Download PDF by Martin Gardner: Aha! Insight

By Martin Gardner

ISBN-10: 071671017X

ISBN-13: 9780716710172

Aha! perception demanding situations the reader's reasoning strength and instinct whereas encouraging the advance of 'aha! reactions'.

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Desk des matières du livre :

Chapitre I. — Opérations sur les nombres entiers
    1. Les nombres entiers
    2. Addition. Somme
    3. Multiplication. Produit
    4. Suites d’additions et de multiplications. — utilization des parenthèses
    5. Produits de sommes
    6. Pratique de l’addition
    7. Pratique de los angeles multiplication
    8. Soustraction. Différence
    9. Polynômes arithmétiques
    10. Produits de différences
    11. Pratique de l. a. soustraction
    12. Multiples et diviseurs d’un nombre. — Quotient exact
    13. Multiples et diviseurs d’un nombre (suite)
    14. Quotient de deux nombres à une unité près

Chapitre II. — Divisibilité
    15. Divisibilité par 2 et 5 ; par four et 25
    16. Divisibilité par nine et par 3
    17. Multiples et diviseurs communs à deux ou plusieurs nombres
    18. Nombres premiers
    19. Décomposition d’un nombre en un produit de facteurs premiers
    20. Recherche des diviseurs d’un nombre
    21. Plus grand commun diviseur
    22. Plus petit commun multiple
    23. Nombres premiers entre eux
    Problèmes sur le chapitre II

Chapitre III. — Fractions et nombres décimaux
    24. thought de fraction
    25. Fractions égales
    26. Simplification des fractions
    27. Réduction des fractions au même dénominateur
    28. Multiplication des fractions
    29. department des fractions
    30. Addition des fractions
    31. Comparaison des fractions. — Soustraction des fractions
    32. Opérations sur les sommes, différences et produits de nombres entiers ou fractionnaires
    33. Fractions décimales. — Nombres décimaux
    34. Opérations sur les nombres décimaux
    35. Quotient de deux nombres à une unité décimale près
    36. Fractions ordinaires et nombres décimaux
    Problèmes sur le chapitre III

Chapitre IV. — Nombres complexes
    37. Nombres complexes

Chapitre V. — Arithmétique littérale. — Résolution algébrique des problèmes
    38. Expressions littérales
    39. Égalités et équations
    40. Résolution algébrique des problèmes

Chapitre VI. — Racine carrée
    41. Racine carrée
    42. Recherche de los angeles racine carrée d’un nombre
    43. Extraction de l. a. racine carrée d’un nombre
    Problèmes sur le chapitre VI

Chapitre VII. — Rapports et proportions. — Applications
    44. Rapport de deux nombres
    45. Proportions
    46. Suite de rapports égaux. — Nombres proportionnels
    47. Grandeurs proportionnelles
    48. Pourcentages et bénéfices
    49. Intérêts simples
    50. Escompte commercial
    Problèmes sur le chapitre VII

Extra resources for Aha! Insight

Example text

Figure 11 shows a dozen interesting shapes on which the reader is invited to try his skill. Each 32 CHAPTER THREE Figure 10 Edgar Allan Poe's carved ivory tangram set requires all seven pieces. The rhomboid, the only asymmetrical tan, may be placed either side up. One figure in the illustration is not possible. Can the reader identify it and prove its impossibility? The paired tangrams in Figure 12 are samples of delightful paradoxes introduced by Loyd. ) Although the figure at the right in each case seems to be exactly the same as its mate, except for a missing portion, each is made with all seven tans!

Who, for example, can look . . at Lady Belinda . . without soon feeling the haughty expression . . Then look again at the stork, and see how it is suggested to the mind that the leg is actually much more slender than any one of the pieces employed. It is really an optical illusion. Again, notice in the case of the yacht TANGRAMS, PART 1 35 how, by leaving that little angular point at the top, a complete mast is suggested. " One can mix two or more sets of tans to produce more elaborate figures.

The star sequence begins 1,13,37,73,121,181,253,337,433,541,. . Adding 12n to the nth star produces the next star. A hex contains six triangles. Adding six more triangles to its six sides produces a star; consequently any hex number becomes a star number if we double it and subtract 1. The first n stars add up to 2n3 - n. Is this sum ever a square? Yes, but only when n = 1 or 169. This was established in 1973 by John Harris, on the basis ofresults reported by Louis J. Mordell on page 271 of his Diophantine Equations.

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Aha! Insight by Martin Gardner

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