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Calculating Numerical Roots = = 1.37480222744
#10 in Fundamentals of Applied Math Series Calculating Numerical Roots Richard J. Nelson Introduction – What is a root? Do you recognize this number(1)? 1.41421 35623 73095 04880 16887 24209 69807 85696 71875 37694 80731 76679 73799 07324 78462 10703 88503 87534 32764 15727 35013 84623 09122 97024 92483 60558 50737 21264 41214 97099 93583 14132 22665 92750 55927 55799 95050 11527 82060 57147 01095 59971 60597 02745 34596 86201 47285 17418 64088 91986 09552 32923 04843 08714 32145 08397 62603 62799 52514 07989 68725 33965 46331 80882 96406 20615 25835 Fig. 1 - HP35s √ key. 23950 54745 75028 77599 61729 83557 52203 37531 85701 13543 74603 40849 … If you have had any math classes you have probably run into this number and you should recognize it as the square root of two, . The square root of a number, n, is that value when multiplied by itself equals n. 2 x 2 = 4 and = 2. Calculating the square root of the number is the inverse operation of squaring that number = n. The "√" symbol is called the "radical" symbol or "check mark." MS Word has the radical symbol, √, but we often use it with a line across the top. This is called the "vinculum" circa 12th century. The expression " (2)" is read as "root n", "radical n", or "the square root of n". The vinculum extends over the number to make it inclusive e.g. Most HP calculators have the square root key as a primary key as shown in Fig. 1 because it is used so much. Roots and Powers Numbers may be raised to any power (y, multiplied by itself x times) and the inverse operation, taking the root, may be expressed as shown below. -
Calculating Solutions Powered by HP Learn More
Issue 29, October 2012 Calculating solutions powered by HP These donations will go towards the advancement of education solutions for students worldwide. Learn more Gary Tenzer, a real estate investment banker from Los Angeles, has used HP calculators throughout his career in and outside of the office. Customer corner Richard J. Nelson Learn about what was discussed at the 39th Hewlett-Packard Handheld Conference (HHC) dedicated to HP calculators, held in Nashville, TN on September 22-23, 2012. Read more Palmer Hanson By using previously published data on calculating the digits of Pi, Palmer describes how this data is fit using a power function fit, linear fit and a weighted data power function fit. Check it out Richard J. Nelson Explore nine examples of measuring the current drawn by a calculator--a difficult measurement because of the requirement of inserting a meter into the power supply circuit. Learn more Namir Shammas Learn about the HP models that provide solver support and the scan range method of a multi-root solver. Read more Learn more about current articles and feedback from the latest Solve newsletter including a new One Minute Marvels and HP user community news. Read more Richard J. Nelson What do solutions of third degree equations, electrical impedance, electro-magnetic fields, light beams, and the imaginary unit have in common? Find out in this month's math review series. Explore now Welcome to the twenty-ninth edition of the HP Solve Download the PDF newsletter. Learn calculation concepts, get advice to help you version of articles succeed in the office or the classroom, and be the first to find out about new HP calculating solutions and special offers. -
HP-16C Computer Scientist
I ~4 HEWLETT-PACKARD HP-16C Computer Scientist OWNER S HANDBOOK Us I .III ieSSSSIImini iiiiii «iawl ^37=- (-W) Ris=i(+W) -3 mmn mtrnt mrmi M*m* tmtm i WKtni W4MU WK0013 7W7WW TltflU tWMII MM It'l JBF47Sf2 H7F37W tWHN NOTICE Hewlett-Packard Company makes no express or implied warranty with regard to the keystroke procedures and program material offered or their merchantability or their fitness for any particular purpose. The keystroke procedures and program material are made available solely on an "as is" basis, and the entire risk as to their quality and performance is with the user. Should the keystroke procedures or program material prove defective, the user (and not Hewlett-Packard Company nor any other party) shall bear the entire cost of all necessary correction and all incidental or consequential damages. Hewlett-Packard Company shall not be liable for any incidental or consequential damages in connection with or arising out of the furnishing, use, or performance of the keystroke procedures or program material. Thai HEWLETT m^f!M PACKARD HP-16C Computer Scientist Owner's Handbook April 1982 00016-90001 Printed in U.S.A. © Hewlett-Packard Company 1 982 Introduction Welcome to the world of the Hewlett-Packard Computer Scientist! You're in good company with HP—the calculator of choice for astronauts in the space shuttle, climbers on Mt. Everest, yachtsmen in the America's Cup, and engineers, scientists, and students the world over. The HP-16C is a versatile and unique calculator, especially designed for the many professionals and students who work with computers and microprocessors—whether as programmers or designers. -
HP Scientific Calculators Which One Is Right for You?
HP Calculators HP Scientific Calculators Which one is right for you? HP Scientific calculators are equipped with easy-to-use problem solving tools, enhanced capabilities and customized options, plus award-winning HP support. When choosing the right scientific calculator, make sure to purchase the one that best fits your needs. Use the comparison chart below to compare HP scientific calculator models. HP 10s+ HP 300s+ HP 35s Perfect for Students in middle and high school Students in middle and high school University students and technical professionals Key Characteristics User-friendly design, easy-to-read display Sophisticated calculator with easy-to-read Professional performance featuring RPN* and a wide range of algebraic, trigonometric, 4-line display, unit conversions as well mode, keystroke programming, the HP Solve** probability and statistics functions. as algebraic, trigonometric, logarithmic, application as well as algebraic, trigonometric, probability and statistics functions. logarithmic and statistics functions, Calculation Mode(s) Algebraic Algebraic Algebraic and RPN Display Size 2 lines x 12 characters, linear display 4 lines x 15 characters, linear display 2 lines , 14 characters, linear display Built-in Functions 240+ 315+ 100+ Size (L x W x D) 5.79 x 3.04 x 0.59 in 5.79 x 3.04 x 0.59 in 6.22 x 3.23 x 0.72 in Subject Suitability General mathematics, Arithmetic, Algebra, General mathematics, Arithmetic, Algebra, Mathematics geared towards Engineering, Trigonometry, Statistics probability Trigonometry, Statistics, Probability Surveying, Science, Medicine Additional Features Solar power plus a battery backup, decimal/ Table-based statistics data editor, solar 800 storage registers, physical constants, hexadecimal conversions, nine memory power plus a battery backup, integer division, unit conversions, adjustable contrast display, registers, slide-on protective cover. -
RPN Calculators for Linux
LinuxFocus article number 319 http://linuxfocus.org RPN calculators for Linux by Guido Socher (homepage) About the author: Abstract: My first RPN calculator was a HP15c and it was RPN stands for Reverse Polish Notation. Reverse Polish Notation was love at first sight. developed in 1920 by Jan Lukasiewicz as a way to write a mathematical expression without using parentheses and brackets. It takes a few minutes to learn RPN but you will soon see that this entry method is superior to the algbraic format. _________________ _________________ _________________ Introduction RPN pocket calculators became popolar with the HP calculators. HP used this entry method already for it's first calculator in 1968. If you search the internet you will find that there is a whole fan club behind those HP calculators. I have made a number of very good links available at the end of this article. Most of those HP calculators are today collectors items and sell now for much more than their original price. In this article will present some of the RPN desktop calculators available for Linux. We will not only look at the HP emulators which are available but also other RPN calculators which are totally independent of HP. What is RPN? Why RPN? RPN calculators use a stack and all mathematical operations are executed immediately on the lower level of the stack. The stack is used as a memory to save results which you need to further evaluate your formula. Therefore you do not need any brackets on an RPN calculator. You first enter the numbers, push them up the stack, and then you say what you want to do with those numbers. -
Rplsh: an Interactive Shell for Stack-Based Numerical Computation
RPLsh: An Interactive Shell for Stack-based Numerical Computation Kevin P. Rauch Dept. of Astronomy, University of Maryland, College Park, MD 20742 Abstract. RPL shell1, or RPLsh, is an interactive numerical shell designed to combine the convenience of a hand-held calculator with the computa- tional power and advanced numerical functionality of a workstation. The user interface is modeled after stack-based scientific calculators such as those made by Hewlett-Packard (RPL2 is the name of the Forth-like pro- gramming language used in the HP 48 series), but includes many features not found in hand-held devices, such as a multi-threaded kernel with job control, integrated extended precision arithmetic, a large library of spe- cial functions, and a dynamic, resizable window display. As a native C/C++ application, it is over 1000 times faster than HP 48 emulators (e.g., Emu483) in simple benchmarks; for extended precision numerical analysis, its performance can exceed that of Mathematica R by similar amounts. Current development focuses on interactive user functionality, with comprehensive programming/debugging support to follow. 1. Introduction The notion of progress in computer hardware has always been closely tied to the speed and sophistication with which numerical calculations can be performed. While the continuation of Moore's Law has resulted in hand-held devices more powerful than the 30 ton ENIAC machine, there is a growing gap between the speed and capabilities of hand-held scientific calculators as compared to desk- top workstations|the result of both market forces (pricing pressure) and phys- ical limitations (keyboard/screen size). Numerical analysis packages such as Mathematica or IDL, by contrast, are oriented towards script or command line processing, and lack the interactive amenities found in a traditional calculator. -
Electronic Calculators: Which Notation Is the Better?
Applied Ergonomics 1980, 11.1, 2-6 Electronic calculators: which notation is the better? S.J. Agate and C.G. Drury Department of Industrial Engineering, State University of New York at Buffalo Tests of an Algebraic Notation Calculator and a Reverse Polish Notation Calculator showed the latter to be superior in terms of calculation speed, particularly for subjects with a technical background. The differences measured were shown not to be due to differences in calculation speed of the calculators nor to differences in dexterity between the subjects. Introduction parentheses where execution of operators must be delayed." (Whitney, Rode and Tung, 1972.) The advent of the electronic calculator has had a tremendous effect on the working life of many scientists It is surprising that the two rival sides of the pocket and technologists and is now beginning to affect the lives calculator industry should not have published experimental of ordinary consumers. The change from the cams and data to support their claims. A literature search revealed gears of electromagnetic machines to integrated circuits two articles in Consumer Reports (1975a and b) suggesting has brought with it large changes in the industry that RPN "takes some getting used to" and that a simple manufacturing these devices, (Anon, 1976), but more rather than a scientific calculator should be used for importantly it has forced each manufacturer to opt for a simple calculations such as checkbook balancing. Another particular logic routine. This is the set of rules governing article published by the Consumers' Association ("Which?". the sequencing of input to the machine by the operator 1973), where 20 different calculators were tested for various operating functions that a person should look at The two logic routines in general use are Algebraic Notation (AN) and Reverse Polish Notation (RPN). -
Introduction to UIL High School Calculator Applications Contest
Introduction to UIL High School Calculator Applications Contest Andy Zapata Azle High School Andy Zapata Azle ISD – 1974 to present Azle HS – Physics teacher Married – 4 children & 2 grandchildren Co-founded Texas Math and Science Coaches Association (TMSCA) Current president of TMSCA Coached all 4 UIL math & science events + slide rule Current UIL Elem/JH number sense, mathematics and calculator consultant [email protected] The Calculator Applications Contest is exactly what the title of the contest implies. It is not a mathematics contest where proofs of geometry or algebra theorems are worked out; it is not a typing contest where the fastest button pusher always has the superior score. It is a contest where engineering type problems are solved. I am not an engineer, but I know a few people that do engineering work, and the ability to use the calculator as a tool to solve; or least begin the problem solving process is very important. But I will also be the first to tell you that the problem topics covered in these contest papers cover finance problems, navigation problems, exponential and compound growth and decay problem, problems involving probability and problems involving calculus that go beyond the averaging processes that occur when calculus cannot be used. If you have students that are curious and competitive, they like math and they like to solve problems; then here is a great opportunity for them to flourish and learn more about the problem solving process than they would normally learn in the high school math program. In 1982 I moved up from teaching seventh grade math to teaching a few classes of physics and different math classes until there were enough students taking physics so that I could have all my classes be physics classes. -
HP 35S Quick Start Guide English EN F2215-90201 Edition 1 V 4.Book
HP 35s Scientific Calculator Quick Start Guide Edition 1 HP part number: F2215-90201 Legal Notices This manual and any examples contained herein are provided "as is" and are subject to change without notice. Hewlett-Packard Company makes no warranty of any kind with regard to this manual, including, but not limited to, the implied warranties of merchantability, non-infringement and fitness for a particular purpose. In this regard, HP shall not be liable for technical or editorial errors or omissions contained in the manual. Hewlett-Packard Company shall not be liable for any errors or for incidental or consequential damages in connection with the furnishing, performance, or use of this manual or the examples contained herein. Copyright © 2008 Hewlett-Packard Development Company, L.P. Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws. Hewlett-Packard Company 16399 West Bernardo Drive San Diego, CA 92127-1899 USA Printing History Edition 1, version 4, Copyright December 2008 Table of Contents Welcome to your HP 35s Scientific Calculator ........................ 1 Turning the Calculator On and Off ........................................ 2 Adjusting Display Contrast.................................................... 2 Keyboard ........................................................................... 3 Alpha Keys ......................................................................... 4 Cursor Keys ....................................................................... -
The HP-41C: a Literate Calculator?
System Review The HP-41C: A Literate Calculator? Brian P Hayes Scientific American 415 Madison Ave New York NY 10017 Calculator vs Computer can be full of surprises, often to the frustration of the pro The computer and the programmable calculator seem grammer. to be following paths of convergent evolution. As the one The HP-41C, which was introduced by the Hewlett- is made smaller while the other gains in capability, the Packard Company about a year ago, is among the pro line of demarcation between them becomes more and grammable calculators that lie closest to the computer more arbitrary. For now at least, the programmable borderline. It comes close enough for the jargon of com calculator remains a distinct and lesser species, but it puters to be useful in describing it. At the Corvallis Divi shares many of the attributes of the computer. Moreover, sion of Hewlett-Packard, where the HP-41C is made, the shared attributes are chiefly the ones that make the they refer to the calculator itself as the ''mainframe" and computer an interesting machine. Both devices offer an to its accessory devices as the "peripherals." The intimate acquaintance with the powers and pleasures of calculator comes equipped with four input/output (I/O) algorithms. Both exhibit an enigmatic unpredictability: ports, through which the various elements of the system the response of the machine to any given stimulus is are interconnected. Because the peripherals do some data wholly deterministic, yet the behavior of a large program processing internally, the system might even be said to have "distributed intelligence." When compared with a computer, most programmable calculators have a rich instruction set, but they are defi cient in memory capacity and in facilities for communica tion with the user. -
An Evolutionary RPN Calculator for Technical Professionals
An Evolutionary RPN Calculator for Technical Professionals Symbolic algebraic entry, an indefinite operation stack size, and a variety of data types are some of the advancements in HP's latest scientific calculator. by William C. Wickes THE HP-28C (Fig. 1} provides the most extensive • Symbolic algebra and calculus mathematical capabilities ever available in a hand An automated numerical root-finder (see article on page held calculator. Its built-in feature set exceeds even 30. the capabilities of the earlier HP-71B Handheld Computer1 • Vector and matrix math operations with its Math ROM.2 Furthermore, the HP-28C introduces Automatic plotting of functions and statistical data a new dimension in calculator math operations — symbolic Unit conversions among arbitrary combinations of 120 algebra and calculus. A user can perform many real and built-in units and user-defined units complex number calculations with purely symbolic quan • Integer base arithmetic, bit manipulations, and logic op tities, delaying numerical evaluation indefinitely. This al erations in either binary, octal, decimal, or hexadecimal lows a user to formulate a problem, work through to a notation solution, and study the mathematical properties of the so A keystroke-capture programming language enhanced lution entirely on the calculator. by high-level program control structures The HP-28C has the following features: An infrared printer interface for printing and graphics An RPN calculator interface allowing an indefinite output on the optional HP 82240A Infrared Printer. number of stack levels and a variety of data types The HP-28C's physical package differs from that of the A softkey menu system for key-per-function execution HP-18C Business Consultant (see page 4) in only two as of all built-in and user-defined procedures and data pects. -
HP-45 Owner's Handbook
Hewlett-Packard's interest in computation evolved as a natural extension of our traditional involvement in measurement problem solving. At an early date, HP recognized the growing need for a family of computational products designed to work easily and effectively with scientific instruments. In 1966 we introduced the first digital minicomputer specifically designed to meet this need. Soon after, we followed up with our first programmable calculator. From these beginnings, HP has now become an acknowledged leader in the field of computational problem solving. More than 20,000 HP programmable calculators and digital computers are at work in a wide range of applications in science, industry, education, medicine, and business. Their ef fectiveness is further enhanced by a complete line of accessory devices, ranging from digital tape and disc drives to card and tape readers, printers, and plotters. Lately we've coupled our experience in scientific problem solving and computational technology to bring you new dimensions in personal computation-the HP-80 Business Pocket Calculator for solving problems in business and finance, the HP-35 Scientific Pocket Calculator for engineering/ scientific applications, and now the HP-45 Advanced Scientific Pocket Calculator whose expanded functional capability and multiple storage registers allow complex problems to be handled with unprecedented ease. <CI HEWLETT· PACKARD COMP"NY, 1973 Attention Please! To give you more computing power, your HP-45 works in a con sistent and natural way that may be slightly different from previous calculators you have operated. Even though your new HP-45 is simple to operate, and you can start solving problems immediately by following the Quick Reference Guide accompanying the HP-45, you will find it worthwhile to read this handbook.