A History of Mathematics- From Mesopotamia to Modernity

250 A History ofMathematics Fig. 5The ‘Smale horseshoe map’ is often quoted as an example of chaotic behaviour. The mapftakes th ...

AChaoticEnd? 251 Fig. 6This object (also called a ‘string worldsheet’) is (a) a surface, (b) the story of two strings which (rea ...

252 A History ofMathematics All this was familiar to me from my research in high-energy physics, but until that moment I had onl ...

AChaoticEnd? 253 ++ Fig. 7The ‘classical’ model of the helium atom: two electrons orbiting a nucleus. The quantum model, ...

254 A History ofMathematics for many mathematicians there is a strong temptation to see Fritiof Capra’s intoxicated description ...

AChaoticEnd? 255 considered either a hopeless pursuit or a backwater was revived by Ken Ribet’s work in linking it to a central ...

256 A History ofMathematics 2 1 0 1 –0.5 0 0.5 1 x 1.5 –1 –2 0 0 Fig. 8Graph ofy^2 =x^3 −x. Fig. 9A torus (again); this is the ...

AChaoticEnd? 257 given until we reach §9. For the present I shall only say that the justification lies in the fact that the huma ...

258 A History ofMathematics Solutions to exercises These are perhaps unduly hard, but it is almost impossible to find easier one ...

AChaoticEnd? 259 In the casen=4, 2n− 1 =15;z=exp( 2 kπ/ 15 ).Ifk=0,zis of period 1 (fixed), while ifk=5, 10,zis of period 2 (usi ...

Conclusion Yesterday all the past. The language of size Spreading to china along the trade-routes; the diffusion Of the counting ...

Conclusion 261 Is the development of algorithms (the word comes by a circuitous route from the name al-Khw ̄arizm ̄i, chapter 5) ...

262 A History ofMathematics nodding acquaintance with intellectual property law. As in ancient Babylon, the military-industrial ...

Bibliography Ab ̄uK ̄amil,Shuj ̄a ibn Aslam: The Algebra of Ab ̄uK ̄amil in a commentary by Mordecai Finzi, tr. and ed. Martin L ...

264 Bibliography Bonola, Roberto,Non-Euclidean Geometry: with a supplement containing ‘The Theory of Parallels’ by Nicholas Loba ...

Bibliography 265 Dick, Auguste (tr. H. I. Blocher),Emmy Noether, 1882–1935. Boston, MA, Basel, New York, Stüttgart: Birkhäuser, ...

266 Bibliography Greenberg, Marvin Jay, Euclidean and Non-Euclidean Geometries: Development and History. San Francisco, CA: W.H. ...

Bibliography 267 Khayyam, Omar (‘Umar al-Khayy ̄ ̄ am ̄i),The Algebra of Omar Khayyam(trans. and ed. Daoud S. Kasir). New York: ...

268 Bibliography Newton, Isaac, in D. T. Whiteside et al.(ed.),The Mathematical Papers of Isaac Newton, 8 vols, Cambridge: Cambr ...

Bibliography 269 Spengler, Oswald,Decline of theWest, London: George Allen and Unwin, 1934. Steele and Imhausen (eds.), Under On ...