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  1. Pi : the next generation : a sourcebook on the recent history of Pi and its computation

    Bailey, David H.
    Switzerland : Springer, 2016.

    This book contains a compendium of 25 papers published since the 1970s dealing with pi and associated topics of mathematics and computer science. The collection begins with a Foreword by Bruce Berndt. Each contribution is preceded by a brief summary of its content as well as a short key word list indicating how the content relates to others in the collection. The volume includes articles on actual computations of pi, articles on mathematical questions related to pi (e.g., ℓ́ℓIs pi normal?ℓ́ℓ), articles presenting new and often amazing techniques for computing digits of pi (e.g., the ℓ́ℓBBPℓ́ℓ algorithm for pi, which permits one to compute an arbitrary binary digit of pi without needing to compute any of the digits that came before), papers presenting important fundamental mathematical results relating to pi, and papers presenting new, high-tech techniques for analyzing pi (i.e., new graphical techniques that permit one to visually see if pi and other numbers are ℓ́ℓnormalℓ́ℓ). his volume="" is="" a="" companion="" to Pi: A Source Book whose third edition released in 2004. The present collection begins with 2 papers from 1976, published by Eugene Salamin and Richard Brent, which describe ℓ́ℓquadratically convergentℓ́ℓ algorithms for pi and other basic mathematical functions, derived from some mathematical work of Gauss. Bailey and Borwein hold that these two papers constitute the beginning of the modern era of computational mathematics. This time period (1970s) also corresponds with the introduction of high-performance computer systems (supercomputers), which since that time have increased relentlessly in power, by approximately a factor of 100,000,000, advancing roughly at the same rate as Mooreℓ́ℓs Law of semiconductor technology. This book may be of interest to a wide range of mathematical readers; some articles cover more advanced research questions suitable for active researchers in the field, but several are highly accessible to undergraduate mathematics students.

    Online SpringerLink

  2. The number [pi]

    Eymard, Pierre
    Providence, R.I. : American Mathematical Society, c2004.

    '[In the book] we are dealing with a theme which cuts across the mathematics courses classically taught in the first four years of college. Thus it offers the reader the opportunity to learn, review and give long-term thought to the concepts covered in these programmes by following the guiding thread of this favoured number' - from the Preface. This is a clever, beautiful book. The authors trace the thread of $\pi$ through the long history of mathematics. In so doing, they touch upon many major subjects in mathematics: geometry (of course), number theory, Galois theory, probability, transcendental numbers, analysis, and, as their crown jewel, the theory of elliptic functions, which connects many of the other subjects.By this device, the authors provide a tour through mathematics, one that mathematicians of all levels, amateur or professional, may appreciate. In many cases, the tour visits well-known topics from particular special interest groups. Remarkably, $\pi$ is often found at the places of deepest beauty. The volume includes many exercises with detailed solutions. Anyone from undergraduate mathematics majors through university professors will find many things to enjoy in this book.

  3. Study of the D0 ---> pi- pi+ pi- pi+ decay [electronic resource].

    Washington, D.C. : United States. Dept. of Energy. ; Oak Ridge, Tenn. : distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 2007

    Using data from the FOCUS (E831) experiment at Fermilab, they present new measurements for the Cabbibo-suppressed decay mode D° → π⁻π⁺π⁻π⁺. They measure the branching ratio Λ(D° → π⁺π⁻π⁺π⁻)/Λ(D° → K⁻ π⁺π⁻π⁺) = 0.0914 ± 0.0018 ± 0.0022. An amplitude analysis has been performed, a first for this channel, in order to determine the resonant substructure of this decay mode. The dominant component is the decay D° → a₁(1260)⁺π⁻, accounting for 60% of the decay rate. The second most dominant contribution comes from the decay D° → ρ(770)°ρ(770)°, with a fraction of 25%. They also study the a₁(1260) line shape and resonant substructure. Using the helicity formalism for the angular distribution of the decay D° → ρ(770)°ρ(770)°, they measure a longitudinal polarization of P{sub L} = (71 ± 4 ± 2)%.

    Online OSTI

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  1. Tibetan Studies

    Stanford Libraries' Tibetan Studies collections support faculty and student research and teaching across campus. Our collections cover topics such as religion, medicine, history, and art, with a focus on the pre-modern period.

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    Stanford Libraries' large collection of historical and contemporary maps, globes, and atlases circulates from the Branner Earth Sciences Library. The David Rumsey Map Center also holds over 16,000 historic maps and cartographic objects.

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  1. AMS China : Pi-chieh Region (Raster Image)

    Harvard Map Collection, Harvard College Library
    1954

    This layer is a georeferenced raster image of the Army Map Service (AMS) Series L500, China 1:250,000 topographic map of the Pi-chieh (Bijie) regio...

  2. De Ghelegentheyt ende Belegheringhe van Schencken-Schans

    Visscher, Claes Jansz., 1586 or 1587-1652, Schort, Jahann Jakob, and Blaeu, Joan, 1596-1673
    1635

    Curyeus gemeeten ende geteeckent by den ervaren Ingenieur Ioannes Iacobi Schort. Relief shown pictorially. 2 bar scales on map, given in "Pieds", a...

  3. Condominiums Assessor, Riverside County California, 2019

    Riverside County (Calif.). Geographic Information Services
    2019

    To graphically represent taxable condominiums within Riverside County. This layer is also joined with Assessor tables to provide additional informa...

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