Mathematics, poetry, and beauty
Mathematical recreations Mathematics Poetry in mathematics education e-böcker
World Scientific
2014
EISBN 9789814602952
""Contents""; ""Introduction: Magic""; ""Mathematics and Poetry""; ""Displacement""; ""Part I: Order""; ""The Curious Case of the Ants on the Pole""; ""Hidden Order""; ""The power of concepts""; ""The chocolate problem""; ""To Discover or to Invent""; ""Platonism""; ""The sum of an arithmetic sequence""; ""Is poetry invented or discovered?""; ""Order and Beauty""; ""Saving energy""; ""Mathematical Harmonies""; ""Rhythm and prediction""; ""Pythagoras""; ""Helmholtz""; ""Mystical numbers""; ""Sobering up""; ""Why â?š2 is Not a Rational Number""; ""The Real Numbers""; ""The Miracle of Order""
""Menages a Trois""""Imagination""; ""Fantasy and imagination""; ""Mathematical similarity""; ""Isomorphism""; ""A Magic Number""; ""Compound interest""; ""Secret friend""; ""Geometric mean""; ""A differential equation""; ""Reality or Imagination""; ""Don�t trust them too far""; ""Imaginary and complex numbers""; ""The fundamental theorem of algebra""; ""How complex numbers were born""; ""The world�s most beautiful formula?""; ""Unexpected Combinations""; ""Eureka""; ""Unexpected combinations in poetry""; ""Harnessed together""; ""What is Mathematics?""; ""The hard life of the definer""
""One more step""""Generalization""; ""Formal proof""; ""The Book in Heaven""; ""A proof from the book for the sum of a geometric series""; ""Poetical Ping-Pong""; ""Concealed ping-pong""; ""Laws of Conservation""; ""How to become rich by using a law of conservation""; ""Conservation of inner truth""; ""An Idea from Somewhere Else""; ""The metaphor""; ""Three Types of Mathematics""; ""Continuous mathematics""; ""Algebra""; ""Discrete mathematics""; ""Topology""; ""The fixed point theorem""; ""The Borsuk-Ulam Theorem""; ""An application in discrete mathematics""; ""Matchmaking""
""Part II: How Mathematicians and Poets Think""""Poetic Image, Mathematical Image""; ""Words""; ""The poetical picture""; ""A mathematical picture: The number line""; ""A coordinate system""; ""The Power of the Oblique""; ""What did the poet mean?""; ""Indirect proofs""; ""An irrational number to the power of a rational number""; ""The pigeonhole principle""; ""Independent sets""; ""Co-prime numbers""; ""Compression""; ""Why don�t people understand mathematics?""; ""Mathematical Ping-Pong""; ""“How to solve it�""; ""The sum of a geometrical series""; ""A conceptual leap""
""The unreasonable effectiveness of mathematics""""Order in the world and order in mathematics""; ""Beauty and truth""; ""Simple Conjectures, Complex Proofs""; ""Kepler�s sphere packing problem""; ""The four colors theorem""; ""Ascending and descending sequences""; ""The twin primes conjecture""; ""Independent Events""; ""Independence""; ""Independence and probability""; ""Positive correlation, negative correlation""; ""Why is the Twin Primes Conjectures almost certainly correct?""; ""The Twin Prime Number Conjecture, with some spare""; ""From million to infinity""
""Menages a Trois""""Imagination""; ""Fantasy and imagination""; ""Mathematical similarity""; ""Isomorphism""; ""A Magic Number""; ""Compound interest""; ""Secret friend""; ""Geometric mean""; ""A differential equation""; ""Reality or Imagination""; ""Don�t trust them too far""; ""Imaginary and complex numbers""; ""The fundamental theorem of algebra""; ""How complex numbers were born""; ""The world�s most beautiful formula?""; ""Unexpected Combinations""; ""Eureka""; ""Unexpected combinations in poetry""; ""Harnessed together""; ""What is Mathematics?""; ""The hard life of the definer""
""One more step""""Generalization""; ""Formal proof""; ""The Book in Heaven""; ""A proof from the book for the sum of a geometric series""; ""Poetical Ping-Pong""; ""Concealed ping-pong""; ""Laws of Conservation""; ""How to become rich by using a law of conservation""; ""Conservation of inner truth""; ""An Idea from Somewhere Else""; ""The metaphor""; ""Three Types of Mathematics""; ""Continuous mathematics""; ""Algebra""; ""Discrete mathematics""; ""Topology""; ""The fixed point theorem""; ""The Borsuk-Ulam Theorem""; ""An application in discrete mathematics""; ""Matchmaking""
""Part II: How Mathematicians and Poets Think""""Poetic Image, Mathematical Image""; ""Words""; ""The poetical picture""; ""A mathematical picture: The number line""; ""A coordinate system""; ""The Power of the Oblique""; ""What did the poet mean?""; ""Indirect proofs""; ""An irrational number to the power of a rational number""; ""The pigeonhole principle""; ""Independent sets""; ""Co-prime numbers""; ""Compression""; ""Why don�t people understand mathematics?""; ""Mathematical Ping-Pong""; ""“How to solve it�""; ""The sum of a geometrical series""; ""A conceptual leap""
""The unreasonable effectiveness of mathematics""""Order in the world and order in mathematics""; ""Beauty and truth""; ""Simple Conjectures, Complex Proofs""; ""Kepler�s sphere packing problem""; ""The four colors theorem""; ""Ascending and descending sequences""; ""The twin primes conjecture""; ""Independent Events""; ""Independence""; ""Independence and probability""; ""Positive correlation, negative correlation""; ""Why is the Twin Primes Conjectures almost certainly correct?""; ""The Twin Prime Number Conjecture, with some spare""; ""From million to infinity""
