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1,500 | Editors' remarks (on two complexity theory surveys in the Bulletin) | math.HO | The authors discuss the role of controversy in mathematics as a preface to
two opposing articles on computational complexity theory: "Some basic
information on information-based complexity theory" by Beresford Parlett
[math.NA/9201266] and "Perspectives on information-based complexity" by J. F.
Traub and Henryk Wo\'zni... | math |
1,501 | Two notes on notation | math.HO | The author advocates two specific mathematical notations from his popular
course and joint textbook, "Concrete Mathematics". The first of these,
extending an idea of Iverson, is the notation "[P]" for the function which is 1
when the Boolean condition P is true and 0 otherwise. This notation can
encourage and clarify t... | math |
1,502 | ``Theoretical mathematics'': Toward a cultural synthesis of mathematics and theoretical physics | math.HO | Is speculative mathematics dangerous? Recent interactions between physics and
mathematics pose the question with some force: traditional mathematical norms
discourage speculation, but it is the fabric of theoretical physics. In
practice there can be benefits, but there can also be unpleasant and
destructive consequence... | math |
1,503 | Responses to ``Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics'', by A. Jaffe and F. Quinn | math.HO | This article is a collection of letters solicited by the editors of the
Bulletin in response to a previous article by Jaffe and Quinn
[math.HO/9307227]. The authors discuss the role of rigor in mathematics and the
relation between mathematics and theoretical physics. | math |
1,504 | Response to comments on ``Theoretical mathematics'' | math.HO | The authors discuss various objections and rejoinders in the collected
responses [math.HO/9404229,math.HO/9404236] to their original article on the
relationship between mathematics and theoretical physics [math.HO/9307227]. | math |
1,505 | Editor's column (on an article by Jaffe and Quinn) | math.HO | This note is a preface to various responses [math.HO/9404229,math.HO/9404236]
to an opinion piece by Jaffe and Quinn [math.HO/9307227] on the relationship
between mathematics and theoretical physics. | math |
1,506 | On proof and progress in mathematics | math.HO | In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms
of progress in mathematics that are not captured by formal proofs of theorems,
especially in his own work in the theory of foliations and geometrization of
3-manifolds and dynamical systems. | math |
1,507 | Electronic Mathematics Journals | math.HO | In the Forum section of the November, 1993 Notices of the American
Mathematical Society, John Franks discussed the electronic journal of the
future. Since then, the New York Journal of Mathematics, the first electronic
general mathematics journal, has begun publication. In this article, we explore
the issues of electro... | math |
1,508 | Mathematics Journals Should Be Electronic and Free | math.HO | Many important journal functions would be lost if the mathematical community
replaced all paper journals with electronic media. Electronic media are useful
for some purposes, but they will not be the basis for a publishing revolution
in the near future. | math |
1,509 | Interactive games, dialogues and the verbalization | math.HO | The note is devoted to an interactive game theoretic formalization of
dialogues as psycholinguistic phenomena and the unraveling of a hidden dialogue
structure of 2-person differential interactive games. In the field-theoretic
description of interactive games the dialogues are defined naively as
interactive games of di... | math |
1,510 | On the section of a cone | math.HO | A problem from Democritus is used to illustrate the building, and use, of
infinitesimal covectors from its regularized, finite, counterpart. | math |
1,511 | Caleidoscope-roulette: the resonance phenomena in perception games | math.HO | Kaleidoscope-roulettes, a proper class of perception games, is described.
Kaleidoscope-roulette is defined as a perception and, hence, verbalizable
interactive game, whose hidden dialogue consists of quasirandom sequences of
``words''. The resonance phenomena in such games and their controlling are
discussed. | math |
1,512 | On the babylonian method of extracting root squares | math.HO | We discuss the babylonian method of extracting the root square of a number,
from the point of view of modern mathematics. We also speculate that the
babylonian mathematics was rich enough for a generalization of this method,
despite the lack of general statements and justified procedures in their
mathematics. | math |
1,513 | Poincaré's Proof of the so-called Birkhoff-Witt Theorem | math.HO | A methodical analysis of the research related to the article, ``Sur les
groupes continus'', of Henri Poincar\'{e} reveals many historical
misconceptions and inaccuracies regarding his contribution to Lie theory. A
thorough reading of this article confirms the precedence of his discovery of
many important concepts, espe... | math |
1,514 | Representative dynamics | math.HO | This short note is devoted to the representative dynamics, which realizes a
link between the theory of controlled systems and representation theory.
Dynamical inverse problem of representation theory for controlled systems is
considered: to solve it means to correspond a representative dynamics to the
controlled system... | math |
1,515 | A Mathematical Theory of Origami Numbers and Constructions | math.HO | We give a hierarchial set of axioms for mathematical origami. The hierachy
gives the fields of Pythagorean numbers, first discussed by Hilbert, the field
of Euclidean constructible numbers which are obtained by the usual
constructions of straightedge and compass, and the Origami numbers, which is
also the field generat... | math |
1,516 | q-Newton binomial: from Euler to Gauss | math.HO | A counter-intuitive result of Gauss (formulae (1.6), (1.7) below) is made
less mysterious by virtue of being generalized through the introduction of an
additional parameter. | math |
1,517 | The Modular Tree of Pythagorus | math.HO | The Pythagorean triples have the structure of a ternary rooted tree; the tree
is based on the Cayley graph of a free subgroup of the modular group | math |
1,518 | On Fermat's marginal note: a suggestion | math.HO | A suggestion is put forward regarding a partial proof of FLT(case1), which is
elegant and simple enough to have caused Fermat's enthusiastic remark in the
margin of his Bachet edition of Diophantus' "Arithmetica". It is based on an
extension of Fermat's Small Theorem (FST) to mod p^k for any k>0, and the cubic
roots of... | math |
1,519 | Notes to the early history of the Knot Theory in Japan | math.HO | We give a description of the growth of research on Knot Theory in Japan. We
place our report in a general historical context. In particular, we compare the
development of research on mathematical topology in Japan with that in Poland
and USA, observing several similarities. Toward the end of XIX century and at
the begi... | math |
1,520 | Tolstoy's Mathematics in "War and Peace" | math.HO | The nineteenth century Russian author Leo Tolstoy based his egalitarian views
on sociology and history on mathematical and probabilistic views, and he also
proposed a mathematical theory of waging war. | math |
1,521 | Short Calculus | math.HO | This paper has been withdrawn by the author. | math |
1,522 | The Rational Cuboid Table of Maurice Kraitchik | math.HO | The original tables of body cuboids by Maurice Kraitchik are corrected,
restoring 159 missing cuboids. His table range is then extended for all odd
sides less than 1,000,000 to a new limit of 4,294,967,295. Over this new range,
12,517 unique body cuboids are listed, from the original 416. | math |
1,523 | Kepler's Area Law in the Principia: Filling in some details in Newton's proof of Prop. 1 | math.HO | During the past 25 years there has been a controversy regarding the adequacy
of Newton's proof of Prop. 1 in Book 1 of the {\it Principia}. This proposition
is of central importance because its proof of Kepler's area law allowed Newton
to introduce a geometric measure for time to solve problems in orbital dynamics
in t... | math |
1,524 | The Life and Works of Raoul Bott | math.HO | a 10-page biography of Raoul Bott followed by a 25-page discussion of his
major papers | math |
1,525 | Weierstraß | math.HO | We give a short biographical sketch of Karl Weierstrass. | math |
1,526 | Foundations of Mathematics | math.HO | This article discusses what can be proved about the foundations of
mathematics using the notions of algorithm and information. The first part is
retrospective, and presents a beautiful antique, Godel's proof, the first
modern incompleteness theorem, Turing's halting problem, and a piece of
postmodern metamathematics, t... | math |
1,527 | Noether | math.HO | We give a short biographical sketch of Emmy Noether. | math |
1,528 | Hypothesis of the Functional Semantic Constructions and Mathematics in the Functional Semantic Aspect | math.HO | This essay contains three parts. The first part of essay focuses on the
hypothesis of the functional semantic constructions (FSC-Hypothesis). This
hypothesis explains that a language, a number, a money are the functional
semantic constructions. In the second part the author considers the Mathematics
with respect to the... | math |
1,529 | On the intelligibility of the universe and the notions of simplicity, complexity and irreducibility | math.HO | We discuss views about whether the universe can be rationally comprehended,
starting with Plato, then Leibniz, and then the views of some distinguished
scientists of the previous century. Based on this, we defend the thesis that
comprehension is compression, i.e., explaining many facts using few theoretical
assumptions... | math |
1,530 | Scholarly mathematical communication at a crossroads | math.HO | This essay was invited for publication in Nieuw Archief voor Wiskunde; it
will also appear in translation in the SMF Gazette and in the DMV Mitteilungen.
I discuss the recent trends in scholarly communication in mathematics, the
current state and intentions of the arXiv, and a proposal to reform peer review
with the ... | math |
1,531 | On the information-theoretic approach to Gödel's incompleteness theorem | math.HO | In this paper we briefly review and analyze three published proofs of
Chaitin's theorem, the celebrated information-theoretic version of G\"odel's
incompleteness theorem. Then, we discuss our main perplexity concerning a key
step common to all these demonstrations. | math |
1,532 | Some non-conventional ideas about algorithmic complexity | math.HO | In this paper the author presents some non-conventional thoughts on the
complexity of the Universe and the algorithmic reproducibility of the human
brain, essentially sparked off by the notion of algorithmic complexity. We must
warn that though they evoke suggestive scenarios, they are still quite
speculative. | math |
1,533 | International comparisons in mathematics education: an overview | math.HO | The paper opens with an overview of the discussion of international
comparisons (including goals) in mathematics education. Afterwards, the two
most important recent international studies, the PISA Study and TIMSS-Repeat,
are described. After a short description of the qualitative-quantitative
debate, a qualitatively o... | math |
1,534 | Graphical explanation for the speed of the Fast Fourier Transform | math.HO | For a sample set of 1024 values, the FFT is 102.4 times faster than the
discrete Fourier transform (DFT). The basis for this remarkable speed advantage
is the `bit-reversal' scheme of the Cooley-Tukey algorithm. Eliminating the
burden of `degeneracy' by this means is readily understood using vector
graphics. | math |
1,535 | Two philosophical applications of algorithmic information theory | math.HO | Two philosophical applications of the concept of program-size complexity are
discussed. First, we consider the light program-size complexity sheds on
whether mathematics is invented or discovered, i.e., is empirical or is a
priori. Second, we propose that the notion of algorithmic independence sheds
light on the questi... | math |
1,536 | First Case of Fermat's Last Theorem | math.HO | In this paper two conjectures are proposed based on which we can prove the
first case of Fermat's Last Theorem(FLT) for all primes $p \equiv -1
(\bmod~6)$. With Pollaczek's result {\bf [1]} and the conjectures the first
case of FLT can be proved for all primes greater than 3. With a computer
Conjecture1 was verified to... | math |
1,537 | From Philosophy to Program Size | math.HO | Most work on computational complexity is concerned with time. However this
course will try to show that program-size complexity, which measures
algorithmic information, is of much greater philosophical significance. I'll
discuss how one can use this complexity measure to study what can and cannot be
achieved by formal ... | math |
1,538 | Sur l'origine des chiffres arabes | math.HO | Sur l'origine des chiffres arabes A. Boucenna 1 From the pagination of an
Algerian Arabic manuscript of the beginning of the 19th century,we rediscover
the original shape that the Arabic numerals had before passing in Europe and
underwent the transformation that gave the modern Arabic numerals. This
original shape,whos... | math |
1,539 | Teaching linear algebra at university | math.HO | Linear algebra represents, with calculus, the two main mathematical subjects
taught in science universities. However this teaching has always been
difficult. In the last two decades, it became an active area for research works
in mathematics education in several countries. Our goal is to give a synthetic
overview of th... | math |
1,540 | Popularizing mathematics: from eight to infinity | math.HO | It is rare to succeed in getting mathematics into ordinary conversation
without meeting all kinds of reservations. In order to raise public awareness
of mathematics effectively, it is necessary to modify such attitudes. In this
paper, we point to some possible topics for general mathematical conversation. | math |
1,541 | Reforms of the university mathematics education for non-mathematical specialties | math.HO | This article is a part of the report for the research project ``Reform of the
Course System and Teaching Content of Higher Mathematics (For Non-Mathematical
Specialties)'' in 1995, supported by the National Ministry of Education. There
are thirteen universities participated in this project. The Report not only
reflects... | math |
1,542 | The teaching of proof | math.HO | This panel draws on research of the teaching of mathematical proof, conducted
in five countries at different levels of schooling. With a shared view of proof
as essential to the teaching and learning of mathematics, the authors present
results of studies that explore the challenges for teachers in helping students
lear... | math |
1,543 | "Algebraic truths" vs "geometric fantasies": Weierstrass' Response to Riemann | math.HO | In the 1850s Weierstrass succeeded in solving the Jacobi inversion problem
for the hyper-elliptic case, and claimed he was able to solve the general
problem. At about the same time Riemann successfully applied the geometric
methods that he set up in his thesis (1851) to the study of Abelian integrals,
and the solution ... | math |
1,544 | From quaternions to cosmology: spaces of constant curvature, ca. 1873-1925 | math.HO | After mathematicians and physicists had learned that the structure of
physical space was not necessarily Euclidean, it became conceivable that the
global topological structure of space was non-trivial. In the context of the
late 19th century debates on physical space this speculation gave rise to the
problem of classif... | math |
1,545 | The third approach to the history of mathematics in China | math.HO | The first approach to the history of mathematics in China led by Li Yan
(1892--1963) and Qian Baocong (1892--1974) featured discovering {\it what}
mathematics had been done in China's past. From the 1970s on, Wu Wen-tsun and
others shifted this research paradigm to one of recovering {\it how}
mathematics was done in an... | math |
1,546 | Passages of Proof | math.HO | In this paper we propose a new perspective on the evolution and history of
the idea of mathematical proof. Proofs will be studied at three levels:
syntactical, semantical and pragmatical. Computer-assisted proofs will be give
a special attention. Finally, in a highly speculative part, we will anticipate
the evolution o... | math |
1,547 | Thoughts on the Riemann hypothesis | math.HO | The simultaneous appearance in May 2003 of four books on the Riemann
hypothesis (RH) provoked these reflections. We briefly discuss whether the RH
should be added as a new axiom, or whether a proof of the RH might involve the
notion of randomness. | math |
1,548 | The Informal Logic of Mathematical Proof | math.HO | Informal logic is a method of argument analysis which is complementary to
that of formal logic, providing for the pragmatic treatment of features of
argumentation which cannot be reduced to logical form. The central claim of
this paper is that a more nuanced understanding of mathematical proof and
discovery may be achi... | math |
1,549 | Leibniz, Information, Math and Physics | math.HO | The information-theoretic point of view proposed by Leibniz in 1686 and
developed by algorithmic information theory (AIT) suggests that mathematics and
physics are not that different. This will be a first-person account of some
doubts and speculations about the nature of mathematics that I have entertained
for the past... | math |
1,550 | Embodied Mathematics and the Origins of Geometry | math.HO | In this paper, we propose that 'embodied mathematics' should be studied not
only by reduction to the present individual bodily experience but in an
historical context as well, as far as the origins of mathematics are concerned.
Some early mathematical results are the Theorems of Geometry and arose as
attempts to object... | math |
1,551 | Der rechnende Dichter (The calculating poet) | math.HO | A small and unsystematic selection of my favorite appearances of
mathematicians and mathematics in German literature. It includes classic and
romantic (Lessing, Goethe, Wezel, F. Schlegel, Kleist, Novalis, Grillparzer,
Heine), modern (Wedekind, Doeblin, Morgenstern, Musil, Brecht, Eich), as well
as post-modern authors ... | math |
1,552 | The Number System of the Old European Script | math.HO | The oldest (c. 4000 BC) undeciphered language is the Old European Script
known from approximately 940 inscribed objects (82% of inscriptions on pottery)
found in excavations in the Vinca-Tordos region Transylvania. Also, it is not
known for what the script was used, but the prevailing theory is that it had a
religious ... | math |
1,553 | Why I don't like "pure mathematics" | math.HO | An opiniated essay on what pure mathematics is and why the adjective "pure"
in "pure mathematics" is not a good choice. | math |
1,554 | Solving the quartic with a pencil | math.HO | This expository paper presents the general solution of a quartic equation as
a jump off point to introduce Lefschetz fibrations. It should be accessible to
a broad audience. | math |
1,555 | Smarandache Sequences: Explorations and Discoveries with a Computer Algebra System | math.HO | We study Smarandache sequences of numbers, and related problems, via a
Computer Algebra System. Solutions are discovered, and some conjectures
presented. | math |
1,556 | A short constructive proof of Jordan's decomposition theorem | math.HO | Although there are many simple proofs of Jordan's decomposition theorem in
the literature (see [1], the references mentioned there, and [2]), our proof
seems to be even more elementary. In fact, all we need is the theorem on the
dimensions of rang and kernel and the existence of eigenvalues of a linear
transformation o... | math |
1,557 | Biography of John Rainwater | math.HO | The following paragraphs will describe the origins of John Rainwater, the
impact of his work, the motivations for various parts of it and the prospects
for his future. | math |
1,558 | A Brief Survey of the History of the Calculus of Variations and its Applications | math.HO | In this paper, we trace the development of the theory of the calculus of
variations. From its roots in the work of Greek thinkers and continuing through
to the Renaissance, we see that advances in physics serve as a catalyst for
developments in the mathematical theory. From the 18th century onwards, the
task of establi... | math |
1,559 | Role of Mathematics in Physical Sciences | math.HO | The role of mathematics in physical sciences is discussed, particularly how
higher mathematics found applications in empirical problems. Several examples
are given to illustrate this role. | math |
1,560 | Meta Math! The Quest for Omega | math.HO | This book presents a personal account of the mathematics and metamathematics
of the 20th century leading up to the discovery of the halting probability
Omega. The emphasis is on history of ideas and philosophical implications. | math |
1,561 | Fibonacci Rectangles | math.HO | Is there any other proportion for a rectangle, other than the Golden
Proportion, that will allow the process of cutting off successive squares to
produce an infinite paving of the original rectangle by squares of different
sizes? The answer is: No. The only proportion that allows this pattern is the
Golden Ratio. Two p... | math |
1,562 | Course of linear algebra and multidimensional geometry | math.HO | This is a standard textbook for the course of linear algebra and
multidimensional geometry as it was taught in 1991-1998 at Mathematical
Department of Bashkir State University. Both coordinate and invariant
approaches are used, but invariant approach is preferred. | math |
1,563 | The Eudoxus Real Numbers | math.HO | This note describes a representation of the real numbers due to Schanuel. The
representation lets us construct the real numbers from first principles. Like
the well-known construction of the real numbers using Dedekind cuts, the idea
is inspired by the ancient Greek theory of proportion, due to Eudoxus. However,
unlike... | math |
1,564 | Leibniz, Randomness and the Halting Probability | math.HO | This paper, which is dedicated to Alan Turing on the 50th anniversary of his
death, gives an overview and discusses the philosophical implications of
incompleteness, uncomputability and randomness. | math |
1,565 | Areal Optimization of Polygons | math.HO | We will first solve the following problem analytically: given a piece of wire
of specified length, we will find where the wire should be cut and bent to form
two regular polygons not necessarily having the same number of sides, so that
the combined area of the polygons thus formed is maximized, minimized, greater
than,... | math |
1,566 | Consecutive, Reversed, Mirror, and Symmetric Smarandache Sequences of Triangular Numbers | math.HO | We use the Maple system to check the investigations of S. S. Gupta regarding
the Smarandache consecutive and the reversed Smarandache sequences of
triangular numbers [Smarandache Notions Journal, Vol. 14, 2004, pp. 366-368].
Furthermore, we extend previous investigations to the mirror and symmetric
Smarandache sequence... | math |
1,567 | Totally real origami and impossible paper folding | math.HO | This paper gives one set of axioms for origami constructions, and describes
the set of constructible points under these axioms. The determination of the
set of cunstructible points for this particular set of axioms is related to
Hilbert's 17 th problem. | math |
1,568 | On Bernoulli Numbers and Its Properties | math.HO | In this survey paper, I first review the history of Bernoulli numbers, then
examine the modern definition of Bernoulli numbers and the appearance of
Bernoulli numbers in expansion of functions. I revisit some properties of
Bernoulli numbers and the history of the computation of big Bernoulli numbers. | math |
1,569 | Philosophy as a cultural resource and medium of reflection for Hermann Weyl | math.HO | Here we review a kind of post-World-War-II "Nachtrag" to H. Weyl's
philosophical comments on mathematics and the natural sciences published in the
middle of the 1920s. In a talk given at Z\"urich in the late 1940s, Weyl
discussed F.Gonseth's dialectical epistemology and considered it as being
restricted too strictly to... | math |
1,570 | Irreducible Complexity in Pure Mathematics | math.HO | By using ideas on complexity and randomness originally suggested by the
mathematician-philosopher Gottfried Leibniz in 1686, the modern theory of
algorithmic information is able to show that there can never be a "theory of
everything" for all of mathematics. | math |
1,571 | How real are real numbers? | math.HO | We discuss mathematical and physical arguments against continuity and in
favor of discreteness, with particular emphasis on the ideas of Emile Borel
(1871-1956). | math |
1,572 | On Amicable Numbers With Different Parity | math.HO | In this paper we provide a straightforward proof that if a pair of amicable
numbers with different parity exists (one number odd and the other one even),
then the odd amicable number must be a perfect square, while the even amicable
number has to be equal to the product of a power of 2 and an odd perfect
square. | math |
1,573 | Looking through newly to the amazing irrationals | math.HO | We survay some nice result concerning the irrationals with a metric space
point of view.Here is ofcourse nothing new may be or an expert in this field. | math |
1,574 | Mathematical Education | math.HO | This essay, originally published in the Sept 1990 Notices of the AMS,
discusses problems of our mathematical education system that often stem from
widespread misconceptions by well-meaning people of the process of learning
mathematics. The essay also discusses ideas for fixing some of the problems.
Most of what I wrote... | math |
1,575 | The Uses of Argument in Mathematics | math.HO | Stephen Toulmin once observed that `it has never been customary for
philosophers to pay much attention to the rhetoric of mathematical debate'.
Might the application of Toulmin's layout of arguments to mathematics remedy
this oversight?
Toulmin's critics fault the layout as requiring so much abstraction as to
permit ... | math |
1,576 | Notes on Theory of Quadratic Residues | math.HO | The Law of Quadratic Reciprocity was conjectured by Euler and Legendre who
both found an incomplete proof. Gauss called this law "Theorema Fundamentale",
and he was the first who gave a complete proof, he also highlighted the
equivalence of his formulation with those of Euler and Legrendre. Hereby notes
gives a overvie... | math |
1,577 | Epistemology as Information Theory: From Leibniz to Omega | math.HO | In 1686 in his Discours de Metaphysique, Leibniz points out that if an
arbitrarily complex theory is permitted then the notion of "theory" becomes
vacuous because there is always a theory. This idea is developed in the modern
theory of algorithmic information, which deals with the size of computer
programs and provides... | math |
1,578 | Laplace transformation updated | math.HO | The traditional theory of Laplace transformation in its currently prevalent
form is unsatisfactory. Its deficiencies can be traced back to a mismatch of
the definition intervals of the original function and of the inverse
L-transform. A new approach is outlined by which Laplace transformation becomes
liberated from its... | math |
1,579 | Saunders Mac Lane, the Knight of Mathematics | math.HO | This is a short obituary of Saunders Mac Lane (1909--2005). | math |
1,580 | Traits | math.HO | Reminiscences about Alexandr Danilovich Alexandrov (1912--1999) | math |
1,581 | Group actions in number theory | math.HO | Students having had a semester course in abstract algebra are exposed to the
elegant way in which finite group theory leads to proofs of familiar facts in
elementary number theory. In this note we offer two examples of such group
theoretical proofs using the action of a group on a set. The first is Fermat's
little theo... | math |
1,582 | Counting the Positive Rationals: A Brief Survey | math.HO | We discuss some examples that illustrate the countability of the positive
rational numbers and related sets. Techniques include radix representations,
Godel numbering, the fundamental theorem of arithmetic, continued fractions,
Egyptian fractions, and the sequence of ratios of successive hyperbinary
representation numb... | math |
1,583 | Asymptotic behaviour of Turing Machines | math.HO | This paper has been withdrawn. See published paper
http://arxiv.org/math.HO/0512390 | math |
1,584 | Asymptotic behavior and halting probability of Turing Machines | math.HO | Through a straightforward Bayesian approach we show that under some general
conditions a maximum running time, namely the number of discrete steps
performed by a computer program during its execution, can be defined such that
the probability that such a program will halt after that time is smaller than
any arbitrary fi... | math |
1,585 | How to axiomatize school geometry | math.HO | This is an attempt to present axioms for Euclidean geometry, aiming at the
following goals: to work with geometric notions (thus not merely identify
points with pairs of numbers, giving a special status to a particular
coordinate system); to be appropriate to the way geometry is done in science
and engineering - not to... | math |
1,586 | Zeno's Paradoxes. A Cardinal Problem 1. On Zenonian Plurality | math.HO | In this paper the claim that Zeno's paradoxes have been solved is contested.
Although no one has ever touched Zeno without refuting him (Whitehead), it will
be our aim to show that, whatever it was that was refuted, it was certainly not
Zeno. The paper is organised in two parts. In the first part we will
demonstrate th... | math |
1,587 | Good reduction, bad reduction | math.HO | We give some general properties of good and bad reduction, and some recent
examples (worked out with Dipendra Prasad) of varieties having bad reduction
not accounted for by their cohomology. We include some consequences of our
remarks for varieties over number fields having good reduction everywhere. | math |
1,588 | The Tao of Mathematics, and Think Locally | math.HO | An informal discussion of Serre's conjecture on the modularity of odd
irreducible representations of Gal(\bar Q|Q) into GL_2(\bar F_p), using
Ramanujan's tau-function as an illustrative example. Also, a word about the
importance of thinking locally. | math |
1,589 | Numbers and periods | math.HO | A somewhat pretentious presentation of number systems (N, Z, Q, R, C, Q_p,
>...). The problem of a p-adic characterisation of good-reduction p-adic curves
is posed. | math |
1,590 | Variations on an inequality from IMO'2001 | math.HO | Some extensions of an inequality from IMO'2001 are proven by means of the
Lagrange multiplier criterion. | math |
1,591 | On projective two-dimensional Finsler spaces with special metric | math.HO | We present the English translation of the paper where one special class of
Finsler spaces was introduced. Now this class is known as so called "Kropina
spaces". The article was written in 1958 and published in Russian in "Trudy
seminara po vektornomu i tenzornomu analizu" ("Workshops of the Seminar in
vector and tensor... | math |
1,592 | Lanchester combat models | math.HO | An overview of Lanchester combat models, emphasising their pedagogical
possibilities. After a description of the aimed-fire model and comments on the
literature, we introduce briefly a range of further topics: a discrete
equivalent, the unaimed-fire model, mixed forces, the meaning of a 'unit',
support troops, Bracken'... | math |
1,593 | Origin of the numerals | math.HO | Through the pagination of an Arabian Algerian manuscript of the beginning of
the 19th century, we rediscover the original shape, the "Ghubari" shape, of the
numerals. Contrary to some assumptions, particularly those which claim that
they are derived from Indian characters, this "Ghubari" shape, whose use has
completely... | math |
1,594 | Max Dehn, un mathématicien aux préoccupations universelles | math.HO | This is a free summary of a much longer article published in german in
"Forschung Frankfurt". This article presents facts concerning the works of Max
Dehn and the history of Frankfurt University.
E. Hellinger, R. Moufang, C. L. Siegel, A. Weil, P. Epstein, W. Hartner are
named among others. Of course these texts are ... | math |
1,595 | The History of Barbilian's Metrization Procedure | math.HO | Barbilian spaces are metric spaces with a metric induced by a special
procedure of metrization which is inspired by the study of the models of
non-Euclidean geometry. In the present material we discuss the history of
Barbilian spaces and the evolution of the theory. We point out that some of the
current references to t... | math |
1,596 | Euler and magic squares (De quadratis magicis) | math.HO | Magic squares have always been and are still fascinating for many people, be
it only because of their mathematical properties. Their origin is still but
certain : we find no magic squares in Greece, and only a 3x3 one in China at
the beginning of our era. Most of their development was made in islamic
countries. In Euro... | math |
1,597 | The prime analog of the Kepler-Bouwkamp constant | math.HO | The prime analog of the Kepler-Bouwkamp constant is evaluated. | math |
1,598 | The regularized product of the Fibonacci numbers | math.HO | The regularized product of the Fibonacci numbers is evaluated. | math |
1,599 | A geometric method to compute some elementary integrals | math.HO | An elementary, albeit higher dimensional, argument is used to compute the
area under the power function curve between 0 and 1. | math |
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