Measurement of Mathematical Constant P and Physical Quantity Pi
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The Enigmatic Number E: a History in Verse and Its Uses in the Mathematics Classroom
To appear in MAA Loci: Convergence The Enigmatic Number e: A History in Verse and Its Uses in the Mathematics Classroom Sarah Glaz Department of Mathematics University of Connecticut Storrs, CT 06269 [email protected] Introduction In this article we present a history of e in verse—an annotated poem: The Enigmatic Number e . The annotation consists of hyperlinks leading to biographies of the mathematicians appearing in the poem, and to explanations of the mathematical notions and ideas presented in the poem. The intention is to celebrate the history of this venerable number in verse, and to put the mathematical ideas connected with it in historical and artistic context. The poem may also be used by educators in any mathematics course in which the number e appears, and those are as varied as e's multifaceted history. The sections following the poem provide suggestions and resources for the use of the poem as a pedagogical tool in a variety of mathematics courses. They also place these suggestions in the context of other efforts made by educators in this direction by briefly outlining the uses of historical mathematical poems for teaching mathematics at high-school and college level. Historical Background The number e is a newcomer to the mathematical pantheon of numbers denoted by letters: it made several indirect appearances in the 17 th and 18 th centuries, and acquired its letter designation only in 1731. Our history of e starts with John Napier (1550-1617) who defined logarithms through a process called dynamical analogy [1]. Napier aimed to simplify multiplication (and in the same time also simplify division and exponentiation), by finding a model which transforms multiplication into addition. -
Euler Number in Vedic Physics
The Purpose of the Euler Number in Vedic Physics By John Frederic Sweeney Abstract The Euler Number, or e logarithm, arises naturally from our combinatorial universe, the result of the interactive combination of three distinct states of matter. This paper provides the details about how this combinatorial process takes place and why the range of visible matter extends from Pi to the Euler Number. 1 Table of Contents Introduction 3 Wikipedia on the Euler Number 5 Vedic Physics on the Euler Number 6 Conclusion 8 Bibliography 9 2 Introduction The author posted a few papers on Vixra during 2013 which made statements about Pi and the Euler Number that lacked support. This paper offers the support for those statements. Since the explanation is mired, twisted and difficult to follow, the author wished to make other aspects of Vedic Particle Physics clear. This paper begins with Wikipedia on Euler, then to the Vedic Explanation. This paper, along with Why Pi? Which explains the reason why Pi carries such importance in a combinatorial world, should make it easier for readers to grasp the fundamental concepts of Vedic Particle Physics. Essentially, three states of matter exist in a combinatorial world, the axes of the states run from Pi to the Euler number. The simple formula of n + 1 suggests Pascal’s Triangle or Mount Meru, and the author has published a paper on this theme about Clifford Algebras, suggesting them as a most useful tool in a combinatorial universe. Someone once said that only those with clear understanding can explain things clearly and simply to others. -
Package 'Constants'
Package ‘constants’ February 25, 2021 Type Package Title Reference on Constants, Units and Uncertainty Version 1.0.1 Description CODATA internationally recommended values of the fundamental physical constants, provided as symbols for direct use within the R language. Optionally, the values with uncertainties and/or units are also provided if the 'errors', 'units' and/or 'quantities' packages are installed. The Committee on Data for Science and Technology (CODATA) is an interdisciplinary committee of the International Council for Science which periodically provides the internationally accepted set of values of the fundamental physical constants. This package contains the ``2018 CODATA'' version, published on May 2019: Eite Tiesinga, Peter J. Mohr, David B. Newell, and Barry N. Taylor (2020) <https://physics.nist.gov/cuu/Constants/>. License MIT + file LICENSE Encoding UTF-8 LazyData true URL https://github.com/r-quantities/constants BugReports https://github.com/r-quantities/constants/issues Depends R (>= 3.5.0) Suggests errors (>= 0.3.6), units, quantities, testthat ByteCompile yes RoxygenNote 7.1.1 NeedsCompilation no Author Iñaki Ucar [aut, cph, cre] (<https://orcid.org/0000-0001-6403-5550>) Maintainer Iñaki Ucar <[email protected]> Repository CRAN Date/Publication 2021-02-25 13:20:05 UTC 1 2 codata R topics documented: constants-package . .2 codata . .2 lookup . .3 syms.............................................4 Index 6 constants-package constants: Reference on Constants, Units and Uncertainty Description This package provides the 2018 version of the CODATA internationally recommended values of the fundamental physical constants for their use within the R language. Author(s) Iñaki Ucar References Eite Tiesinga, Peter J. Mohr, David B. -
Improving the Accuracy of the Numerical Values of the Estimates Some Fundamental Physical Constants
Improving the accuracy of the numerical values of the estimates some fundamental physical constants. Valery Timkov, Serg Timkov, Vladimir Zhukov, Konstantin Afanasiev To cite this version: Valery Timkov, Serg Timkov, Vladimir Zhukov, Konstantin Afanasiev. Improving the accuracy of the numerical values of the estimates some fundamental physical constants.. Digital Technologies, Odessa National Academy of Telecommunications, 2019, 25, pp.23 - 39. hal-02117148 HAL Id: hal-02117148 https://hal.archives-ouvertes.fr/hal-02117148 Submitted on 2 May 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Improving the accuracy of the numerical values of the estimates some fundamental physical constants. Valery F. Timkov1*, Serg V. Timkov2, Vladimir A. Zhukov2, Konstantin E. Afanasiev2 1Institute of Telecommunications and Global Geoinformation Space of the National Academy of Sciences of Ukraine, Senior Researcher, Ukraine. 2Research and Production Enterprise «TZHK», Researcher, Ukraine. *Email: [email protected] The list of designations in the text: l -
The Exponential Constant E
The exponential constant e mc-bus-expconstant-2009-1 Introduction The letter e is used in many mathematical calculations to stand for a particular number known as the exponential constant. This leaflet provides information about this important constant, and the related exponential function. The exponential constant The exponential constant is an important mathematical constant and is given the symbol e. Its value is approximately 2.718. It has been found that this value occurs so frequently when mathematics is used to model physical and economic phenomena that it is convenient to write simply e. It is often necessary to work out powers of this constant, such as e2, e3 and so on. Your scientific calculator will be programmed to do this already. You should check that you can use your calculator to do this. Look for a button marked ex, and check that e2 =7.389, and e3 = 20.086 In both cases we have quoted the answer to three decimal places although your calculator will give a more accurate answer than this. You should also check that you can evaluate negative and fractional powers of e such as e1/2 =1.649 and e−2 =0.135 The exponential function If we write y = ex we can calculate the value of y as we vary x. Values obtained in this way can be placed in a table. For example: x −3 −2 −1 01 2 3 y = ex 0.050 0.135 0.368 1 2.718 7.389 20.086 This is a table of values of the exponential function ex. -
Certain Investigations Regarding Variable Physical Constants
IJRRAS 6 (1) ● January 2011 www.arpapress.com/Volumes/Vol6Issue1/IJRRAS_6_1_03.pdf CERTAIN INVESTIGATIONS REGARDING VARIABLE PHYSICAL CONSTANTS 1 2 3 Amritbir Singh , R. K. Mishra & Sukhjit Singh 1 Department of Mathematics, BBSB Engineering College, Fatehgarh Sahib, Punjab, India 2 & 3 Department of Mathematics, SLIET Deemed University, Longowal, Sangrur, Punjab, India. ABSTRACT In this paper, we have investigated details regarding variable physical & cosmological constants mainly G, c, h, α, NA, e & Λ. It is easy to see that the constancy of G & c is consistent, provided that all actual variations from experiment to experiment, or method to method, are due to some truncation or inherent error. It has also been noticed that physical constants may fluctuate, within limits, around average values which themselves remain fairly constant. Several attempts have been made to look for changes in Plank‟s constant by studying the light from quasars and stars assumed to be very distant on the basis of the red shift in their spectra. Detail Comparison of concerned research done has been done in the present paper. Keywords: Fundamental physical constants, Cosmological constant. A.M.S. Subject Classification Number: 83F05 1. INTRODUCTION We all are very much familiar with the importance of the 'physical constants‟, now in these days they are being used in all the scientific calculations. As the name implies, the so-called physical constants are supposed to be changeless. It is assumed that these constants are reflecting an underlying constancy of nature. Recent observations suggest that these fundamental Physical Constants of nature may actually be varying. There is a debate among cosmologists & physicists, whether the observations are correct but, if confirmed, many of our ideas may have to be rethought. -
Variable Planck's Constant
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 29 January 2021 doi:10.20944/preprints202101.0612.v1 Variable Planck’s Constant: Treated As A Dynamical Field And Path Integral Rand Dannenberg Ventura College, Physics and Astronomy Department, Ventura CA [email protected] Abstract. The constant ħ is elevated to a dynamical field, coupling to other fields, and itself, through the Lagrangian density derivative terms. The spatial and temporal dependence of ħ falls directly out of the field equations themselves. Three solutions are found: a free field with a tadpole term; a standing-wave non-propagating mode; a non-oscillating non-propagating mode. The first two could be quantized. The third corresponds to a zero-momentum classical field that naturally decays spatially to a constant with no ad-hoc terms added to the Lagrangian. An attempt is made to calibrate the constants in the third solution based on experimental data. The three fields are referred to as actons. It is tentatively concluded that the acton origin coincides with a massive body, or point of infinite density, though is not mass dependent. An expression for the positional dependence of Planck’s constant is derived from a field theory in this work that matches in functional form that of one derived from considerations of Local Position Invariance violation in GR in another paper by this author. Astrophysical and Cosmological interpretations are provided. A derivation is shown for how the integrand in the path integral exponent becomes Lc/ħ(r), where Lc is the classical action. The path that makes stationary the integral in the exponent is termed the “dominant” path, and deviates from the classical path systematically due to the position dependence of ħ. -
Testable Criterion Establishes the Three Inherent Universal Constants
Applied Physics Research; Vol. 8, No. 6; 2016 ISSN 1916-9639 E-ISSN 1916-9647 Published by Canadian Center of Science and Education Testable Criterion Establishes the Three Inherent Universal Constants Gordon R. Kepner1 1 Membrane Studies Project, USA Correspondence: Gordon R. Kepner, Membrane Studies Project, USA. E-mail: [email protected] Received: September 11, 2016 Accepted: November 18, 2016 Online Published: November 24, 2016 doi:10.5539/apr.v8n6p38 URL: http://dx.doi.org/10.5539/apr.v8n6p38 Abstract Since the late 19th century, differing views have appeared on the nature of fundamental constants, how to identify them, and their total number. This concept has been broadly and variously interpreted by physicists ever since with no clear consensus. There is no analysis in the literature, based on specific criteria, for establishing what is or is not an inherent universal constant. The primary focus here is on constants describing a relation between at least two of the base quantities mass, length and time. This paper presents a testable criterion to identify these unique constants of our local universe. The value of a constant meeting these criteria can only be obtained from experimental measurement. Such constants set the scales of these base quantities that describe, in combination, the observable phenomena of our universe. The analysis predicts three such constants, uses the criterion to identify them, while ruling out Planck’s constant and introducing a new physical constant. Keywords: fundamental constant, inherent universal constant, new inherent constant, Planck’s constant 1. Introduction The analysis presented here is conceptually and mathematically simple, while going directly to the foundations of physics. -
5.3.43The First Relativistic Models of the Universe
AN INTRODUCTION TO GALAXIES AND COSMOLOGY 5.3.43The first relativistic models of the Universe According to general relativity, the distribution of energy and momentum determines the geometric properties of space–time, and, in particular, its curvature. The precise nature of this relationship is specified by a set of equations called the field equations of general relativity. In this book you are not expected to solve or even manipulate these equations, but you do need to know something about them, particularly how they led to the introduction of a quantity known as the cosmological constant. For this purpose, Einstein’s field equations are discussed in Box 5.1. BOX 5.13EINSTEIN’S FIELD EQUATIONS OF GENERAL RELATIVITY When spelled out in detail the Einstein field equations planetary motion in the Solar System and to predict the are vast and complicated, but in the compact and non-Newtonian deflection of light by the Sun. powerful notation used by general relativists they can Einstein published his first paper on relativistic be written with deceptive simplicity. Using this modern cosmology in the following year, 1917. In that paper he notation, the field equations that Einstein introduced in tried to use general relativity to describe the space–time 1916 can be written as geometry of the whole Universe, not just the Solar −8πG System. While working towards that paper he realized G = T (5.7) c 4 that one of the assumptions he had made in his 1916 paper was unnecessary and inappropriate in the broader Different authors may use different conventions for context of cosmology. -
Physical Constant - Wikipedia
4/17/2018 Physical constant - Wikipedia Physical constant A physical constant, sometimes fundamental physical constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. It is contrasted with a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measurement. There are many physical constants in science, some of the most widely recognized being the speed of light in vacuum c, the gravitational constant G, Planck's constant h, the electric constant ε0, and the elementary charge e. Physical constants can take many dimensional forms: the speed of light signifies a maximum speed for any object and is expressed dimensionally as length divided by time; while the fine-structure constant α, which characterizes the strength of the electromagnetic interaction, is dimensionless. The term fundamental physical constant is sometimes used to refer to universal but dimensioned physical constants such as those mentioned above.[1] Increasingly, however, physicists reserve the use of the term fundamental physical constant for dimensionless physical constants, such as the fine-structure constant α. Physical constant in the sense under discussion in this article should not be confused with other quantities called "constants" that are assumed to be constant in a given context without the implication that they are in any way fundamental, such as the "time constant" characteristic of a given system, or material constants, such as the Madelung constant, -
Crystals of Golden Proportions
THE NOBEL PRIZE IN CHEMISTRY 2011 INFORMATION FOR THE PUBLIC Crystals of golden proportions When Dan Shechtman entered the discovery awarded with the Nobel Prize in Chemistry 2011 into his notebook, he jotted down three question marks next to it. The atoms in the crystal in front of him yielded a forbidden symmetry. It was just as impossible as a football – a sphere – made of only six- cornered polygons. Since then, mosaics with intriguing patterns and the golden ratio in mathematics and art have helped scientists to explain Shechtman’s bewildering observation. “Eyn chaya kazo”, Dan Shechtman said to himself. “There can be no such creature” in Hebrew. It was the morning of 8 April 1982. The material he was studying, a mix of aluminum and manganese, was strange- looking, and he had turned to the electron microscope in order to observe it at the atomic level. However, the picture that the microscope produced was counter to all logic: he saw concentric circles, each made of ten bright dots at the same distance from each other (fgure 1). Shechtman had rapidly chilled the glowing molten metal, and the sudden change in temperature should have created complete disorder among the atoms. But the pattern he observed told a completely different story: the atoms were arranged in a manner that was contrary to the laws of nature. Shechtman counted and recounted the dots. Four or six dots in the circles would have been possible, but absolutely not ten. He made a notation in his notebook: 10 Fold??? BRIGHT DOTS will DARKNESS results appear where wave where crests and crests intersect and troughs meet and reinforce each other. -
An Unknown Physical Constant Missing from Physics
Applied Physics Research; Vol. 7, No. 5; 2015 ISSN 1916-9639 E-ISSN 1916-9647 Published by Canadian Center of Science and Education An Unknown Physical Constant Missing from Physics 1 Koshun Suto 1 Chudaiji Buddhist Temple, Isesaki, Japan Correspondence: Koshun Suto, Chudaiji Buddhist Temple, 5-24, Oote-Town, Isesaki, 372-0048, Japan. Tel: 81-270-239-980. E-mail: [email protected] Received: April 24, 2014 Accepted: August 21, 2015 Online Published: August 24, 2015 doi:10.5539/apr.v7n5p68 URL: http://dx.doi.org/10.5539/apr.v7n5p68 Abstract Planck constant is thought to belong to the universal constants among the fundamental physical constants. However, this paper demonstrates that, just like the fine-structure constant α and the Rydberg constant R∞, Planck constant belongs to the micro material constants. This paper also identifies the existence of a constant smaller than Planck constant. This new constant is a physical quantity with dimensions of angular momentum, just like the Planck constant. Furthermore, this paper points out the possibility that an unknown energy level, which cannot be explained with quantum mechanics, exists in the hydrogen atom. Keywords: Planck constant, Bohr's quantum condition, hydrogen atom, unknown energy level, fine-structure constant, classical electron radius 1. Introduction In 1900, when deriving a equation matching experimental values for black-body radiation, M. Planck proposed the quantum hypothesis that the energy of a harmonic oscillator with frequency ν is quantized into integral multiple of hν. This was the first time that Planck constant h appeared in physics theory. Since this time, Planck constant has been thought to be a universal constant among fundamental physical constants.