure shod ~ 12 inches converts to cm exactly ~ 30 cm Cubit - the elbow (cubitum) various definitions ~1.5 ft -convenient for construction - local standards back to ancient Egypt [45cm] Yard - stick or rod - nose to fingertipss - convenient for cloth. Standardized in England at various times: Henry I c. 1100, Edward I c. 1300, Elizabeth I in Standard yard 3 ft, ~ 90 cm [85 cm] Fathom - span of outstretched arms - defined as 6 ft ~1.8 m. Nautical origin - measure of depth from use of lead line. [5.5 ft 1.7 m] Hand 4 inches ~ 10 cm still used for horses inch once defined as 3 barley corns placed end to end [~1 finger joint] Since late 1800 s 1 inch = 2.54 cm exactly. It s not just a good idea - It s the LAW!
4 Distance: miles Origin of mile - Latin mille passum roman paces Roman pace is double pace - i.e. left foot to left foot. Pace ~ 5 feet [4.5 ft] Roman mile = ft ~ 1500 m [Morse mile ~1400m] 1593 Replaced by statute mile in England to regularize land measure
5 Length & Area: rod, furlong, acre, hectare Furlong - length of furrow plowed by ox team 1 furlong = 40 Rods = 220 yards = 660 ft Rod = 5.5 yards = 16.5 ft 1 furlong 4 Rods 66 ft 1 acre = 1 furlong x 4 rods = 160 square rods = sq ft US high school football field (no end zones) 100 yards x yards = sq ft =1.1 acres football field with end zones = 0.53 ha soccer field = 0.6 ha US high school soccer field 110 yards x 65 yards = sq ft =~1.5 acres 1 are = 10 m x 10 m 1 hectare = 100 are = sq m 1 ha = acre 1 hectare
6 Why the nautical mile? Astrolabe and cross-staff Direction to pole star 90º of 60 minutes = 5400 minutes of arc. Define 1 minute of arc as 1 nautical mile. Equator to pole = 5400 nautical miles circumference = nautical miles 90º from horizon 1 Nautical mile = 6076 ft 1.15 statute miles A few early measurements of size of 1 nautical mile Equator 0º from horizon Eratosthenes ~250 BC - size of Earth at Alexandria in Egypt Al Ma mun ~830 AD - length of 1degree of arc in the desert of modern northern Iraq
7 Whence the kilometer? Direction to pole star SI - new unit of angle 100 grads of 100 centigrads = centigrads of arc. Define 1 centigrad of arc as 1 kilometer Equator to pole = kilometers circumference = kilometers 100 grads from horizon 1 nautical mile = 1852 km Equator 0 grads from horizon
8 Results? Some students enjoyed the romp through the units Many later knew how the kilometer was arrived at Some internalized their personal units For some it was water off a duck s back Occasionally a student picked up on the notion of exploring units and history and would bring back a few discoveries of their own ramorse@rcn.com
9 Some Sources Lynn White, Jr., Medieval Technology and Social Change Andro Linklater, Measuring America Jim Al-Khalili, The House of Wisdom various Wikipedia articles on many topics
10 What about the ark? Genesis 6:15 - And this [is the fashion] which thou shalt make it [of]: The length of the ark [shall be] three hundred cubits, the breadth of it fifty cubits, and the height of it thirty cubits. 300 cubits x 50 cubits x 30 cubits 150 yds x 25 yds x 15 yds Ark top view 0.77 acre medieval 1 acre field Ark side view This page is an Easter Egg - not enough time to include it in talk - since ark measured in cubits, I wanted to compare it in size to an acre, and to a modern ship. The ark we see depicted in medieval art does not look well proportioned, but the dimensions as given are the similar - except in length - to those of the famous S.S. Edmund Fitzgerald - a great lakes bulk carrier Edmund Fitzgerald 243 yds x 25 yds x13 yds
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Activity One 1a) Conversions 1 cm = mm 5 ft = in 6 yds = ft 2 lbs = oz 5 g = mg 160 oz = lbs 5 L = ml 6 quarts = pints 5 gallons = quarts b) Choose the correct answer Which measurement is closest to 3
12-2 Area of Circles. Find the area of each circle. Round to the nearest tenth. 1. ANSWER: m 2. ANSWER: 12.6 yd 2 ANSWER: 132.
Find the area of each circle. Round to the nearest tenth. 1. 6. A motion detector at the corner of a building can detect motion outside within a radius of 20 feet as shown. Within what area can it detect
Math 110 Sec 6.2 Proportions. Name Find the unit price. (Sec 6.1) 1) $52.00 for 5 compact discs. 2) $0.90 for 2 onions
Math 110 Sec 6.2 Proportions Name Find the unit price. (Sec 6.1) 1) $52.00 for 5 compact discs 2) $0.0 for 2 onions Find the unit price and decide which is the better buy. Round to three decimal places.
Trapped in AesopÊs Fables!
A Wayne Scott LifeHouse Theater-On-The-Air Production Trapped in AesopÊs Fables! An Original Adaptation by George Christison & Sarah Christison Curriculum Guide Copyright MMX by W.R. Scott - LifeHouse