Recovery of the Ancient System of Foot/Cubit/Stadion – Length Units
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The Beautiful Cubit System I Douglas 2019 the Beautiful Cubit System
The Beautiful Cubit System I Douglas 2019 The Beautiful Cubit System Ian Douglas, B.Sc [email protected] 30 June 2019 Version 1.0.0 DOI: https://doi.org/10.5281/zenodo.3263864 This work is licensed under the Creative Commons Attribution 4.0 International License. Abstract An analysis of the Egyptian Royal cubit, presenting some research and opinions flowing from that research, into what I believe was the original cubit, and how it was corrupted. I show various close arithmetic approximations and multiple ways of getting the divisions of the cubit, as well as some related measures. The cubit also encapsulates the basic components for the metric system. Keywords: Egyptology, metrology, royal cubit, cubit, metre, foot, metric system Contents 1. Introduction 2. Overview of current understanding 3. An alternative origin 4. Different ways of approximating the royal cubit 5. Different ways of getting the cubit divisions 6. Geometry, the Royal Cubit and the metric system 7. Bibliography 1. Introduction The cubit is a well-know ancient measure of length, used around various places in the Middle East and Mediterranean region in the distant past. 1 The Beautiful Cubit System I Douglas 2019 It is allegedly based on the length of a human (male) fore-arm. It is typically measured from the back of the elbow to some point between the wrist and the end of the outstretched middle finger, or in some variants, a point beyond that. The problem with this approach is that everyone’s arm is a different length. If the heights of the dynastic Egyptians is taken as representative, then their arms would have been too short to justify the accepted lengths. -
Guide for the Use of the International System of Units (SI)
Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S. -
Yd.) 36 Inches = 1 Yard (Yd.) 5,280 Feet = 1 Mile (Mi.) 1,760 Yards = 1 Mile (Mi.)
Units of length 12 inches (in.) = 1 foot (ft.) 3 feet = 1 yard (yd.) 36 inches = 1 yard (yd.) 5,280 feet = 1 mile (mi.) 1,760 yards = 1 mile (mi.) ©www.thecurriculumcorner.com Units of length 12 inches (in.) = 1 foot (ft.) 3 feet = 1 yard (yd.) 36 inches = 1 yard (yd.) 5,280 feet = 1 mile (mi.) 1,760 yards = 1 mile (mi.) ©www.thecurriculumcorner.com Units of length 12 inches (in.) = 1 foot (ft.) 3 feet = 1 yard (yd.) 36 inches = 1 yard (yd.) 5,280 feet = 1 mile (mi.) 1,760 yards = 1 mile (mi.) ©www.thecurriculumcorner.com 1. Find the greatest length. 2. Find the greatest length. 9 in. or 1 ft. 3 ft. or 39 in. ©www.thecurriculumcorner.com ©www.thecurriculumcorner.com 3. Find the greatest length. 4. Find the greatest length. 1 ft. 7 in. or 18 in. 4 ft. 4 in. or 55 in. ©www.thecurriculumcorner.com ©www.thecurriculumcorner.com 5. Find the greatest length. 6. Find the greatest length. 1 ft. 9 in. or 2 ft. 7 ft. or 2 yd. ©www.thecurriculumcorner.com ©www.thecurriculumcorner.com 7. Find the greatest length. 8. Find the greatest length. 26 in. or 2 ft. 6 yd. or 17 ft. ©www.thecurriculumcorner.com ©www.thecurriculumcorner.com 9. Find the greatest length. 10. Find the greatest length. 5 ft. or 1 ½ yd. 112 in. or 3 yd. ©www.thecurriculumcorner.com ©www.thecurriculumcorner.com 11. Find the greatest length. 12. Find the greatest length. 99 in. or 3 yd. 11,000 ft. or 2 mi. ©www.thecurriculumcorner.com ©www.thecurriculumcorner.com 13. -
Snow Science Fact Sheet
BASIC FORMULAS 1. Typical Material Cost Breakdown of a Snowmaking System 2. Snowmaking Technology Energy Use Comparison 3. Typical Air Compressor Discharge Temperature 4. Calculating Friction Loss of Water in Pipe-lines 5. Calculating Air Pressure Loss Due to Friction 6. Calculating Horsepower For Water Pump 7. Calculating Operating Cost 8. Water Snow Relationships 3.2 Gallons = 1 FT³ of Snow 1 Gallon = 8.342 lbs 1 FT³ Water = 7.48 Gallons 1 Acre = 43,560 FT² 1 Acre Foot of Snow = 180,000 Gallons of Water 9. English to Metric Conversion Factors English Units Multiply By Metric Units Gallons (GAL.) 3.785 Litres (L) Gallons Per Minute (GPM) 3.785 Litres Per Minute (LPM) Gallons Per Minute (GPM) 0.0631 Litres Per Second (LPS) Acres 0.40469 Hectares Acres 4046.9 Meters² Feet 0.3048 Meters Cubic Feet (FT³) 0.0283 Cubic Meters (M 3) Horsepower (HP) 0.7457 Kilowatts Pounds Per Square Inch (PSI) 6.895 Kilopascals (KPA) Gal/Min 0.2271 M³/HR Hectare-M 10,000 M³ 10. How to Determine Snow Quality One could collect fresh snow samples and determine weight per Cubic Foot or Cubic Meter and state the quality in density like pounds per Cubic Foot or density per Cubic Meter. A far simpler and practical method is to test the snow on the ground in the production plume while snow guns are operating by doing a Snow Ball Test. The quality can be determined on a scale from 1 to 6 according to the table below: The Snowball Test Snow Quality Description 1 Snow cannot be packed, powder 2 Snow can only be packed into a loose ball that falls apart 3 Snow can be packed into a ball that can be broken apart 4 Snow can be packed into a dense ball that does not change color when squeezed 5 Snow can be packed into a dense ball that changes to a darker color when squeezed but little or no water comes out 6 Snow can be packed into a dense ball that discharges water when squeezed . -
Water System Operator's Guide
MATH REVIEW For a rectangular tank: Most math problems a water treatment plant To find the capacity of a rectangular or square operator solves requires plugging numbers into tank: formulas and calculating the answer. When working with formulas, here are some simple Multiply length (L) by width (W) to get area (A). rules to follow. • Work from left to right. Multiply area by height (H) to get volume (V). • Do anything in parenthesis first. Multiply volume by 7.48 gallons per cubic foot to get capacity (C). • Do multiplication and division in the numerator (above the line) and in the A = L x W denominator (below the line), then do V = A x H addition and subtraction in the numerator C = V x 7.48 and denominator. • Divide the numerator by the denominator Find the capacity of a rectangular tank 15 feet (ft) last. long, 12 ft wide, and 10 ft high: Volume A = 15 ft x 12 ft = 180 square feet (ft2) The volume of a tank in cubic feet is equal to V = 180 ft2 x 10 ft = 1,800 cubic feet (ft3) the tank area multiplied by the tank height. The C = 1,800 ft3 x 7.48 gal/ft3 =13,464 gal capacity in gallons is equal to the volume in cubic feet multiplied by 7.48 gallons per cubic foot. For a circular tank: Area (A) = (3.14) x diameter squared (D2) / divided by 4 Volume (V) = A x H Capacity (C) = V x 7.48 gal/ft3 A = [ x (D2)/4] V = A x H C = V x 7.48 49 Find the capacity of a circular tank with a For an oval tank: diameter of 15 ft and a height of 12 ft: To find the gallons in an oval tank: A = [3.14 x (15 ft2)/4] = 177 ft2 Multiply the height by width by (3.14) divided by 4 to get the area of the oval. -
615 Water Conversion Table
Form No. 615 R03/2012 WATER CONVERSION TABLE GPM = Gallons per minute CFS = Cubic feet per second AF = Acre-feet 1 Cubic foot of water equals ............................................................ 7.48 Gallons 1 AF of water equals .............................................................................. 1 foot of water on 1 acre .................................................................................................. 325,851 Gallons .................................................................................................... 43,560 Cubic feet 1 CFS equals ................................................................................. 448.8 GPM ........................................................................................................ 1.98 AF per day ........................................................................................................... 40 Miner's inches 1 GPM equals ................................................................................ 1,440 Gallons per 24 hour day ........................................................................................................ 1.61 AF per year 1 Surface Acre equals ................... Size of area in square feet 43,560 QUICK CONVERSIONS MI X 11.22 = GPM CFS X 40 = MI MI 40 = CFS CFS X 448.8 = GPM MI X .0495 = AF/DAY CFS X 1.98 = AF/DAY GPM 11.22 = MI AF/DAY 1.98 = CFS GPM 448.8 = CFS AF/DAY X 226.67 = GPM GPM 226.67 = AF/DAY AF/DAY .0495 = MI GENERAL WATER REQUIREMENTS DOMESTIC USE 1 family - up to 5 people . 1 AF/YR -
Measurement Benchmarks
Lesson 12.1 Name Reteach Measurement Benchmarks You can use benchmarks to estimate measurements. The chart shows benchmarks for customary units of measurement. Benchmarksarks forfor SomeSom Customary Units CUP 1 ft 1 yd about 1 about 1 about 1 about 1 about 1 about 1 foot yard cupcup gallon ounce pound Here are some more examples of estimating with customary units. • The width of a professional football is about 1 foot . • A large fish bowl holds about 1 gallon of water. • A box of cereal weighs about 1 pound . The chart shows benchmarks for metric units of measurement. Benchmarks for Some Metric Units about about about about about about 1 centimeter 1 meter 1 milliliter 1 liter 1 gram 1 kilogram Here are some more examples of estimating with metric units. • The width of a large paper clip is about 1 centimeter . • A pitcher holds about 1 liter of juice. • Three laps around a track is about 1 kilometer . Use benchmarks to choose the customary unit you would use to measure each. 1. length of a school bus 2. weight of a computer Use benchmarks to choose the metric unit you would use to measure each. 3. the amount of liquid a bottle of 4. distance between two cities detergent holds Chapter Resources 12-5 Reteach © Houghton Mifflin Harcourt Publishing Company Lesson 12.1 Name Measurement Benchmarks Measurement and Data— Essential Question How can you use benchmarks to understand 4.MD.A.1 the relative sizes of measurement units? MATHEMATICAL PRACTICES MP1, MP5 UnlockUnlock thethe ProblemProblem Jake says the length of his bike is about four yards. -
History of Measurement
BUILDING INDUSTRY TECHNOLOGY ACADEMY: YEAR ONE CURRICULUM Short History of Measurement Directions: Working with a partner read the following statements concerning the history of our modern measurement terms. Clues to solving each statement are contained within each statement and the measurement vocabulary can be found in the Word Bank below. yard inch cubit kerosene acre hand foot metric system tobacco 1. This measurement of approximately 4 inches is still used to calculate how tall a horse is. It is the ______________________________. 2. Tired of relying on the length of the previous king’s girdles in determining the length of this unit of measurement, Henry the First decreed: “Henceforth, the shall be the distance from the tip of my nose to the tip of my thumb.” 3. The most common unit of measurement in the United States, the Romans referred to it as “one- twelfth of a foot.” It roughly equals the width of a person’s thumb, but since 1959, the has officially equaled 2.54 Dcentimeters. 4. In 1812, Napoleon noted that the French people were still clinging to traditional units of measurement; even though the was officially adopted by the French government in 1795. This system of Dmeasurement originally derived its name from the Greek word “metron”, meaning “measure”. Today it is also known by the initials SI, or System International, and was legalized in the United States in 1866. 5. The is one of the earliest known units of measurement. It was the standard unit of measurement for thousands of years in many civilizations, though it has widely gone out of popular use today. -
Ancient Egyptian Cubits – Origin and Evolution
Ancient Egyptian Cubits – Origin and Evolution by Antoine Pierre Hirsch A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Near and Middle Eastern Civilizations University of Toronto © Copyright by Antoine Pierre Hirsch 2013 i Ancient Egyptian Cubits – Origin and Evolution Antoine Pierre Hirsch Doctor of Philosophy Near and Middle Eastern Civilizations University of Toronto 2013 Abstract This thesis suggests that prior to Ptolemaic and Roman times, ancient Egypt had two distinct and parallel linear systems: the royal system limited to official architectural projects and land measurements, and a great (aA) system used for everyday measurements. A key 1/3 ratio explains ancient Egyptian linear measurements and their agricultural origin. Emmer is 1/3 lighter than barley, consequently, for an equal weight, a container filled with emmer will be 1/3 greater than a container filled with barley. The lengths derived from both containers share the same 1/3 ratio. The second chapter, Previous Studies, lists the work of scholars involved directly or indirectly with ancient Egyptian metrology. The third chapter, The Royal Cubit as a Converter and the Scribe’s Palette as a Measuring Device, capitalizes on the colour scheme (black and white on the reproduction of Appendix A) appearing on the Amenemope cubit artifact to show the presence of two cubits and two systems: the black (royal system) and the white (great [aA] system) materialized by the scribe's palette of 30, 40, and 50 cm. The royal cubit artifacts provide a conversion bridge between the royal and the great systems. The information derived from the visual clues on the Amenemope cubit artifact are tested against a database of artifacts scattered in museums around the world. -
The International System of Units (SI) - Conversion Factors For
NIST Special Publication 1038 The International System of Units (SI) – Conversion Factors for General Use Kenneth Butcher Linda Crown Elizabeth J. Gentry Weights and Measures Division Technology Services NIST Special Publication 1038 The International System of Units (SI) - Conversion Factors for General Use Editors: Kenneth S. Butcher Linda D. Crown Elizabeth J. Gentry Weights and Measures Division Carol Hockert, Chief Weights and Measures Division Technology Services National Institute of Standards and Technology May 2006 U.S. Department of Commerce Carlo M. Gutierrez, Secretary Technology Administration Robert Cresanti, Under Secretary of Commerce for Technology National Institute of Standards and Technology William Jeffrey, Director Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose. National Institute of Standards and Technology Special Publications 1038 Natl. Inst. Stand. Technol. Spec. Pub. 1038, 24 pages (May 2006) Available through NIST Weights and Measures Division STOP 2600 Gaithersburg, MD 20899-2600 Phone: (301) 975-4004 — Fax: (301) 926-0647 Internet: www.nist.gov/owm or www.nist.gov/metric TABLE OF CONTENTS FOREWORD.................................................................................................................................................................v -
Which Cubit for Noah's Ark?
Papers Which cubit for Noah’s Ark? Tim Lovett Noah’s Ark is the earliest ship known to man. Amazingly, an accurate record of its dimensions has survived to this day, in Genesis 6:15. However, the Bible uses cubits, an ancient measure that may have been anywhere from 445 mm (17.5 in) to more than 609 mm (2 ft) long, depending on when and where it was used. The standard chronology places the Tower of Babel so soon after Noah’s Ark that they must have shared the same cubit. After the dispersion this cubit should have found its way into early structures and monuments. Today, when we look in the ancient Near East for the best clues, we find that the earliest major works in Egypt and Babylon used long cubits. Could this be the one that Noah used? The cubit Table 1 shows cubit lengths chosen by key creationist authors dealing with Noah’s Ark, all clearly driven by a he length of the Ark shall be three hundred conservative space argument. cubits, the breadth of it fifty cubits, and the ‘T In every case the ‘common’ cubit has been chosen, height of it thirty cubits’ (Genesis 6:15). How long is a cubit? The word comes from the despite clear evidence that it was the ‘royal’ cubit Latin cubitum1 which refers to the forearm. It was measured that dominated major building projects of the earliest from the elbow to the fingertip. This provides a foolproof civilizations, Noah’s immediate descendents. The dominant 4 method of gauging the size of Noah’s Ark—at least ap- primary source is the 1959 paper by R.B.Y. -
The History and Mathematics of Conversions
THE HISTORY AND MATHEMATICS OF CONVERSIONS BY JAMES D. NICKEL THE METRIC SYSTEM I f you live in the United States of America, you have to work with two systems of measure. These two sys- tems are called (1) British Imperial system of measure and (2) Metric system of measure. In the British sys- Item, with its long and storied history, there are many sub-systems where different bases are used. The pint- gallon system is base 8, the inches-foot system is base 12, the yard-foot system is base 3, the week-day system is base 7, the month-year system is base 12, the yard-mile system is base 1760, and the foot-mile system is base 5280. In contrast, the Metric system of measurement is, like most national currencies, decimalized (base 10). As we have already noted, it was developed in France in the late 18th century.1 Since the 1960s the International System of Units (SI) (Système International d'Unités in French, hence “SI”) has been the internationally recognized standard metric system. Metric units are widely used around the world for personal, commercial and scientific purposes. Of all the nations of the world (Date: early 21st century), only Liberia, Myanmar and the United States have not yet officially adopt- ed the Metric system. Metric units consist of a standard set of prefixes in multiples of 10 that may be used to derive larger and smaller units. Work- ing with these units is as easy as multiply- ing or dividing by 10 (or powers of 10).