Mathematics, the Language of Watchmaking
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
NOTE: to Set Any Watch Function, the Digit(S) MUST Be Flashing
CONGRATULATIONS! You have selected a quality timepiece that will assist you in remembering tasks, managing your time and keeping focused. Perfect for reminders for medication and medical conditions, timing presentations or procedures, for cooking, parking meters and for keeping on schedule. The uses are endless. Set the “vibration” feature for alarm settings and countdown timer when you do not want to alert or disturb others or when you cannot hear an audible alarm. This unique watch has been carefully designed to give user satisfaction and to be user friendly. The large display is easy to read. Prompts are displayed to assist in easy setting. User options are easily set. Enjoy the many benefits of this wonderful watch. OPERATING MODES: CALENDAR ALARM CHRONO TIMER OPTION CLOCK (STOPWATCH) Vibra LITE 8 is a trademark of GLOBAL ASSISTIVE DEVICES, INC. Page 1 NOTE: To set any watch functions, the digit(s) that you want to set MUST BE FLASHING. When setting Calendar/Clocks, Alarms or Timer: if a delay of approx. 3 minutes occurs without buttons being pushed, digits will stop flashing and watch will return to Calendar/Clock Mode. Watch display will automatically return to Calendar/Clock Mode from Option Mode when no buttons are pushed in approx. 3 minutes. SETTING TIME OF DAY AND CALENDAR NOTE: THIS IS TIME ZONE 1 & MUST BE SET CORRECTLY FOR THE TIME OF DAY AS THE ALARMS WILL WORK BASED ON THIS TIME. Three Time Zones are available. Set Time Zone 1 for the time of day of your home location. This is the default Time and will show on the watch at all times when it is in the Calendar/Clock mode. -
Special Chronograph Instructions & Warranty
IMPORTANT! Register for your warranty Special Chronograph online at www.reactorwatch.com Instructions & Warranty Welcome IMPORTANT! REACTOR watches were conceived, Every analog REACTOR watch is fitted designed and built to withstand the real with a screw-down crown to ensure world of sport enthusiasts. We are very maximum water resistance. However, proud of what we have accomplished using your watch in water with the crown and we are excited to welcome you to unscrewed or only partially screwed our ever-growing family. down may result in leakage. While your REACTOR watch is built for ALWAYS CHECK THAT THE CROWN IS maximum durability, it should ALWAYS be COMPLETELY SCREWED DOWN BEFORE rinsed thoroughly after use in salt water. SUBMERGING YOUR WATCH! www.reactorwatch.com www.reactorwatch.com Warranty Service Our warranty is simple and straight If your watch needs service, return it to: forward: if anything goes wrong with Reactor Service your REACTOR watch in the first two 5312 Derry Ave., Suite B years of ownership, we will either repair Agoura Hills, CA 91301 or replace it at our expense. Please download the Repair Form from Here’s the “not so small print”: the Service section of our website, Normal wear and tear and abuse are not complete it, and include it with your considered manufacturing defects and watch. Our service center is committed are not covered by our warranty. to having your watch back to you in no more than 10 working days. www.reactorwatch.com www.reactorwatch.com Setting the Watch 1. Unscrew crown and pull to pos. 2. -
Pioneers in Optics: Christiaan Huygens
Downloaded from Microscopy Pioneers https://www.cambridge.org/core Pioneers in Optics: Christiaan Huygens Eric Clark From the website Molecular Expressions created by the late Michael Davidson and now maintained by Eric Clark, National Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32306 . IP address: [email protected] 170.106.33.22 Christiaan Huygens reliability and accuracy. The first watch using this principle (1629–1695) was finished in 1675, whereupon it was promptly presented , on Christiaan Huygens was a to his sponsor, King Louis XIV. 29 Sep 2021 at 16:11:10 brilliant Dutch mathematician, In 1681, Huygens returned to Holland where he began physicist, and astronomer who lived to construct optical lenses with extremely large focal lengths, during the seventeenth century, a which were eventually presented to the Royal Society of period sometimes referred to as the London, where they remain today. Continuing along this line Scientific Revolution. Huygens, a of work, Huygens perfected his skills in lens grinding and highly gifted theoretical and experi- subsequently invented the achromatic eyepiece that bears his , subject to the Cambridge Core terms of use, available at mental scientist, is best known name and is still in widespread use today. for his work on the theories of Huygens left Holland in 1689, and ventured to London centrifugal force, the wave theory of where he became acquainted with Sir Isaac Newton and began light, and the pendulum clock. to study Newton’s theories on classical physics. Although it At an early age, Huygens began seems Huygens was duly impressed with Newton’s work, he work in advanced mathematics was still very skeptical about any theory that did not explain by attempting to disprove several theories established by gravitation by mechanical means. -
Differential Geometry
Differential Geometry J.B. Cooper 1995 Inhaltsverzeichnis 1 CURVES AND SURFACES—INFORMAL DISCUSSION 2 1.1 Surfaces ................................ 13 2 CURVES IN THE PLANE 16 3 CURVES IN SPACE 29 4 CONSTRUCTION OF CURVES 35 5 SURFACES IN SPACE 41 6 DIFFERENTIABLEMANIFOLDS 59 6.1 Riemannmanifolds .......................... 69 1 1 CURVES AND SURFACES—INFORMAL DISCUSSION We begin with an informal discussion of curves and surfaces, concentrating on methods of describing them. We shall illustrate these with examples of classical curves and surfaces which, we hope, will give more content to the material of the following chapters. In these, we will bring a more rigorous approach. Curves in R2 are usually specified in one of two ways, the direct or parametric representation and the implicit representation. For example, straight lines have a direct representation as tx + (1 t)y : t R { − ∈ } i.e. as the range of the function φ : t tx + (1 t)y → − (here x and y are distinct points on the line) and an implicit representation: (ξ ,ξ ): aξ + bξ + c =0 { 1 2 1 2 } (where a2 + b2 = 0) as the zero set of the function f(ξ ,ξ )= aξ + bξ c. 1 2 1 2 − Similarly, the unit circle has a direct representation (cos t, sin t): t [0, 2π[ { ∈ } as the range of the function t (cos t, sin t) and an implicit representation x : 2 2 → 2 2 { ξ1 + ξ2 =1 as the set of zeros of the function f(x)= ξ1 + ξ2 1. We see from} these examples that the direct representation− displays the curve as the image of a suitable function from R (or a subset thereof, usually an in- terval) into two dimensional space, R2. -
House Watch Application Return Completed Form To: 218-326-4663 (Fax) | 440 1St Ave NE, Grand Rapids, MN 55744 | [email protected]
House Watch The Itasca County Sheriff’s Office provides the following house watch service to the residents of Itasca County. The following rules will apply; failure to comply will result in dismissal of your house watch. 1. The house watch program is available to residents that reside year-round in Itasca County. o Any person that has seasonal property or goes out of state for the winter is not eligible for a watch. 2. The house watch programs is available if your vacation is longer than 5 days and not longer than 30 days. o Any person gone for less than 5 days should have a neighbor/friend watch the residence. o Any person gone for more than 30 days should consider having an alarm installed along with a neighbor/friend watching the residence. 3. All house watches will be performed when officers have available time. 4. Any residence that has an alarm will not be eligible. 5. The house watch program requires that access to your property be kept clear and maintained year-round. 6. The house watch programs is designed to check for vandalism, property damage, and break- ins. 7. In the event that there would be a problem with your residence, we require that a key holder be named to take care of the problem. J: SHF>Records Deputy>House Watch House Watch Application Return completed form to: 218-326-4663 (fax) | 440 1st Ave NE, Grand Rapids, MN 55744 | [email protected] Homeowner Information Name: Street Address: City: State: Zip: Telephone: Cell Phone: Dates of Vacation: Location of Vacation: Key Holder Information Key Holder #1 Name: Daytime Phone: Nighttime Phone: Key Holder #2 Name: Daytime Phone: Nighttime Phone: Additional Information: Signature Date J: SHF>Records Deputy>House Watch . -
On the Isochronism of Galilei's Horologium
IFToMM Workshop on History of MMS – Palermo 2013 On the isochronism of Galilei's horologium Francesco Sorge, Marco Cammalleri, Giuseppe Genchi DICGIM, Università di Palermo, [email protected], [email protected], [email protected] Abstract − Measuring the passage of time has always fascinated the humankind throughout the centuries. It is amazing how the general architecture of clocks has remained almost unchanged in practice to date from the Middle Ages. However, the foremost mechanical developments in clock-making date from the seventeenth century, when the discovery of the isochronism laws of pendular motion by Galilei and Huygens permitted a higher degree of accuracy in the time measure. Keywords: Time Measure, Pendulum, Isochronism Brief Survey on the Art of Clock-Making The first elements of temporal and spatial cognition among the primitive societies were associated with the course of natural events. In practice, the starry heaven played the role of the first huge clock of mankind. According to the philosopher Macrobius (4 th century), even the Latin term hora derives, through the Greek word ‘ώρα , from an Egyptian hieroglyph to be pronounced Heru or Horu , which was Latinized into Horus and was the name of the Egyptian deity of the sun and the sky, who was the son of Osiris and was often represented as a hawk, prince of the sky. Later on, the measure of time began to assume a rudimentary technical connotation and to benefit from the use of more or less ingenious devices. Various kinds of clocks developed to relatively high levels of accuracy through the Egyptian, Assyrian, Greek and Roman civilizations. -
Evolute-Involute Partner Curves According to Darboux Frame in the Euclidean 3-Space E3
Fundamentals of Contemporary Mathematical Sciences (2020) 1(2) 63 { 70 Evolute-Involute Partner Curves According to Darboux Frame in the Euclidean 3-space E3 Abdullah Yıldırım 1,∗ Feryat Kaya 2 1 Harran University, Faculty of Arts and Sciences, Department of Mathematics S¸anlıurfa, T¨urkiye 2 S¸ehit Abdulkadir O˘guzAnatolian Imam Hatip High School S¸anlıurfa, T¨urkiye, [email protected] Received: 29 February 2020 Accepted: 29 June 2020 Abstract: In this study, evolute-involute curves are researched. Characterization of evolute-involute curves lying on the surface are examined according to Darboux frame and some curves are obtained. Keywords: Curve, surface, geodesic, curvature, frame. 1. Introduction The interest of special curves has increased recently. Some of these are associated curves. They are curves where one of the Frenet vectors at opposite points is linearly dependent to the other curve. One of the best examples of these curves is the evolute-involute partner curves. An involute thought known to have been used in his optical work came up in 1658 by C. Huygens. C. Huygens discovered involute curves while trying to make more accurate measurement studies [5]. Many researches have been conducted about evolute-involute partner curves. Some of them conducted recently are Bilici and C¸alı¸skan [4], Ozyılmaz¨ and Yılmaz [9], As and Sarıo˘glugil[2]. Bekta¸sand Y¨uceconsider the notion of the involute-evolute curves lying on the surfaces for a special situation. They determine the special involute-evolute partner D−curves in E3: By using the Darboux frame of the curves they obtain the necessary and sufficient conditions between κg , ∗ − ∗ ∗ τg; κn and κn for a curve to be the special involute partner D curve. -
Watch Instructions
ENGLISH Thank you for purchasing this MICHELE watch. The precision and quality of the quartz movement assures excellent accuracy and never needs winding. The following instructions are provided to help you familiarize yourself with the proper operation and care of your MICHELE watch. To ensure correct use, please read and follow the instructions carefully. All diamonds used on MICHELE watches are genuine diamonds and sourced from non-conflict areas. The total carat weight and number of stones are marked on the back of the case. 1 2 AND 3 HANDS MODELS (RONDA 703, 762, 773, 783, 713, 753, 763, 1069) Hour Minute Hour Minute I II I II Seconds Seconds Hour Minute I II Time Setting 1. Pull crown out to position II. 2. Turn crown clockwise to rotate hour and minute hands to desired time. 3. Push crown back to position I. 2 DATE MODELS (RONDA 705, 715, 785) Setting the Time Closed Setting the Date Rotate to set hour & minute I II III hands. Date advances with each 24 hour rotation of hour hand. Rapid correction of date Display 1 Display 2 Display 3 Closed Rotate to set hour & minute I II III hands. Date advances with each 24 hour rotation of hour hand. Rapid correction of date Display 1 Display 2 Display 3 Do not change the date between the hours of 10pm and 2am. This is the time when the movement is in position to carry out the automatic date change, and any interference may cause damage to the movement. For rapid correction of date, turn the crown either clockwise or counter-clockwise to set the date. -
Computer-Aided Design and Kinematic Simulation of Huygens's
applied sciences Article Computer-Aided Design and Kinematic Simulation of Huygens’s Pendulum Clock Gloria Del Río-Cidoncha 1, José Ignacio Rojas-Sola 2,* and Francisco Javier González-Cabanes 3 1 Department of Engineering Graphics, University of Seville, 41092 Seville, Spain; [email protected] 2 Department of Engineering Graphics, Design, and Projects, University of Jaen, 23071 Jaen, Spain 3 University of Seville, 41092 Seville, Spain; [email protected] * Correspondence: [email protected]; Tel.: +34-953-212452 Received: 25 November 2019; Accepted: 9 January 2020; Published: 10 January 2020 Abstract: This article presents both the three-dimensional modelling of the isochronous pendulum clock and the simulation of its movement, as designed by the Dutch physicist, mathematician, and astronomer Christiaan Huygens, and published in 1673. This invention was chosen for this research not only due to the major technological advance that it represented as the first reliable meter of time, but also for its historical interest, since this timepiece embodied the theory of pendular movement enunciated by Huygens, which remains in force today. This 3D modelling is based on the information provided in the only plan of assembly found as an illustration in the book Horologium Oscillatorium, whereby each of its pieces has been sized and modelled, its final assembly has been carried out, and its operation has been correctly verified by means of CATIA V5 software. Likewise, the kinematic simulation of the pendulum has been carried out, following the approximation of the string by a simple chain of seven links as a composite pendulum. The results have demonstrated the exactitude of the clock. -
ALBERT VAN HELDEN + HUYGENS’S RING CASSINI’S DIVISION O & O SATURN’S CHILDREN
_ ALBERT VAN HELDEN + HUYGENS’S RING CASSINI’S DIVISION o & o SATURN’S CHILDREN )0g-_ DIBNER LIBRARY LECTURE , HUYGENS’S RING, CASSINI’S DIVISION & SATURN’S CHILDREN c !@ _+++++++++ l ++++++++++ _) _) _) _) _)HUYGENS’S RING, _)CASSINI’S DIVISION _) _)& _)SATURN’S CHILDREN _) _) _)DDDDD _) _) _)Albert van Helden _) _) _) , _) _) _)_ _) _) _) _) _) · _) _) _) ; {(((((((((QW(((((((((} , 20013–7012 Text Copyright ©2006 Albert van Helden. All rights reserved. A H is Professor Emeritus at Rice University and the Univer- HUYGENS’S RING, CASSINI’S DIVISION sity of Utrecht, Netherlands, where he resides and teaches on a regular basis. He received his B.S and M.S. from Stevens Institute of Technology, M.A. from the AND SATURN’S CHILDREN University of Michigan and Ph.D. from Imperial College, University of London. Van Helden is a renowned author who has published respected books and arti- cles about the history of science, including the translation of Galileo’s “Sidereus Nuncius” into English. He has numerous periodical contributions to his credit and has served on the editorial boards of Air and Space, 1990-present; Journal for the History of Astronomy, 1988-present; Isis, 1989–1994; and Tractrix, 1989–1995. During his tenure at Rice University (1970–2001), van Helden was instrumental in establishing the “Galileo Project,”a Web-based source of information on the life and work of Galileo Galilei and the science of his time. A native of the Netherlands, Professor van Helden returned to his homeland in 2001 to join the faculty of Utrecht University. -
1 Functions, Derivatives, and Notation 2 Remarks on Leibniz Notation
ORDINARY DIFFERENTIAL EQUATIONS MATH 241 SPRING 2019 LECTURE NOTES M. P. COHEN CARLETON COLLEGE 1 Functions, Derivatives, and Notation A function, informally, is an input-output correspondence between values in a domain or input space, and values in a codomain or output space. When studying a particular function in this course, our domain will always be either a subset of the set of all real numbers, always denoted R, or a subset of n-dimensional Euclidean space, always denoted Rn. Formally, Rn is the set of all ordered n-tuples (x1; x2; :::; xn) where each of x1; x2; :::; xn is a real number. Our codomain will always be R, i.e. our functions under consideration will be real-valued. We will typically functions in two ways. If we wish to highlight the variable or input parameter, we will write a function using first a letter which represents the function, followed by one or more letters in parentheses which represent input variables. For example, we write f(x) or y(t) or F (x; y). In the first two examples above, we implicitly assume that the variables x and t vary over all possible inputs in the domain R, while in the third example we assume (x; y)p varies over all possible inputs in the domain R2. For some specific examples of functions, e.g. f(x) = x − 5, we assume that the domain includesp only real numbers x for which it makes sense to plug x into the formula, i.e., the domain of f(x) = x − 5 is just the interval [5; 1). -
Variation Analysis of Involute Spline Tooth Contact
Brigham Young University BYU ScholarsArchive Theses and Dissertations 2006-02-22 Variation Analysis of Involute Spline Tooth Contact Brian J. De Caires Brigham Young University - Provo Follow this and additional works at: https://scholarsarchive.byu.edu/etd Part of the Mechanical Engineering Commons BYU ScholarsArchive Citation De Caires, Brian J., "Variation Analysis of Involute Spline Tooth Contact" (2006). Theses and Dissertations. 375. https://scholarsarchive.byu.edu/etd/375 This Thesis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. VARIATION ANALYSIS OF INVOLUTE SPLINE TOOTH CONTACT By Brian J. K. DeCaires A thesis submitted to the faculty of Brigham Young University in partial fulfillment of the requirements for the degree of Master of Science Department of Mechanical Engineering Brigham Young University April 2006 Copyright © 2006 Brian J. K. DeCaires All Rights Reserved BRIGHAM YOUNG UNIVERSITY GRADUATE COMMITTEE APPROVAL of a thesis submitted by Brian J. K. DeCaires This thesis has been read by each member of the following graduate committee and by majority vote has been found to be satisfactory. ___________________________ ______________________________________ Date Kenneth W. Chase, Chair ___________________________ ______________________________________ Date Carl D. Sorensen ___________________________