數(shù)學(xué)那些事兒

1、The Mathematical UniverseYubo1An argue on newsmth Who is the greatest mathematician in history?GaussianNewtonEuclidEulerArchimedes2A BookThe Mathematical Universe:An Alphabetical Journey Through the Great Proofs, Problems, and Personalities3ContentsAn ancient and interesting theorem the Pythagorean

2、TheoremA legendary and productive mathematicianLeonhard Euler(1707-1783)A fascinating and fundamental paradoxRussells paradox(1903)4ContentsAn ancient and interesting theorem the Pythagorean TheoremA legendary and productive mathematicianLeonhard Euler(1707-1783)A fascinating and fundamental paradox

3、Russells paradox(1903)5Pythagorean TheoremHow to prove it?There are hundreds of different proofs!6Pythagorean TheoremBAHGFEDC7Pythagorean TheoremAEBDC8ContentsAn ancient and interesting theorem the Pythagorean TheoremA legendary and productive mathematicianLeonhard Euler(1707-1783)A fascinating and

4、fundamental paradoxRussells paradox(1903)9Master Leonhard EulerSwiss mathematicianGreat contribution in infinitesimal calculus and graph theory865 paper, 32 booksBlind since 177110Master Leonhard EulerPart of his contributionMathematical notation y=F(x)sin(x) cos(x)natural logarithm eAnalysisFound n

5、early 60 pairs of amicable numbersCalculated numbers of infinite series11ContentsAn ancient and interesting theorem the Pythagorean TheoremA legendary and productive mathematicianLeonhard Euler(1707-1783)A fascinating and fundamental paradoxRussells paradox(1903)12Russells paradoxOne conceptcollecti

6、on A=1,2,3B=1,2,3C=C,3Two types of collection1,2,3, a,b,c note these collections as Russell collectionsA=A,2,3, B=B,b,c non-Russell collections13Russells paradoxSo, we get two big collectionsX=1,2,3,a,b,c, contains all the Russell collectionsY=A,2,3,B,b,c, contains all the non-Russell collectionsEve

7、ry collection in the world will belong to either X or Y14Russells paradoxHere comes the paradoxConsider the collection XX is the collection contains all the Russell collectionsFirstly, X is a collectionThen X belongs to either X or YX belongs to X?Then X contains X-X is an non-Russell collection-X belongs to YX belongs to Y?Then Y contains X-X doesnt contains X-X is a Russell collection-X belongs to XParadox!15Russells paradoxBarber paradoxA barber claims he will give thos