100 Great Problems of Elementary Mathematics

Heinrich Dörrie

Publisher:

Dover Publications

Publication Date:

1965

Number of Pages:

393

Format:

Paperback

Price:

12.95

ISBN:

0486613488

Category:

General

MAA Review
Table of Contents

We do not plan to review this book.

ARITHMETICAL PROBLEMS
	1.	Archimedes' Problem Bovinum
	2.	The Weight Problem of Bachet de Méziriac
	3.	Newton's Problem of the Fields and Cows
	4.	Berwick's Problem of the Seven Sevens
	5.	Kirkman's Schoolgirl Problem
	6.	The Bernoulli-Euler Problem of the Misaddressed Letters
	7.	Euler's Problem of Polygon Division
	8.	Lucas' Problem of the Married Couples
	9.	Omar Khayyam's Binomial Expansion
	10.	Cauchy's Mean Theorem
	11.	Bernoulli's Per Sum Problem
	12.	The Euler Number
	13.	Newton's Exponential Series
	14.	Nicolaus Macerator's Logarithmic Series
	15.	Newton's Sine and Cosine Series
	16.	André's Derivation of the Secant and Tangent Series
	17.	Gregory's Arc Tangent Series
	18.	Buffon's Needle Problem
	19.	The Fermat-Euler Prime Number Theorem
	20.	The Fermat Equation
	21.	The Fermat-Gauss Impossibility Theorem
	22.	The Quadratic Reciprocity Law
	23.	Gauss' Fundamental Theorem of Algebra
	24.	Sturm's Problem of the Number of Roots
	25.	Abel's Impossibility Theorem
	26.	The Hermite-Lindemann Transcendence Theorem
	PLANIMETRIC PROBLEMS
	27.	Euler's Straight Line
	28.	The Feuerbach Circle
	29.	Castillon's Problem
	30.	Malfatti's Problem
	31.	Monge's Problem
	32.	The Tangency Problem of Apollonius
	33.	Mascheroni's Compass Problem
	34.	Steiner's Straight-edge Problem
	35.	The Delian Cube-doubling Problem
	36.	Trisection of an Angle
	37.	The Regular Heptadecagon
	38.	Archimedes' Determination of the Number Pi
	39.	Fuss' Problem of the Chord-Tangent Quadrilateral
	40.	Annex to a Survey
	41.	Alhazen's Billiard Problem
	PROBLEMS CONCERNING CONIC SECTIONS AND CYCLOIDS
	42.	An Ellipse from Conjugate Radii
	43.	An Ellipse in a Parallelogram
	44.	A Parabola from Four Tangents
	45.	A Parabola from Four Points
	46.	A Hyperbola from Four Points
	47.	Van Schooten's Locus Problem
	48.	Cardan's Spur Wheel Problem
	49.	Newton's Ellipse Problem
	50.	The Poncelet-Brianchon Hyperbola Problem
	51.	A Parabola as Envelope
	52.	The Astroid
	53.	Steiner's Three-pointed Hypocycloid
	54.	The Most Nearly Circular Ellipse Circumscribing a Quadrilateral
	55.	The Curvature of Conic Sections
	56.	Archimedes' Squaring of a Parabola
	57.	Squaring a Hyperbola
	58.	Rectification of a Parabola
	59.	Desargue's Homology Theorem (Theorem of Homologous Triangles)
	60.	Steiner's Double Element Construction
	61.	Pascal's Hexagon Theorem
	62.	Brianchon's Hexagram Theorem
	63.	Desargues' Involution Theorem
	64.	A Conic Section from Five Elements
	65.	A Conic Section and a Straight Line
	66.	A Conic Section and a Point
	STEREOMETRIC PROBLEMS
	67.	Steiner's Division of Space by Planes
	68.	Euler's Tetrahedron Problem
	69.	The Shortest Distance Between Skew Lines
	70.	The Sphere Circumscribing a Tetrahedron
	71.	The Five Regular Solids
	72.	The Square as an Image of a Quadrilateral
	73.	The Pohlke-Schwartz Theorem
	74.	Gauss' Fundamental Theorem of Axonometry
	75.	Hipparchus' Stereographic Projection
	76.	The Mercator Projection
	NAUTICAL AND ASTRONOMICAL PROBLEMS
	77.	The Problem of the Loxodrome
	78.	Determining the Position of a Ship at Sea
	79.	Gauss' Two-Altitude Problem
	80.	Gauss' Three-Altitude Problem
	81.	The Kepler Equation
	82.	Star Setting
	83.	The Problem of the Sundial
	84.	The Shadow Curve
	85.	Solar and Lunar Eclipses
	86.	Sidereal and Synodic Revolution Periods
	87.	Progressive and Retrograde Motion of the Planets
	88.	Lambert's Comet Problem
	EXTREMES
	89.	Steiner's Problem Concerning the Euler Number
	90.	Fagnano's Altitude Base Point Problem
	91.	Fermat's Problem for Torricelli
	92.	Tacking Under a Headwind
	93.	The Honeybee Cell (Problem by Réaumur)
	94.	Regiomontanus' Maximum Problem
	95.	The Maximum Brightness of Venus
	96.	A Comet Inside the Earth's Orbit
	97.	The Problem of the Shortest Twilight
	98.	Steiner's Ellipse Problem
	99.	Steiner's Circle Problem
	100.	Steiner's Sphere Problem
	Index of Names