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Honsberger R. — Mathematical Delights
Honsberger R. — Mathematical Delights

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Название: Mathematical Delights

Автор: Honsberger R.

Аннотация:

Mathematical Delights is a collection of 90 short elementary gems from algebra, geometry, combinatorics, and number theory. Honsberger presents us with some surprising results, brilliant ideas, and beautiful arguments in mathematics, written in his wonderfully lucid style.

Among the many pleasures you will find in this volume are:

* a lovely safe-cracking problem
* a brief discussion of Archimedes circles in the arbelos
* a characterization of Euler's congruent numbers
* a formula for Einstein's triples
* an essay on Cipollas's Pseudoprimes and two characterizations of twin primes

The book is a mathematical entertainment to be read at a leisurely pace. College and advanced high school students should be well equipped to handle the problems presented in the book. The topics are entirely independent and can be read in any order. A useful set of indices helps the reader locate topics in the text.

Ross Honsberger has published thirteen best-selling books with the Mathematical Association of America (eleven in the Dolciani series alone) including: Mathematical Diamonds, Mathematical Chestnuts from Around the World, From Erdцs to Kiev, and Ingenuity in Mathematics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 262

Добавлена в каталог: 04.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$f(2) \geq 3^n$ for a certain function f(x)      1
A 1997 USA Olympiad problem involving radical axes      4
A 1998 Putnam problem in triangle-geometry      4
A certain Diophantine equation in n variables      6
A certain sum of binomial coefficients      2
A chessboard problem concerning black squares      1
A counterfeit coin and an equal-arm balance      9
A curious property of a parabola      5
A difficult recursion      15
A game with piles of matches      9
A locus problem concerning equilateral triangles      8
A nasty integral      6
A note on perfect numbers      4
A prize problem of M. V. Subbarao      6
A problem concerning two incircles of triangles      1
A problem from From Erdos to Kiev revisited      13
A problem from In Polya ’s Footsteps revisited      13
A problem on concurrency      7
A problem on concurrent altitudes      1
A property involving an isosceles right triangle      7
A property of 5 points on a sphere      4
A property of a rectangle in a circle      1
A property of a rectangle with an extended side      7
A property of fans of abutting triangles      17
A property of six points in space      1
A property of the incircle and certain tangents in a triangle      7
A property of the series expansion of $1/(1 — 2x — x^2)$      4
A property of trapezoids      7
A property of two-colorings of six points (in the Appendix)      2
A property related to two angle bisectors in a triangle      7
A safe-cracking problem      13
A special set of rational points on the unit circle      4
A surprising property of a circle      4
Algebraic number      4
An inequality concerning triangles of perimeter 2      4
An observation concerning algebraic numbers      4
Anastasiu, Doru Popescu      6
Andreescu, Titu      1 Challenges
Angles in a polygon      8 9
Another surprise from Leon Bankoff      6
Arbelos      4
Archimedes’ circles      4
Archimedes’ theorem of the broken chord      13
Archimedes’ Theorem of the Broken Chord (in the Appendix)      14
Arithetic mean-geometric mean inequality      1 8
Arithmetic congruence      9
Ashbacher, Charles      6
Asymptotic functions      6
Atanasov, Emanuil      1
Bankoff, Leon      6
Bankoff’s surprise      6
Barbara, Roy      4
Barry, P.D.      5
Berzsenyi, George      11
Binomial coefficients      2
Bipartite graph      4
Bisecting a series      2
Bloom, David      5
Brahmagupta’s theorem      11
Brown, Bud      5
Bruckman, Paul S.      6
Characterizations of Twin primes      18
Chebyshev polynomials      15
Chessboard, (Bishop’s problem)      4 11
Cipolla, Michele      18
Cipolla’s pseudoprimes      18
Circumcenter of a triangle      4 7
Clement, P.A.      18
Concerning cars A, B, C, D on a highway      1
Concurrency      4 7 11
Constructing a perpendicular with a special tool      9
Convex sets      14
Counterfeit coin      9
Cryptography      10
Cuoco, Al      5
De Moivre’s Theorem      2
Diminnie, Charles R.      15
Diophantine equation      4 6
Dodge, Clayton      4
Dubrovsky, Vladimir      11
Eddie      13
Eddie’s problem      13
Edmunds, E. J.      12
Eisenstein triples      5
ellipse      5 14
Equal-arm balance, heaviest stones      9
Euler line      11
Euler’s congruent numbers      5
Evagelopoulos, George      16
Fermat’s equation      6
Fermat’s Simple theorem      18
Fielstad, Paul      5
Finding all k that make $\sin\theta + k \cos\theta = \sqrt{7}$ solvable      8
Finding heaviest of 32 stones with an equal-arm balance      9
Finding terms of a certain sequence that are divisible by 11      4
Fomin, Dimitry      9
Fukagawa, Hidetosi      17
Gebhardt, Robert      10
Gelca, Razvan      Challenges
Graph, time-distance      1
Graph, time-distance of a function      10
Hahn, Liong-shin      8 13 14
Hammer, Peter      5
Helly’s theorem      14
Heron’s formula      5
How to construct a tangent to an ellipse      5
Incenter of a triangle (vector specification)      6
Incircle of a triangle      7 11
Indiameter of a right triangle      6
Induction      9 14 15
Inequality (geometric)      4
Infinite descent      1
Integer solutions of a system of equations      9
integral      6
Intermediate Value Theorem      6
Just, Erwin      4
Kanel, A.      Challenges
Kirichenko, Alexey      9
Knox, Stephen W.      15
Koltchinskii, V.      14
Kovaldzhi, A.      Challenges
Kuiper, Amy      6
Kulanin, E.      11
Kushnir, I.      11 Challenges
Larson, Loren      3
Law of Cosines      4 5 17
Leavitt, W.G.      18
Lehmer, D.H.      6
Mabry, Rick      5
Mathematics without words      5
Maurer, Stephen      10
Mouse-clicking on a $98\times 98$ chessboard      4
Mullin,A.A.      18
Mycielski, Jan      4
Nelsen, Roger B.      5
Novel ways of adding and multiplying geometrically      5
On 2n-gons inscribed in a circle      7
On a certain array of asterisks in a matrix      1
On a certain cryptographic method, base 5      10
On a certain Diophantine equation      4
On a certain equation in two variables      6
On a certain family of intersecting spheres      4
On a certain maximum sum-free subset      16
On a certain quadrilateral in a circle      8
On a certain red-black coloring of the cells of a matrix      4
On a certain regular polygon      7
On a certain star polygon      9
On a certain sum of greatest odd divisors      16
On a certain way of placing 1,2,..., 100 around a circle      9
On a monchromatic similar triangle in a 2-coloring of a plane      15
On a painted $n\times n\times n$ cube      6
On a series that is won by a lead of two games      4
On a set of integers: sum of each five divides their product      9
On an octagon and a square in a circle      4
On Archimedes circles in the arbelos      4
On arithmetic progressions      9
On certain 70-million-digit integers      9
On certain prime numbers and powers of 3      16
On certain subsets of {1, 2,..., n}      4 9
On Eisenstein triples      5
On Euler’s congruent numbers      5
On folding the corners of a quadrilateral      8
On integers x, y, such that $\sqrt{l984} = \sqrt{x} + \sqrt{y}$      10
On lines that bisects both perimeter and area in a triangle      6
On nonintersecting graphs of functions f(x) and g(x)      10
On planting maple, oak, and birch trees      10
On properties of $\tan(3\pi/8)$      8
On reflecting the foot of an altitude in a side of a triangle      7
On removing a member from a certain set of 2n + 1 integers      3
On ten people around a circle      2
On the circumcenter of a certain triangle      7
On the indiameter of a right triangle (in the Appendix)      6
On the locations of points that make certain isosceles triangles      8
On the magnitudes of sums of powers of a desired sequence      8
On the minimum of a certain sequence of surds      8
On the radical axis of two circles (in the Appendix)      4
On the smallest circular cover of a triangle of unit perimeter      14
On the Smarandache functions S(n) and Z(n)      6
On would-be solutions of Fermat’s equation      6
Ordering 1,2,...,100, so neighbors differ by at least 50      9
Orthocenter of a triangle      4
Painted cube      6
parabola      5 Challenges
Pedoe, Dan      17
Perfect number      4
Pernice, Stephen G.      4
Planting trees      10
Polygon      13
Polygon, inscribed      4 7
Polygon, regular      7
Pompeiu      1
Pompeiu’s theorem      1
Prasolov, Viktor      7
Pritsker, Boris      11
Proizvolov, V.      11 Challenges
Proof of Bramagupta’s Theorem (in the Appendix)      1
Proof of Helly’s Theorem      14
Proof that arm/base in a 36°, 72°, 72°-triangle is $\tau$      9
Pseudoprime      18
Quadrilateral      2
Quadrilateral in a circle      8
Quadrilateral, folding corners      8
Rabinowitz, Stanley      12
Radical axis      4 7
Rational points on a circle      4
rectangular array      1 4
Recursion      15
Reflection      7
Ribenboim, Paulo      18
Rotation      7
San Gaku      17
Savchev, Svetoslav      1
Schneider, Leo      2
Schoch, Thomas      4
Segal, Arthur C.      5
Sequence (special)      4 8
Sergusov, I.S.A.      18
Series, expansion      4
Series, expansion, of games      4
Shafaryan, V.      11
Sharygin, I.      Challenges
Shier, Douglas      4
Smarandache functions      6
Spanning tree      4
Special sets of integers      3
Spheres      4
Stenlund, Mikko      5
Stereographic projection      5
Subbarao, M.V.      6
Subbarao’s prize problem      6
subsets      2 4
Sum-free sets      16
Tangent, ellipse      5
Tangent, ellipse, trig function      8
The bishop problem      4
The Euler line and isosceles triangles      1
The last problem on the 1988 IMO      1
The number of spanning trees in a $K_{2,n}$      4
The sum of certain angles in a certain figure      8
The vector specification of the incenter of a triangle      6
To construct a certain segment across a triangle      12
Todd, Arthur      6
trapezoid      2 7 8
Trawalter, Sophie      6
Triangle, equilateral      1 8
Triangle, equilateral, 36°-72°-72°      9
Triangle, equilateral, area-penmeter bisector      11
Triangle, equilateral, isosceles      8 11
Twin primes      18
Two proofs of Heron’s formula      5
Two “mathematics without words”      5
Two-colorings of the plane      1
Two-colorings of the plane and Appendix      15
Vasilyev, N.      Challenges
Velleman, Dan      17
Weiner, Paul A.      4
Wells, David      17
Wetzel, John      4
Wilson’s Theorem      18
Woo, Peter Y.      4
Wu, Rex      Challenges
Yiu, Paul      4
Zuehlke, John      6
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