This book has been growing during the last year exploiting many resources: my unfinished notes, recollecting material taught and not taught my time at the University of North Carolina at Charlotte, some of my online notes from these courses, some internet searches, some new ideas during writing,-to make it short out of an unfinished career that was unexpectedly interrupted by my eye problems.After being forced to retire about four years ago, I did continue to occupy myself with sev...

This booklet is grown from careless, partly lost notes that had been sent to relatives and classmates several years ago. It dates back to an era before the flood and pandemic, and war struck worse than ever. Retired because of my poor eyesight, my interest in literature had awakened, and the exchange seemed worthwhile once more. Thus this little booklet has still been gathered. This English translation has been corrected and slightly extended. The older German version is available as an au...

Book Summary:The front cover shows the figure from page 101 about the geometric proof of the law a(bc) = b(ac). This line of reasoning does not presuppose Pappus' theorem, instead we use properties of circles in a Pythagorean plane.A decade long experience of teaching the course Fundamental of Geometry at the University of North Carolina at Charlotte, many notes for exercises, reading and research are the bases for this bulky work. Retired I could find the ...

A smart schoolmate invited each of our final class members to write about themselves. Using some short essays I enjoyed writing, I had gathered enough material for such a booklet. The task of creating a comprehensive autobiography seemed too changing. So I decided to gather my short observations, put them into a loose context and make a book, even though it is clearly incomplete.

A smart schoolmate invited each of our final class members to write about themselves. Using some short essays I enjoyed writing, I had gathered some material for such a booklet. Further sources are my music for flute and piano I have recorded together with pianist Thomas Turner, my completing of the flute sonata BWV 1032 of J.S. Bach, and fantasies about Plato, Mozart and Kafka.The description of professional growth, and the music playing which I have practiced with endurance durin...

A smart schoolmate invited each of our final class members to write about themselves. Using some short essays I enjoyed writing, I had gathered some material for such a booklet. Further sources are my music for flute and piano I have recorded together with pianist Thomas Turner,my completing of the flute sonata BWV 1032 of J.S.Bach, and fantasies about Plato, Mozart and Kafka.The description of professional growth, and the music playing which I have practiced with endurance...

The present fourth volume recalls Hilbert's axioms from the Foundations of Geometry, and elaborates the theory of geometric constructions. Both extensions and restrictions of the classical Euclidean tools, straightedge and compass, are explained and investigated. One finds constructions by a marked ruler, which allows the duplication of the cube and angle trisection, on the other hand proofs for the impossibility of such constructions by the Euclidean tools or Hilbert tools. The connection...

The present fifth volume recalls Hilbert's axioms from the Foundations of Geometry, and elaborates hyperbolic geometry.

A Course in Old and New GeometryVolume I: Axiomatic and Neutral GeometryThe front cover shows the figure from page 132 showing the construction by Hilbert tools to erect an isosceles triangle onto a given segment. Since Hilbert tools are weaker than Euclidean tools, one cannot construct an equilateral triangle in neutral geometry. A decade long experience of teaching the course Fundamental of Geometry at the University of North Carolina at Charlotte, many notes for exercise...

This booklet is grown from careless, partly lost notes that had been sent to relatives and classmatesseveral years ago.It dates back to an era before the flood, pandemic, and war struck worse.Retired because of my poor eyesight, my interest in literature had awakened, and the exchange seemed worthwhile once more.Thus this little booklet has still been gathered.This English translation has been corrected and slightly extended.The older German ...

The present first volume begins with Hilbert's axioms from the \emph{Foundations of Geometry}.After some discussion of logic and axioms in general, incidence geometries, especially the finite ones, and affine and projective geometry in two and three dimensions are treated. As in Hilbert's system, there follow sections about the axioms of order, and congruence in neutral geometry, the axioms of measurement and of completeness, and deviating from Hilbert, about circles.The in...

This booklet is grown from careless, partly lost notes that had been sent to relatives and classmates several years ago. It dates back to an era before the flood and pandemic, and war struck worse than ever. Retired because of my poor eyesight, my interest in literature had awakened, and the exchange seemed worthwhile once more. Thus this little booklet has still been gathered. This English translation has been corrected and slightly extended. The older German version is available as an au...