A Gardner's Workout: Training the Mind and Entertaining the by Martin Gardner

By Martin Gardner

Listed here are forty-one items, which have been formerly released in quite a few educational journals and renowned magazines, by way of the esteemed grasp of mathematical video games and puzzles who wrote the medical American video games column for 25 years. those articles span quite a lot of themes, together with dialogue of why a working laptop or computer will constantly beat a human participant at video games of probability, tiling puzzles, machine and calculator "magic" tips, and a arguable severe assessment of a instructing fad referred to as the "new new Math."

Show description

Read or Download A Gardner's Workout: Training the Mind and Entertaining the Spirit PDF

Best elementary books

Polynomial root-finding and polynomiography

This booklet deals attention-grabbing and glossy views into the idea and perform of the old topic of polynomial root-finding, rejuvenating the sector through polynomiography, an artistic and novel laptop visualization that renders dazzling photos of a polynomial equation. Polynomiography won't in basic terms pave the best way for brand spanking new purposes of polynomials in technology and arithmetic, but in addition in artwork and schooling.

Evolution: A Beginner's Guide (Beginner's Guides (Oneworld))

Overlaying every little thing from fossilized dinosaurs to clever apes, this can be an available consultant to 1 of an important clinical theories of all time. Burt Guttman assumes no earlier medical wisdom at the a part of the reader, and explains all the key principles and ideas, together with average choice, genetics and the evolution of animal habit, in a full of life and informative method.

Mathématiques 1re S et E

Desk des matières :

Chapitre 1. L’outil vectoriel et analytique
    I. Introduction
    II. Le plan vectoriel (rappels)
    III. Les liaisons « plan ponctuel-plan vectoriel »
    IV. L’outil analytique
    V. Compléments

Chapitre 2. L’outil des transformations
    I. Introduction
    II. differences usuelles
    III. motion sur les configurations élémentaires
    IV. modifications associant une determine donnée à une determine donnée
    V. Composition de transformations
    VI. Compléments

Chapitre three. Les angles
    I. Introduction
    II. perspective d’un couple de vecteurs
    III. L’addition des angles
    IV. Propriétés géométriques
    V. Angles et cercles
    VI. Compléments

Chapitre four. Le produit scalaire
    I. Introduction
    II. Produit scalaire de deux vecteurs (rappel)
    III. Produit scalaire en géométrie analytique
    IV. Orthogonalité et cocyclicité
    V. Produit scalaire et lignes de niveau
    VI. Compléments

Chapitre five. Trigonométrie et kinfolk métriques dans le triangle
    I. Introduction
    II. Cosinus et sinus (rappels)
    III. Cosinus et produit scalaire ; sinus et déterminant
    IV. Trigonométrie
    V. family métriques dans le triangle
    VI. Compléments
    Trigonométrie (formulaire récapitulatif)

Chapitre 6. Rotations et isométries fixant un aspect donné
    I. advent (quart de tour)
    II. Rotation de centre O et d’angle α
    III. Rotation : théorèmes de composition et propriétés géométriques
    IV. Isométries fixant un element donné
    V. Compléments

Chapitre 7. Le calcul vectoriel dans l’espace
    I. Introduction
    II. L’espace vectoriel E
    III. Droites et plans : repères et vecteurs directeurs
    IV. Éléments de géométrie analytique dans l’espace
    V. Compléments

Chapitre eight. Le produit scalaire dans l’espace
    I. Introduction
    II. Produit scalaire dans E
    III. functions géométriques du produit scalaire
    IV. Produit scalaire et géométrie analytique
    V. Compléments

Chapitre nine. los angeles sphère
    I. Introduction
    II. los angeles sphère : définition et premières propriétés
    III. part d’une sphère
    IV. Détermination d’une sphère
    V. Surfaces de révolution
    VI. Compléments

Chapitre 10. Statistiques
    I. Introduction
    II. Les caractéristiques de position
    III. Les caractéristiques de dispersion
    IV. Compléments

Additional resources for A Gardner's Workout: Training the Mind and Entertaining the Spirit

Sample text

4 shows that solving equations in Z,, may be quite different from solving equations in 7L. A quadratic equation in 7L has at most two solutions, whereas the quadratic equation x1 ffi [5]0x = [OJ has four solutions in Z6• • Exercises A. I. Write out the addition and multiplication tables for (a) (b) � Z2 (c) 7L7 (d) Z-12 In Exercises 2--8, solve the equation. 2. _ .. eMmog-- .. _:ligl:U�:MpiNit. 3 3. x2 4. ls x4 =[lJ in Zs 5. x2 EB [3J 0 x®[2J = [OJ in Zt, 6. x2 EB [SJ 0 x = [OJin £9 7. x3 EB x2® x®[lJ =[OJ in Zs 8.

A). ] 31. If p is a positive prime, prove that Vfi is irrational. ] 32. (Euclid ) Prove that there are infinitely many primes. [Hint: Use proof by contradiction (Appendix A) . Assume there are only finitely many primes p1, p2, Pk• and reach a contradiction by showing that the number , Pk·l p1p2 Pk + 1 is not divisible by any of Pi. p2, 33. Let p > 1. If 2P - 1 is prime, prove that p is prime. ] • • • · , • • • · • Note: The converse is false by Exercise 2(b). C. 34. Prove or disprove: If n is an integer and n > 2, then there exists a prime p such that n

A2, , an are integers, not all zero, then their greatest common divisor (gcd) is the largest integer d such that d I a1for every i. Prove that there exist integers u1 such that d = a1u1 + a2u2 + + anu,.. [Hint: Adapt the proof of Theorem 1. ] • • • · • · 31. The least common multiple (lcm) of nonzero integers a1, � , ak is the smallest positive integer m such that a1lm for i = 1, 2, , k and is denoted [a1> � , ak1. • • • • ... •• • (a) • Find each of the following: [6, 10], [4, 5, 6, 10], (20, 42], and [2, 3, 14, 36, 42].

Download PDF sample

Rated 4.89 of 5 – based on 30 votes