DOCSLIB.ORG

Sebastian's Space and Forms

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Sebastian's Space and Forms GENERAL ARTICLE Sebastian’s Space and Forms Michele eMMer A strong message that mathematics revealed in the late nineteenth and non-Euclidean hyperbolic geometry) “imaginary geometry,” the early twentieth centuries is that geometry and space can be the because it was in such strong contrast with common sense. realm of freedom and imagination, abstraction and rigor. An example For some years non-Euclidean geometry remained marginal of this message lies in the infi nite variety of forms of mathematical AbStrAct inspiration that the Mexican sculptor Sebastian invented, rediscovered to the fi eld, a sort of unusual and curious genre, until it was and used throughout all his artistic activity. incorporated into and became an integral part of mathema- tics through the general ideas of G.F.B. Riemann (1826–1866). Riemann described a global vision of geometry as the study of intellectUAl ScAndAl varieties of any dimension in any kind of space. According to At the beginning of the twentieth century, Robert Musil re- Riemann, geometry had to deal not necessarily with points or fl ected on the role of mathematics in his short essay “Th e space in the traditional sense but with sets of ordered n-ples. Mathematical Man,” writing that mathematics is an ideal in- Th e erlangen Program of Felix Klein (1849–1925) descri- tellectual apparatus whose task is to anticipate every possible bed geometry as the study of the properties of fi gures that case. Only when one looks not toward its possible utility, were invariant with respect to a particular group of transfor- but within mathematics itself one sees the real face of this mations. Consequently each classifi cation of the groups of science. transformations became a codifi cation of the diff erent types “Mathematics is the bold luxury of pure reason, one of of geometry. the few that remain today. But these are harmless whims, It is important to mention that the discovery (or invention) which play themselves out far from the serious business of of non-Euclidean geometry and of the higher dimensions our lives, whereas it is precisely here that mathematics en- (from the fourth on)—in short, the new idea of space—is compasses some of the most entertaining and intense ad- one of the most interesting examples of the profound re- ventures of human existence,” wrote Musil, adding that aft er percussions that mathematical ideas can have on human- everything had been brought into the most beautiful kind of istic culture and on art. Mathematicians began to produce existence, the mathematicians came upon something wrong less regular and more startling geometric fi gures. Many of in the fundamentals of the whole thing that absolutely could these new and exciting mathematical ideas fi ltered into the not be put right, concluding that there was no other possibil- public sphere and sparked the imagination of writers and ity of having such visionary feeling as mathematicians do, artists [2]. enduring this intellectual scandal in exemplary fashion [1]. Th e scandal was that geometry mutated signifi cantly in Linda D. Henderson analyzed in detail the infl uences that the second half of the nineteenth century. Between 1830 new mathematical ideas had on art and literature at the be- and 1850, Nikolai Lobachevsky (1792–1856) and János Bolyai ginning of the twentieth century [3]. It is worth noting that (1802–1860) developed the fi rst examples of non-Euclidean it is the combination of freedom and rules, between fantasy geometry, in which they consider invalid Euclid’s famous and axioms, that fascinates artists: Th e Euclidean scheme was fi ft h postulate. Not without doubt and confl icts, Lobachev- too rigid, too classic. However, this does not mean that it sky would later call his geometry (which today is called should be abandoned or that Euclid is passé. Mathmatics is an abstract science. Recalling the words of the mathemati- cian Robert Osserman: Michele Emmer (mathematician, fi lmmaker, writer, journalist, editorial adviser), Istituto Veneto Scienze, Lettere Arti, IVSLA, Venezia, Italia. Email: [email protected]. Abstraction works in a variety of ways. First, it carries the See www.mitpressjournals.org/toc/leon/53/2 for supplementary fi les associated power of universality, allowing a single rule to apply in very with this issue. diff erent circumstances . [and] it oft en brings clarity to ©2020 ISAST https://doi.org/10.1162/leon_a_01633 LEONARDO, Vol. 53, No. 2, pp. 151–156, 2020 151 Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/LEON_a_01633 by guest on 01 October 2021 what may be a confused situation. [Another advantage] SebastiAn’S SpAce And Forms is that it provides us with great freedom to let our imagina- From the point of view of a mathematician who looks at the tions roam, permitting us to devise new and alternative ver- links between culture and mathematics, it is of interest to see sions of reality—versions that may or may not correspond how the artist views and interprets some of the great ideas to something in the real world [4]. of geometry, of mathematics. A noteworthy demonstration A strong message that mathematics revealed in the late of the truth of this statement lies in the infinite variety of nineteenth and early twentieth centuries is that geometry forms of mathematical inspiration that the Mexican sculptor and space can be the realm of freedom and imagination, Sebastian has invented, rediscovered and used throughout all abstraction and rigor. Geometric objects and mathemati- his artistic activity (Fig. 1). cal ideas are of universal interest—and are also available to non-mathematicians, artists, writers and musicians—to be used, misinterpreted, mutated or distorted with their essen- tial impact and at the same time, for non-mathematicians, esoteric and mysterious: a search for an order but a victory of imagination. It seems a contradiction but it is not. A MAthematicAl ApproAch to Art The history of the relationships between art and mathematics is a long and winding road. There was an increased interest in these relationships over the last two centuries, and Max Bill wrote intriguing words on this subject in his 1949 ar- ticle “The Mathematical Way of Thinking in the Visual Art of Our Time,” on the relationship between art, form and mathematics. He wrote about mathematics as the science of transformations, relations and connections. Bill wanted to point out that, while mathematical and artistic activity are obviously not interchangeable, the mathematical laws of space and of the relations between objects can and should be of great importance for art. Bill used words very similar to those mathematicians used. A real and clear definition of the way in which the relationships between the two disci- plines—considered by many to be so distant—should be is as follows: It must not be supposed that an art based on the principles of mathematics, such as I have just adumbrated, is in any sense the same thing as a plastic or pictorial interpreta- tion of the latter. Indeed, it employs virtually none of the resources implicit in the term “pure mathematics.” The art in question can, perhaps, best be defined as the building up of significant patterns from the ever-changing relations, rhythms and proportions of abstract forms, each one of which, having its own causality, is tantamount to a law unto itself. As such, it presents some analogy to mathematics itself [5]. [Previously:] By a mathematical approach to art it is hardly necessary to say I do not mean any fanciful ideas for turning out art by some ingenious system of ready reckon- ing with the aid of mathematical formulas. So far as com- position is concerned every former school of art can be said to have had a more or less mathematical basis. There are also many trends in modern art which rely on the same sort of empirical calculations. These, together with the artist’s own individual scales of value, are just part of the ordinary elementary principles of design for establishing the proper relationship between component volumes; that is to say for imparting harmony to the whole [6]. Fig. 1. Sebastian, Red Brancusite, iron and acrylic enamel, 1980. (© Fundación Sebastian) 152 Emmer, Sebastian’s Space and Forms Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/LEON_a_01633 by guest on 01 October 2021 Fig. 2. Sebastian, Picassiana, iron and acrylic enamel, 1979. (© Fundación Sebastian) Héctor Tajonar was surely right when he wrote that the Having quoted and alluded to some of the significant links artist Sebastian “belongs to a tradition which goes back to between art and mathematics over the past centuries, ideas the beginning of western culture and continues to the pres- that were at least partially well known to Sebastian, it is use- ent.” He added: ful to look at some of the artist’s sculptures to highlight what has been the artist’s commitment (Fig. 2). Without forgetting Geometry has always been a fundamental tool for both what D’Arcy W. Thompson wrote in 1917, over 100 years ago: scientists and artists, to interpret the cosmic order. Se- “We are apt to think of mathematical definitions as too strict bastian is a worthy successor of all of the above, having and rigid for common use, but their rigour is combined with been inspired by their knowledge, as well as by the Mö- all but endless freedom” [9]. bius band, combinatorial topology, Buckminster Fuller’s Similarly Enrique X. de Anda Alanís wrote: geodesic dome, and the postulates of Euclidean and non Euclidean geometry [7]. Though Sebastian used mathematical speculations as a source of invention . he constantly revises the harmony It is instructive to read the titles of Sebastian’s work of his world in accordance with proportional models that throughout the years [8]: Purple Dodecahedron, Rhombo- are already implicit in his visual language.
Load more

Recommended publications
  • Euclid's Error: Non-Euclidean Geometries Present in Nature And
    International Journal for Cross-Disciplinary Subjects in Education (IJCDSE), Volume 1, Issue 4, December 2010 Euclid’s Error: Non-Euclidean Geometries Present in Nature and Art, Absent in Non-Higher and Higher Education Cristina Alexandra Sousa Universidade Portucalense Infante D. Henrique, Portugal Abstract This analysis begins with an historical view of surfaces, we are faced with the impossibility of Geometry. One presents the evolution of Geometry solving problems through the same geometry. (commonly known as Euclidean Geometry) since its Unlike what happens with the initial four beginning until Euclid’s Postulates. Next, new postulates of Euclid, the Fifth Postulate, the famous geometric worlds beyond the Fifth Postulate are Parallel Postulate, revealed a lack intuitive appeal, presented, discovered by the forerunners of the Non- and several were the mathematicians who, Euclidean Geometries, as a result of the flaw that throughout history, tried to show it. Many retreated many mathematicians encountered when they before the findings that this would be untrue, some attempted to prove Euclid’s Fifth Postulate (the had the courage and determination to make such a Parallel Postulate). Unlike what happens with the falsehood, thus opening new doors to Geometry. initial four Postulates of Euclid, the Fifth Postulate One puts up, then, two questions. Where can be revealed a lack of intuitive appeal, and several were found the clear concepts of such Geometries? And the mathematicians who, throughout history, tried to how important is the knowledge and study of show it. Geometries, beyond the Euclidean, to a better understanding of the world around us? The study, After this brief perspective, a reflection is made now developed, seeks to answer these questions.
    [Show full text]
  • From One to Many Geometries Transcript
    From One to Many Geometries Transcript Date: Tuesday, 11 December 2012 - 1:00PM Location: Museum of London 11 December 2012 From One to Many Geometries Professor Raymond Flood Thank you for coming to the third lecture this academic year in my series on shaping modern mathematics. Last time I considered algebra. This month it is going to be geometry, and I want to discuss one of the most exciting and important developments in mathematics – the development of non–Euclidean geometries. I will start with Greek mathematics and consider its most important aspect - the idea of rigorously proving things. This idea took its most dramatic form in Euclid’s Elements, the most influential mathematics book of all time, which developed and codified what came to be known as Euclidean geometry. We will see that Euclid set out some underlying premises or postulates or axioms which were used to prove the results, the propositions or theorems, in the Elements. Most of these underlying premises or postulates or axioms were thought obvious except one – the parallel postulate – which has been called a blot on Euclid. This is because many thought that the parallel postulate should be able to be derived from the other premises, axioms or postulates, in other words, that it was a theorem. We will follow some of these attempts over the centuries until in the nineteenth century two mathematicians János Bolyai and Nikolai Lobachevsky showed, independently, that the Parallel Postulate did not follow from the other assumptions and that there was a geometry in which all of Euclid’s assumptions, apart from the Parallel Postulate, were true.
    [Show full text]
  • Models in Geometry and Logic: 1870-1920 ∗
    Models in Geometry and Logic: 1870-1920 ∗ Patricia Blanchette University of Notre Dame 1 Abstract Questions concerning the consistency of theories, and of the independence of axioms and theorems one from another, have been at the heart of logical investigation since the beginning of logic. It is well known that our own contemporary methods for proving independence and consistency owe a good deal to developments in geometry in the middle of the nineteenth century, and especially to the role of models in estab- lishing the consistency of non-Euclidean geometries. What is less well understood, and is the topic of this essay, is the extent to which the concepts of consistency and of independence that we take for granted today, and for which we have clear techniques of proof, have been shaped in the intervening years by the gradual de- velopment of those techniques. It is argued here that this technical development has brought about significant conceptual change, and that the kinds of consistency- and independence-questions we can decisively answer today are not those that first motivated metatheoretical work. The purpose of this investigation is to help clarify what it is, and importantly what it is not, that we can claim to have shown with a modern demonstration of consistency or independence.1 ∗This is the nearly-final version of the paper whose official version appears in Logic, Methodology, and Philosophy of Science - proceedings of the 15th International Congress, edited by Niiniluoto, Sepp¨al¨a,Sober; College Publications 2017, pp 41-61 1Many thanks to the organizers of CLMPS 2015 in Helsinki, and also to audience members for helpful comments.
    [Show full text]
  • The Continuous Transition of Hamiltonian Vector Fields Through Manifolds of Constant Curvature
    THE CONTINUOUS TRANSITION OF HAMILTONIAN VECTOR FIELDS THROUGH MANIFOLDS OF CONSTANT CURVATURE Florin Diacu, Slim Ibrahim, and Je˛drzej Śniatycki Pacific Institute for the Mathematical Sciences and Department of Mathematics and Statistics University of Victoria P.O. Box 1700 STN CSC Victoria, BC, Canada, V8W 2Y2 [email protected], [email protected], [email protected] September 6, 2018 Abstract. We ask whether Hamiltonian vector fields defined on spaces of constant Gaussian curvature κ (spheres, for κ> 0, and hyperbolic spheres, for κ < 0), pass continuously through the value κ = 0 if the potential functions Uκ,κ ∈ R, that define them satisfy the property limκ→0 Uκ = U0, where U0 corresponds to the Euclidean case. We prove that the answer to this question is positive, both in the 2- and 3-dimensional cases, which are of physical interest, and then apply our conclusions to the gravitational N-body problem. 1. Introduction The attempts to extend classical equations of mathematical physics from Eu- clidean space to more general manifolds is not new. This challenging trend started in the 1830s with the work of János Bolyai and Nikolai Lobachevsky, who tried to generalize the 2-body problem of celestial mechanics to hyperbolic space, [2], [14]. This particular topic is much researched today in the context of the N-body problem in spaces of constant curvature, [4], [5], [6], [7], [10], [11], [12]. But ex- arXiv:1510.06327v1 [math.DS] 21 Oct 2015 tensions to various manifolds have also been pursued for PDEs, even beyond the boundaries of classical mechanics, such as for Schrödinger’s equation [1], [3], [13], and the Vlasov-Poisson system, [9], to mention just a couple.
    [Show full text]
  • Lobachevsky, Nikolai
    NIKOLAI LOBACHEVSKY ( December 1, 1792 – February 24, 1856) by HEINZ KLAUS STRICK, Germany NIKOLAI IVANOVICH LOBACHEVSKY was born in Nizhny Novgorod. When his father died in 1799, his mother moved to Kazan on the central Volga. There he began studying medicine at the newly founded university at the age of 15, but switched to mathematics a year later. His professor was MARTIN BARTELS, a friend of CARL FRIEDRICH GAUSS. He had previously worked as a teacher in Germany and was now appointed as a mathematics professor in Kazan. LOBACHEVSKY finished his mathematics studies at the age of 19 and at the age of 24 he was appointed professor at the University of Kazan. Later he became the dean and rector of the university. At the age of 22 he was already concerned with the question of the meaning of the so-called axiom of parallels, that is, the fifth postulate of EUCLID's geometry. Many mathematicians had been concerned with this postulate since antiquity, but it was only LOBACHEVSKY, GAUSS and JANOS BOLYAI who achieved decisive new insights almost simultaneously. However, they were not recognised during their lifetime. LOBACHEVSKY himself also received high honours, such as elevation to the hereditary nobility; however, this was not because of his discovery / invention of a new geometry. His Geometric Investigations of the Theory of Parallels, published in 1840, was viewed by most as the crazy ideas of an otherwise deserving scientist. EUCLID had around 300 BC in the first volume of his Elements proposed a system of five postulates from which all geometrical propositions should be derived: (1) Two points can always be connected by a line.
    [Show full text]
  • Riemannian Reading: Using Manifolds to Calculate and Unfold
    Eastern Illinois University The Keep Masters Theses Student Theses & Publications 2017 Riemannian Reading: Using Manifolds to Calculate and Unfold Narrative Heather Lamb Eastern Illinois University This research is a product of the graduate program in English at Eastern Illinois University. Find out more about the program. Recommended Citation Lamb, Heather, "Riemannian Reading: Using Manifolds to Calculate and Unfold Narrative" (2017). Masters Theses. 2688. https://thekeep.eiu.edu/theses/2688 This is brought to you for free and open access by the Student Theses & Publications at The Keep. It has been accepted for inclusion in Masters Theses by an authorized administrator of The Keep. For more information, please contact [email protected]. The Graduate School� EA<.TEH.NILLINOIS UNJVER.SITY" Thesis Maintenance and Reproduction Certificate FOR: Graduate Candidates Completing Theses in Partial Fulfillment of the Degree Graduate Faculty Advisors Directing the Theses RE: Preservation, Reproduction, and Distribution of Thesis Research Preserving, reproducing, and distributing thesis research is an important part of Booth Library's responsibility to provide access to scholarship. In order to further this goal, Booth Library makes all graduate theses completed as part of a degree program at Eastern Illinois University available for personal study, research, and other not-for-profit educational purposes. Under 17 U.S.C. § 108, the library may reproduce and distribute a copy without infringing on copyright; however, professional courtesy dictates that permission be requested from the author before doing so. Your signatures affirm the following: • The graduate candidate is the author of this thesis. • The graduate candidate retains the copyright and intellectual property rights associated with the original research, creative activity, and intellectual or artistic content of the thesis.
    [Show full text]
  • The Birth of Non-Euclidean Geometry
    The Birth of non-Euclidean Geometry Irina Kogan Department of Math., North Carolina State University, [email protected] https://iakogan.math.ncsu.edu/ Triangle Math Teachers’ Circle, January 23, 2021. https://trianglemtc.wordpress.com/ 1 Euclid of Alexandria Mid-4th century BC - Mid-3th century BC 350 - 250 BC Geometry that we learn at school is called Euclidean geometry. It is based on the Euclidean postulates Why is this man so famous? What is a postulate? 2 How did Euclid look like? Raffaello Sanzio from Wikipedia (Raphael), Jusepe de (source ?) c. 1510, Palazzi Ribera, c. 1630- Pontifici, Vatican 1635, J. Paul Getty Museum 3 Euclid’s Elements circa 300 BC. A fragment of Euclid’s Elements on part of the Oxyrhynchus papyri ∼ 100 AD 4 The earliest preserved complete version: c. 850 AD, First English the Vatican Library version, 1570 4 Elements consist of 13 books containing 465 Propositions about planar and 3D geometry, as well as number theory. This includes: • Most of the theorems for planar geometry we learn at school. • Euclid’s algorithm for finding the greatest common divisor and the least common multiple. • Proof is irrationality of the square roots of non-square integers (e.g. p 2) • Volumes of cones, pyramids, and cylinders in detail by using the method of exhaustion, a precursor to integration. 5 Most of the results are not original! According to W.W. Rouse Ball,“ A Short Account of the History of Mathematics”, 1908 • Pythagoras (c. 570 - 495 BC) was probably the source for most of books I and II; • Hippocrates of Chios (c.
    [Show full text]
  • Math 135 Notes Parallel Postulate .Pdf
    Euclidean verses Non Euclidean Geometries Euclidean Geometry Euclid of Alexandria was born around 325 BC. Most believe that he was a student of Plato. Euclid introduced the idea of an axiomatic geometry when he presented his 13 chapter book titled The Elements of Geometry. The Elements he introduced were simply fundamental geometric principles called axioms and postulates. The most notable are Euclid’s five postulates which are stated in the next passage. 1) Any two points can determine a straight line. 2) Any finite straight line can be extended in a straight line. 3) A circle can be determined from any center and any radius. 4) All right angles are equal. 5) If two straight lines in a plane are crossed by a transversal, and sum the interior angle of the same side of the transversal is less than two right angles, then the two lines extended will intersect. According to Euclid, the rest of geometry could be deduced from these five postulates. Euclid’s fifth postulate, often referred to as the Parallel Postulate, is the basis for what are called Euclidean Geometries or geometries where parallel lines exist. There is an alternate version to Euclid fifth postulate which is usually stated as “Given a line and a point not on the line, there is one and only one line that passed through the given point that is parallel to the given line. This is a short version of the Parallel Postulate called Fairplay’s Axiom which is named after the British math teacher who proposed to replace the axiom in all of the schools textbooks.
    [Show full text]
  • Euclid's Fifth Postulate
    GENERAL ⎜ ARTICLE Euclid’s Fifth Postulate Renuka Ravindran In this article, we review the fifth postulate of Euclid and trace its long and glorious history. That after two thousand years, it led to so much discussion and new ideas speaks for itself. “It is hard to add to the fame and glory of Euclid, who managed to write an all-time bestseller, a classic book read and scrutinized for Renuka Ravindran was on the last twenty three centuries.” The book is called 'The Elements’ the faculty of the Depart- and consists of 13 books all devoted to various aspects of geom- ment of Mathematics, IISc, Bangalore. She was also etry and number theory. Of these, the most quoted is the one on Dean, Science Faculty at the fundamentals of geometry Book I, which has 23 definitions, 5 IISc. She has been a postulates and 48 propositions. Of all the wealth of ideas in The visiting Professor at Elements, the one that has claimed the greatest attention is the various universities in USA and Germany. Fifth Postulate. For two thousand years, the Fifth postulate, also known as the ‘parallel postulate’, was suspected by mathemati- cians to be a theorem, which could be proved by using the first four postulates. Starting from the commentary of Proclus, who taught at the Neoplatonic Academy in Athens in the fifth century some 700 years after Euclid to al Gauhary (9th century), to Omar Khayyam (11th century) to Saccheri (18th century), the fifth postulate was sought to be proved. Euclid himself had just stated the fifth postulate without trying to prove it.
    [Show full text]
  • A Story of Two Postulates Irina Kogan
    A story of two postulates Irina Kogan Department of Math., North Carolina State University, [email protected] SWiM, June 22, 2018. 1 Euclid of Alexandria Mid-4th century BC - Mid-3th century BC 350 - 250 BC Geometry that we learn at school is called Euclidean geometry. It is based on the Euclidean parallel postulate Why is this man so famous? What is a postulate? 2 How did Euclid look like? Raffaello Sanzio from Wikipedia (Raphael), Jusepe de (source ?) c. 1510, Palazzi Ribera, c. 1630- Pontifici, Vatican 1635, J. Paul Getty Museum 3 Euclid’s Elements circa 300 BC. A fragment of Euclid’s Elements on part of the Oxyrhynchus papyri ∼ 100 AD 4 The earliest preserved complete version: c. 850 AD, First English the Vatican Library version, 1570 4 Elements consist of 13 books containing 465 Propositions about planar and 3D geometry, as well as number theory. This includes: • Most of the theorems for planar geometry we learn at school. • Euclid’s algorithm for finding the greatest common divisor and the least common multiple. • Proof is irrationality of the square roots of non-square integers (e.g. p 2) • Volumes of cones, pyramids, and cylinders in detail by using the method of exhaustion, a precursor to integration. 5 Most of the results are not original! According to W.W. Rouse Ball,“ A Short Account of the History of Mathematics”, 1908 • Pythagoras (c. 570 - 495 BC) was probably the source for most of books I and II; • Hippocrates of Chios (c. 470 - 410 BC) for book III; • Eudoxus of Cnidus (c.
    [Show full text]
  • Introduction to Modern Geometry
    Introduction to Modern Geometry Splash 2015 Goal of talk: What is the “flavor” of current mathematics research, particularly in geometry? Don’t worry if things are confusing (professional mathematicians also find them confusing!) Please ask questions! Ancient geometry: Euclid ~300 BC Euclid’s “The Elements” Papyrus from ~AD 75-125 Euclid’s “The Elements” English version from 1570 Euclid’s “The Elements” • Definitive reference on geometry for over two millennia! • One of first examples of giving rigorous (irrefutable!) proofs basic on postulates • Postulate: a fact which is so “basic” and “self-evident” that it cannot be proven from other facts, hence we must just accept that it has to be true “Let the following be postulated” 1. "To draw a straight line from any point to any point.” 2. "To extend a finite straight line continuously in a straight line.” 3. "To describe a circle with any centre and radius.” 4. "That all right angles are equal to one another.” 5. The parallel postulate: "That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles." The troublesome one: The parallel postulate: "That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles." An equivalent formulation of the Parallel Postulate: “In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.” The Parallel Postulate: why so controversial? • it does not seem quite as “self-evident” as the other postulates • people tried for thousands of years to prove that the parallel postulate in terms of the other postulates Nikolai Lobachevsky, b.
    [Show full text]
  • Carl Friedrich Gauss Und Russland: Sein Briefwechsel Mit in Russland Wirkenden Wissenschaftlern De Gruyter, Berlin, 2012
    Sci & Educ (2013) 22:717–721 DOI 10.1007/s11191-012-9507-z BOOK REVIEW Karin Reich and Elena Roussanova: Carl Friedrich Gauss und Russland: Sein Briefwechsel mit in Russland wirkenden Wissenschaftlern De Gruyter, Berlin, 2012. (Abhandlungen der Akademie der Wissenschaften zu Go¨ttingen, Neue Folge, Volume 16), ISBN: 978-3-11-025306-1, 905 pp, $225.00 Andre K. T. Assis Published online: 22 June 2012 Ó Springer Science+Business Media B.V. 2012 This book deals with the relationship between the great German scientist Carl Friedrich Gauss (1777–1855) and Russian politics, society and science of his time. The authors are Karin Reich and Elena Roussanova. Reich is a professor of the history of science. She was born in Mu¨nchen, worked in Stuttgart and was from 1995 until her retirement in 2007 professor at the Institute for the History of Natural Sciences and Mathematics of Hamburg University. Since 2008 she has been the leader of the research project ‘‘Gauss und Russland,’’ financed by Fritz Thyssen Stiftung. Her main research interests are the history of science in the sixteenth, nineteenth and twentieth centuries. In particular, she has focused much of her work in the life and work of Gauss, and also in the history of mathematics and theoretical physics in Hamburg. Between her books there is a biography of Gauss (Reich 1977, new ed. Reich/Biegel 2005). Recently she published, together with Horst Schmidt-Bo¨cking, a biography of Otto Stern (1888–1969), the famous German physicist and Nobel laureate in physics, who worked from 1923 to 1933 at the University of Hamburg, until resigning from his post because of the seizure of power by Hitler (Schmidt-Bo¨cking and Reich 2011).
    [Show full text]