Related papers: Apology of Euclid
We present a formal system, E, which provides a faithful model of the proofs in Euclid's Elements, including the use of diagrammatic reasoning.
This paper is a criticism on "A Mathematician's Apology" by G. H. Hardy.
In this small note I try to summarize some observations about Euclid's remarkable role in mathematics and about the ambient philosophy.
The exposition in Euclid's Elements contains an obvious gap (seemingly unnoticed by most commentators): he often compares not just angles, but *groups* of angles, and at the same time he avoids summing angles (and considering angles greater…
The initial techniques developed in Euclid's Elements, well before the use of the parallel postulate, are reexamined in order to clarify even the most obscure details, particularly those related to equality, superposition and angle…
We work through Book I of Euclid's Elements with our focus on application of areas (I.42, I.44, I.45). We summarize alternate constructions from medieval editions of Euclid's elements and ancient and medieval commentaries. We remark that…
These notes provide an opportunity to discover the beauty of Bourbaki set theory, and I hope that they will facilitate the task to those who find it difficult to read this book, one of the most critical elements of the mathematics of…
This short note contains elementary evaluations of some Euler sums.
Withdrawn due to error. See D. Lowe, L. Susskind and J. Uglum, hep-th/9402136, for correct treatment. Apologies to all recipients.
Barry Mazur published an article some year ago, where he showed, among other things, that the result in the so-called mathematical passage of Plato s Theatetus and Euclid s proposition X.9 in the Elements are very different, while almost…
This article proposes a reading of Book I of Euclid's Elements with an emphasis of the experiences of infinity supplied by it, as a preparatory study for a research on the embodied cognition of infinity and its material anchors. -- Cet…
We give a new proof of the existence of designs, which is much shorter and gives better bounds.
The translation is not verbatim, many parts have been abbreviated and in some case alternative proofs were devised emphasizing intuition.
From the Text: How shall I tribute Andrei Khrennikov in this volume? With an email collection of course! But with what theme? It ought to be something big. One of the troubles of QBism's ontological program is that it is so sideways to the…
This short note is an "elementary'' introduction to the conjectural theory of motives.
We give a simple proof of a characterization of euclidean space due to Aronszajn and derive a well-known characterization due to Jordan & von Neumann as a corollary.
This is an elementary explanation of a cubic composition formula due to Ramanujan.
The expression for entropy sometimes appears mysterious - as it often is asserted without justification. This short manuscript contains a discussion of the underlying assumptions behind entropy as well as simple derivation of this…
This paper aims to provide a careful and self-contained introduction to the theory of topological degree in Euclidean spaces. It is intended for people mostly interested in analysis and, in general, a heavy background in algebraic or…
This is a critique of cond-mat/9709195 . This paper is being submitted at this time for archiving purposes.