DOCSLIB.ORG

Ekahau Site Survey & Heatmap Visualizations

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Ekahau Site Survey & Heatmap Visualizations Ekahau Site Survey & Heatmap Visualizations 7.04.2016 Contents Executive Summary ........................................................................... 4 Introduction ...................................................................................... 4 What do we mean by visualizations? ............................................ 4 What are the different types of Ekahau Site Survey (ESS) visualizations? .............................................................................................. 4 Signal Strength ................................................................................. 5 What is signal strength? ............................................................ 5 How is signal strength displayed in Ekahau Site Survey (ESS)? ....... 7 Why is signal strength important for a Wi-Fi network? .................... 8 What signal strength should I design my network to? .................... 9 AP Selection ...................................................................................... 9 Interference / Noise .......................................................................... 11 Signal to Noise Ratio (SNR) ................................................................ 15 What is Signal to Noise Ratio (SNR)? .......................................... 15 Why is SNR important? ............................................................. 15 What is a good SNR value? ....................................................... 16 How does Ekahau Site Survey visualize SNR? .............................. 16 Data Rate ........................................................................................ 17 How are data rates determined? ................................................ 18 How does Ekahau Site Survey calculate data rate? ....................... 24 Channel Overlap ............................................................................... 29 What is Channel Overlap? ......................................................... 29 2 Copyright © 2016 Ekahau, Inc. All rights reserved. Channel Overlap on 2.4 GHz ...................................................... 29 Channel Overlap on 5 GHz ........................................................ 30 What happens when channels overlap? ....................................... 31 How much is too much Channel Overlap? .................................... 33 So, is the 2.4 GHz band dead then? ............................................ 33 How does Ekahau Site Survey visualize Channel Overlap? ............. 34 Channel Coverage ............................................................................. 35 Channel Bandwidth ........................................................................... 37 Number of APs ................................................................................. 39 Associated Access Point ..................................................................... 41 What does the visualization look like? ......................................... 41 What should you look for? ......................................................... 43 Spectrum Channel Power and Spectrum Utilization ................................ 44 Spectrum Channel Power .......................................................... 44 Spectrum Utilization ................................................................. 45 Visualization Options ................................................................ 46 Survey Inspector ..................................................................... 46 Contact ........................................................................................... 48 3 Copyright © 2016 Ekahau, Inc. All rights reserved. Executive Summary What are visualizations? What do the Ekahau visualizations mean? How can I optimize my design for each visualization? The abovementioned questions are discussed in detail further in this paper. Introduction What do we mean by visualizations? Visualizations are graphical representations of simulated (planning) or measured data (survey) overlaid on a floor plan that is imported by a user to depict the physical structure in which the wireless network is being or has been deployed. The graphical display helps the user understand and interpret the data more effectively than trying to decode an exorbitant amount of tabular data. What are the different types of Ekahau Site Survey (ESS) visualizations? Currently there are 19 ESS visualizations that can be selected to help design, verify, and/or troubleshoot your Wi-Fi network: • Associated Access Point – predicts where the client devices will be associated, or, if Hybrid Site Surveys have been made, displays the actual associated access point throughout the survey. • Capacity: Clients per AP – displays how the end user devices would be distributed between the access points. • Capacity Health – displays whether the network meets the Capacity Requirements. • Channel Bandwidth – displays channel bandwidth to better visualize your 802.11n and 802.11ac network characteristics such as channel bonding. • Channel Coverage – displays the channel of the AP with the strongest signal strength in each location. • Channel Overlap – shows how many APs are overlapping on a single channel in the given area. 4 Copyright © 2016 Ekahau, Inc. All rights reserved. • Data Rate – displays the speed at which the client device and the AP are communicating. • Interference / Noise – displays interference/noise as a result of co-channel interference and other noise that may have an impact on performance. • Network Health – provides a summarized overview of the network based on whether defined network requirements are met or not. • Network Issues – displays which network requirement fails in a given location. • Number of APs – shows how many APs are audible in a given location. • Packet Loss – displays the relative packet loss % over the floor map, as measured from the last 10 packets. • Round-Trip Time – shows the round trip time of the ping packets over the floor map. • Signal Strength – displays the signal strength of the selected set of APs in dBm. By default, the signal strength of the strongest AP per location is displayed. • Signal to Noise Ratio (SNR) – shows the ratio of the signal strength relative to the noise. • Throughput (Max) – displays the theoretical maximum net throughput (excluding overhead) per location, given ideal circumstances and a single user accessing the network. • Difference in Interference – shows the interference difference in measured values between the Primary and Secondary surveys in a given location. • Difference in Signal Strength – shows the signal strength difference in measured values between the Primary and Secondary surveys in a given location. • Difference in Number of APs – shows the change in the number of APs between the Primary and Secondary surveys in a given location. Signal Strength To kick off the series on visualizations we will focus on one of the most recognizable and important requirements when designing a wireless network: signal strength. What is signal strength? People often mistakenly refer to signal strength as Received Signal Strength Indicator (RSSI) value, which is an indication of the power level at the receiving antenna (e.g. Wi-Fi client device). While RSSI can give you an indication of how strong a signal is relativistically, 5 Copyright © 2016 Ekahau, Inc. All rights reserved. it does not provide an absolute measurement. There is no standardized method of determining RSSI between vendors, leading to each providing different RSSI values for the same environment. When engineers refer to power levels in dBm or mW, it is the actual measured signal strength and not a relative calculation as with RSSI. What is dBm or mW? Short answer: dBm is decibels relative to 1 milliwatt and mW is a milliwatt (one thousandth of a watt). The next obvious question is: what are watts and decibels? A watt is a unit of power named after the Scottish engineer James Watt that is used to express the rate of energy conversion or transfer with respect to time. It can be calculated relative to an object’s velocity as Joules per Second (J/S) or in terms of electromagnetism as the rate at which work is done when one Ampere of current flows through an electrical potential difference (Volt), aka Watt = Volts x Amperes. A decibel is a logarithmic unit used to express a ratio between two values. The decibel is used to conveniently represent very large or small values and allow for simple mathematical calculations that would otherwise be difficult for most humans. For the sake of saving time and not derailing the purpose of this post, I recommend checking out WLAN Pros’ “Easy dB Math in 5 Minutes” (http://www.wlanpros.com/easy-db-math-5-minutes/) to understand how to work with dBms. 6 Copyright © 2016 Ekahau, Inc. All rights reserved. How is signal strength displayed in Ekahau Site Survey (ESS)? In ESS the signal strength visualization displays the signal strength of the selected set of Access Points (APs) in dBm. By default, the signal strength of the strongest AP per location will be displayed. To display the signal strength for just one or few access points, select “Show Signal Strength for Selected Access Points” and click to select APs from the map or from the AP list as shown in the screenshot below. More about the AP selections on our next blog post. Signal strength has the following options accessible via the Visualization Options: • Viewed Signal allows you to disregard the signals from the strongest access points, visualizing the
Load more

Recommended publications
  • Abstract 1. Introduction 2. Robert Stirling
    Stirling Stuff Dr John S. Reid, Department of Physics, Meston Building, University of Aberdeen, Aberdeen AB12 3UE, Scotland Abstract Robert Stirling’s patent for what was essentially a new type of engine to create work from heat was submitted in 1816. Its reception was underwhelming and although the idea was sporadically developed, it was eclipsed by the steam engine and, later, the internal combustion engine. Today, though, the environmentally favourable credentials of the Stirling engine principles are driving a resurgence of interest, with modern designs using modern materials. These themes are woven through a historically based narrative that introduces Robert Stirling and his background, a description of his patent and the principles behind his engine, and discusses the now popular model Stirling engines readily available. These topical models, or alternatives made ‘in house’, form a good platform for investigating some of the thermodynamics governing the performance of engines in general. ---------------------------------------------------------------------------------------------------------------- 1. Introduction 2016 marks the bicentenary of the submission of Robert Stirling’s patent that described heat exchangers and the technology of the Stirling engine. James Watt was still alive in 1816 and his steam engine was gaining a foothold in mines, in mills, in a few goods railways and even in pioneering ‘steamers’. Who needed another new engine from another Scot? The Stirling engine is a markedly different machine from either the earlier steam engine or the later internal combustion engine. For reasons to be explained, after a comparatively obscure two centuries the Stirling engine is attracting new interest, for it has environmentally friendly credentials for an engine. This tribute introduces the man, his patent, the engine and how it is realised in example models readily available on the internet.
    [Show full text]
  • Champ Math Study Guide Indesign
    Champions of Mathematics — Study Guide — Questions and Activities Page 1 Copyright © 2001 by Master Books, Inc. All rights reserved. This publication may be reproduced for educational purposes only. BY JOHN HUDSON TINER To get the most out of this book, the following is recommended: Each chapter has questions, discussion ideas, research topics, and suggestions for further reading to improve students’ reading, writing, and thinking skills. The study guide shows the relationship of events in Champions of Mathematics to other fields of learning. The book becomes a springboard for exploration in other fields. Students who enjoy literature, history, art, or other subjects will find interesting activities in their fields of interest. Parents will find that the questions and activities enhance their investments in the Champion books because children of different age levels can use them. The questions with answers are designed for younger readers. Questions are objective and depend solely on the text of the book itself. The questions are arranged in the same order as the content of each chapter. A student can enjoy the book and quickly check his or her understanding and comprehension by the challenge of answering the questions. The activities are designed to serve as supplemental material for older students. The activities require greater knowledge and research skills. An older student (or the same student three or four years later) can read the book and do the activities in depth. CHAPTER 1 QUESTIONS 1. A B C D — Pythagoras was born on an island in the (A. Aegean Sea B. Atlantic Ocean C. Caribbean Sea D.
    [Show full text]
  • EM Waves, Ray Optics, Optical Instruments Mar
    Gen. Phys. II Exam 3 - Chs. 24,25,26 - EM Waves, Ray Optics, Optical Instruments Mar. 26, 2018 Rec. Time Name For full credit, make your work clear. Show formulas used, essential steps, and results with correct units and significant figures. Points shown in parenthesis. For TF and MC, choose the best answer. OpenStax Ch. 24 - Electromagnetic Waves 1. (3) Which type of electromagnetic (EM) waves has the highest frequency in vacuum? a. x-rays. b. infrared. c. red light. d. blue light. e. ultraviolet. f. AM radio. g. all tie. 2. (3) An EM wave is traveling vertically upward with its magnetic field vector oscillating north-south. Its electric field vector is oscillating a. north-south. b. east-west. c. vertically up and down. 3. (3) The first physicist to confirm the generation and detection of EM waves by using LC oscillator circuits was a. Alexander Bell. b. James Watt. c. Andr´e-Marie Amp`ere. d. Heinrich Hertz. e. Carl Friedrich Gauss. 4. (3) TF In vacuum, electromagnetic waves of higher frequencies travel faster than lower frequencies. 5. (3) TF EM waves in vacuum can be considered to be transverse waves. 6. (3) TF Earth's ozone layer is important in blocking dangerous infrared light from the sun. 7. (3) Which physical effect did James Clerk Maxwell add into the equations of electromagnetism that carry his name, based on theoretical reasoning? a. changing magnetic fields produce electric fields. b. changing electric fields produce magnetic fields. c. moving electric charges produce magnetic fields. d. moving electric charges experience magnetic forces.
    [Show full text]
  • 7. Documentation
    7. Documentation Papahänaumokuäkea Marine National Monument 7. Documentation 7.a Photographs, Image Inventory and Other Audiovisual Materials (Photo: James Watt) Table 7.1: Image inventory and authorization Id. No. Format Caption Date Photographer / Copyright owner Contact details: Non- Director of (if different than copyright owner exclusive the video photographer/ cession of director of video) rights Birds 1 JPEG French Frigate Shoals 2005 James Watt Sue Watt Sue@Seapics 1 - Red Footed Boobie 808-329-4253 Sunset Birds 2 JPEG Kure - Laysan 2005 NOAA Andy.Collins@ Y Albatross NOAA.gov Birds 3 JPEG Laysan - Great 2005 James Watt Sue Watt Sue@Seapics 1 frigatebird 808-329-4253 Birds 4 JPEG Laysan - Laysan Duck 2005 James Watt Sue Watt Sue@Seapics 1 808-329-4253 Birds 5 TIF Midway Atoll - White 2007 Sandra Hall USFWS Barbara_ Y Tern Chick [email protected] Cetaceans 1 JPEG Humpback Whale 2007 Doug Perrine HIHWNMS Naomi.Mcintosh@ 2 224 Mother and Calf NOAA.gov Cetaceans 2 JPEG Leaping Dolphin 2005 Andy Collins NOAA Andy.Collins@ Y NOAA.gov Cetaceans 3 JPEG Midway - Spinner 2005 James Watt Sue Watt Sue@Seapics 1 Dolphin bottom view 808-329-4253 Coral & JPEG French Frigate Shoals 2007 JE Maragos USFWS Barbara_ Y Invertebrates - Acropora Coral [email protected] 1 Coral & JPEG French Frigate Shoals 2005 James Watt Sue Watt Sue@Seapics 1 Invertebrates - Table coral 808-329-4253 2 Coral & JPEG Hertwigia Sponge 2007 NOWRAMP NOAA Andy.Collins@ Y Invertebrates NOAA.gov 3 Coral & JPEG Kure - Triton Trumpet 2005 James Watt Sue Watt Sue@Seapics 1 Invertebrates 808-329-4253 4 Coral & JPEG Kure-Banded Spiny 2005 James Watt Sue Watt Sue@Seapics 1 Invertebrates Lobster 808-329-4253 5 7.
    [Show full text]
  • Electronics 101
    Electronics 101 NANT – New York John Sweeny OFF Saturday – September 28th, 2013 Is this your understanding of a Dialysis Machine? 2 Electricity is intimidating because… Human aren’t equipped to detect it …until it’s to late ! You have five senses: ◦ See (10,000 volts) ◦ Hear (5,000 volts) ◦ Taste (???) ◦ Smell (ozone from movement in air) ◦ Feel ( a/c > 20 volts, static > 3,000 volts) Skin is your best protection if it’s dry. Electricity tends to flow on the outside of the body. The heart is mid-torso. 3 Basic Electron Characteristics 4 Electrical Terminology Coulomb (Q) – mks system’s unit of charge. 1 coulom b of charge passing a point in a wire in 1 second equals one ampere. 1 coulomb = 6.24 x 1018 electrons ◦ Charles Augustin Coulomb (1736 – 1806) Volt (()V) – measure of ppgyotential energy in an electric field. 1 volt = one joule of energy per one coulomb of charge. (1 watt = 1 joule/second) ◦ Alessandro Volta (1745 – 1827) ◦ Created the first chemical battery 5 Electrical Terminology Ampere (I) – The unit of current = a “flow rate” of one coulomb per second in a wire ◦ Andre Marie Ampere (1775 – 1836) ◦ Established the relationshippy between electricity and magnetism. Ohm (R or Ω) – the unit of resistance = 1 ohm is the ratio of one volt/one ampere. The reciproca l of resistance is conductance. ◦ Georgg( Simon Ohm (1789 – 1854) ◦ Discovered the direct proportionality of current in a conductor to the voltage applied (V = IR, R = V/I, I = V/R) 6 Electrical Terminology Watt – Unit of power in the mks system.
    [Show full text]
  • Great Moments in Science and Technology English, Spanish, French: 103 X 15 Min
    SCIENCE TECHNOLOGY MEDICINE DOCUMENTARY 15 MIN. VERSIONS Great Moments in Science and Technology English, Spanish, French: 103 x 15 min. Arabic: 89 x 15 min. The viewer gains an insight into both the scientific and the socio-political background to an Portuguese: 33 x 15 min. invention or discovery. Pioneers of science are portrayed, and the nature of their research and its further development through to the present are reconstructed. RIGHTS Not available worldwide. Computer animations are used to make certain processes easier to understand and to show Please contact your regional how various systems function. Re-enacted scenes illustrate the conditions under which the distribution partner. scientists worked and the approach they took. Particularly impressive are the historical film sequences, some of which date back to the early days of cinematography. ORDER NUMBER 24 4110 | 01 – 103 01 Wilhelm C. Röntgen: X-rays 30 Louis Pasteur, Robert Koch: English, Spanish, French 02 The Lumière Brothers: Bacteriology Cinematography 31 Edward Jenner, Paul Ehrlich, 24 4110 | 01 – 89 03 Otto Lilienthal: The Glider Emil von Behring: Vaccination Arabic 04 Werner von Siemens: 32 Alexander Fleming, Howard Florey, The Electric Dynamo Ernst Chain: Penicillin 24 4110 | 01 – 32, 47 05 Nikolaus August Otto: 33 Horace Wells, William Morton, Portuguese The Four-stroke Engine John Warren: Anaesthesia 06 Louis Daguerre: The Camera 34 Joseph Lister, Ignaz Semmelweis: 07 Karl Friedrich Drais: The Bicycle Antisepsis 08 Heinrich Hertz: Electromagnetic Waves 35 Ramón y Cajal: Neuron Theory 09 The Wright brothers: The Aeroplane 36 Frederick Banting, Charles Best, 10 Thomas Alva Edison: The Light Bulb John Macleod, James Collip: Insulin 11 Johann Philipp Reis, 37 Karl Landsteiner: Alexander Graham Bell: The Telephone The AB0 Blood Group System 12 Samuel F.
    [Show full text]
  • Feeling Joules and Watts
    FEELING JOULES AND WATTS OVERVIEW & PURPOSE Power was originally measured in horsepower – literally the number of horses it took to do a particular amount of work. James Watt developed this term in the 18th century to compare the output of steam engines to the power of draft horses. This allowed people who used horses for work on a regular basis to have an intuitive understanding of power. 1 horsepower is about 746 watts. In this lab, you’ll learn about energy, work and power – including your own capacity to do work. Energy is the ability to do work. Without energy, nothing would grow, move, or ​ change. Work is using a force to move something over some distance. ​ ​ work = force x distance Energy and work are measured in joules. One joule equals the work done (or energy ​ ​ used) when a force of one newton moves an object one meter. One newton equals the ​ ​ force required to accelerate one kilogram one meter per second squared. How much energy would it take to lift a can of soda (weighing 4 newtons) up two meters? work = force x distance = 4N x 2m = 8 joules Whether you lift the can of soda quickly or slowly, you are doing 8 joules of work (using 8 joules of energy). It’s often helpful, though, to measure how quickly we are ​ ​ doing work (or using energy). Power is the amount of work (or energy used) in a given ​ ​ amount of time. http://www.rdcep.org/demo-collection page 1 work power = time Power is measured in watts. One watt equals one joule per second.
    [Show full text]
  • A HISTORICAL OVERVIEW of BASIC ELECTRICAL CONCEPTS for FIELD MEASUREMENT TECHNICIANS Part 1 – Basic Electrical Concepts
    A HISTORICAL OVERVIEW OF BASIC ELECTRICAL CONCEPTS FOR FIELD MEASUREMENT TECHNICIANS Part 1 – Basic Electrical Concepts Gerry Pickens Atmos Energy 810 Crescent Centre Drive Franklin, TN 37067 The efficient operation and maintenance of electrical and metal. Later, he was able to cause muscular contraction electronic systems utilized in the natural gas industry is by touching the nerve with different metal probes without substantially determined by the technician’s skill in electrical charge. He concluded that the animal tissue applying the basic concepts of electrical circuitry. This contained an innate vital force, which he termed “animal paper will discuss the basic electrical laws, electrical electricity”. In fact, it was Volta’s disagreement with terms and control signals as they apply to natural gas Galvani’s theory of animal electricity that led Volta, in measurement systems. 1800, to build the voltaic pile to prove that electricity did not come from animal tissue but was generated by contact There are four basic electrical laws that will be discussed. of different metals in a moist environment. This process They are: is now known as a galvanic reaction. Ohm’s Law Recently there is a growing dispute over the invention of Kirchhoff’s Voltage Law the battery. It has been suggested that the Bagdad Kirchhoff’s Current Law Battery discovered in 1938 near Bagdad was the first Watts Law battery. The Bagdad battery may have been used by Persians over 2000 years ago for electroplating. To better understand these laws a clear knowledge of the electrical terms referred to by the laws is necessary. Voltage can be referred to as the amount of electrical These terms are: pressure in a circuit.
    [Show full text]
  • Steam Engines
    Evolving Design Steam Engines Tetsuo Tomiyama ([email protected]) 1 Intelligent Mechanical Systems, Bio-Mechanical Engineering Faculty of Mechanical, Maritime and Materials Engineering Overview • A Small Question • History of Thermodynamics • Steam Engines • Thomas Newcomen • James Watt • After Watt • Improvements • Steam Cars • Steam Locomotives • Steamboats • Exam 2008 Wb3110: Steam Engines 2 ©2011 Tetsuo Tomiyama Which is the Oldest? • MIT 1861 • Second Law of Thermodynamics 1850 Rudolf Julius Emanuel Clausius (1822-1888) • TU Delft 1842 Wb3110: Steam Engines 3 ©2011 Tetsuo Tomiyama Definition of Mechanical Engineering • “To Build and Run a Steam Engine!” • (Unofficial Version@ME MIT) Wb3110: Steam Engines 4 ©2011 Tetsuo Tomiyama History of Thermodynamics • 1660: Robert Boyle Boyle's Law • 1712: Thomas Newcomen • 1741: École Nationale des Ponts et Chaussés • 1765: James Watt (Only the Idea) • 1770: Steam Car • 1776: James Watt (The Engine), Steamboat • 1794: Ecole Polytechnique • 1804: Steam Locomotive • 1824: Sadi Carnot, Carnot Cycle • 1842: TU Delft Wb3110: Steam Engines 5 ©2011 Tetsuo Tomiyama History of Thermodynamics • 1843: James Joule, Mechanical Equivalent of Heat • 1847: Hermann von Helmholtz, Definitive Statement of the First Law of Thermodynamics • 1849: William John Macquorn Rankine, Saturated Vapor Table (Pressure and Temperature) • 1850: Rudolf Clausius, The Second Law of Thermodynamics • 1851: Thomson an Alternative Statement of the Second Law • 1854: Clausius, Found dQ/T, but Did Not Name It • 1854: Rankine, Entropy
    [Show full text]
  • Power Equation Powerpower Lawlaw Ian Woofenden ©2000 Ian Woofenden
    Word Power two units will give you the rest of the equation. If one is above the other, divide. If the remaining two are beside each other, multiply. P (watts) Renewable Energy Terms I E (amps) (volts) Watts = Volts x Amps Power Equation PowerPower LawLaw Ian Woofenden ©2000 Ian Woofenden Derivation: The watt, volt, and amp are named after So there are really three forms of the same equation: three well-known people in the history of energy— Watts = Volts x Amps James Watt, Alessandro Volta, and Andre Ampere. This equation does not seem to have a formal Volts = Watts ÷ Amps name, so I’ll just call it the “power equation.” Amps = Watts ÷ Volts To understand the power equation, you need to We can use this equation to do lots of common understand what power is. Power is the rate at which electrical computations. For example, if a motor is energy is generated or used. Though no analogy is drawing 20 amps at 12 volts, we know that it’s using perfect, energy is like miles traveled, while power is like energy at the rate of 240 watts (watts = volts x amps). If the rate of travel—miles per hour. a lightbulb is drawing 100 watts at 4 amps, we can Power is measured in watts. When we see a 50 watt conclude that the voltage is 25 volts (volts = watts ÷ lightbulb, we know it uses energy at a certain rate. amps). And if we have a 150 watt lightbulb running on Technically, a watt is equal to one joule per second.
    [Show full text]
  • Thermodynamics, Heat Conversion, and Fluid Mechanics Jaime Wisniak*
    PARA QUITARLE EL POLVO La química en la historia, para la enseñanza. William John Macquorn Rankine Thermodynamics, heat conversion, and fluid mechanics Jaime Wisniak* Resumen Life and career William John Macquorn Rankine (1820-1870) fue un William John Macquorn Rankine (Figure 1) was científico, educador e ingeniero muy prolífico y mul- born in Edinburgh on July 5, 1820, the youngest of tifuncional, un pionero en el esfuerzo de llevar los the two sons of David Rankine of the Riffle Brigade, recursos de las matemáticas y la física a los proble - a former army lieutenant and then civil engineer, mas prácticos de la ciencia y la ingeniería. Sus con- and Barbara Grahame, the elder daughter of Archi- tribuciones abarcan un amplio intervalo de activi- bald Grahame, banker in Glasgow. His brother died dades: termodinámica, conversión del calor, in childhood. Rankine records of himself, “My ear- mecánica de fluidos, construcción de barcos, mecá- liest recollection is that of my mother teaching the nica de los sólidos y de los suelos, así como temas Lord’s Prayer, next to my father explaining to me the filosóficos. Él es particularmente famoso por sus character of Jesus Christ;” and further he records, contribuciones a la termodinámica, al entendimien- “My early instruction in arithmetic and elementary to de las máquinas térmicas y al desarrollo de la mechanics and physics was mainly obtained from segunda ley. Entre sus contribuciones en esta área my father.” The mutual dependency thus begun tenemos la escala Rankine de temperaturas y el ciclo continued through as beautiful a life of mutual devo- de vapor Rankine para la conversión de calor en tion between parents and son as can be pictured; for trabajo.
    [Show full text]
  • Some Important Historical Names, Dates,* and Events
    Some Important Historical Names, Dates,* and Events MATHEMATICAL GENERAL Early Beginnings (Before the Sixth Century B.C.) B.C. 30,000 Notched wolf bone B.C. 3300 Menes unites Egypt 8000 Ishango bone 2600 Great Pyramid at Gizeh 2500 Table tablets from Nippur 2100 Code of Hammurabi 1900 Plimpton 322 1500 Phoenician alphabet 1850 Moscow Papyrus 1200 Trojan War 1650 Rhind Papyrus 700 Homer: The Odyssey Classical Period (Sixth Century B.C. to Fifth Century) B.C. 622-547 Thales of Miletus B.C. 558-486 Darius the Great 585-500 Pythagoras of Samos 485-430 Herodotus ca. 470 Theodorus of Cyrene 480 Battle of Thermopylae 460-380 Hippocrates of Chios 469-399 Socrates ca. 420 Hippias of Elis 431 Peloponnesian War 408-355 Euxodus of Cnidos 388 Plato founds Academy 323-285 Euclid 356-323 Alexander the Great 287-212 Archimedes ca. 370 Eudemus of Rhodes 262-190 Apollonius of Perga 331 Foundation of Alexandria ca. 240 Nicomedes 213 Books burned in China ca. 230 Eratosthenes of Cyrene 212 Fall of Syracuse to Romans A.D. ca. 75 Heron of Alexandria 195 Rosetta Stone engraved ca. 100 Nicomachus of Gerasa 106-43 Cicero 85-160 Claudius Ptolemy 44 Assassination of Caesar ca. 250 Diophantus 27 Beginning of Roman Empire ca. 260 Liu Hui A.D. 100 Paper made in China ca. 300 Pappus of Alexandria 272-337 Constantine the Great 365-395 Theon of Alexandria 286 Division of the Empire / d. 415 Hypatia 324 Constantinople founded 410-485 Proclus 455 Vandals sack Rome *Most dates before 600 B.C.
    [Show full text]