Wednesday, September 28, 2011

100 Great Problems of Elementary Mathematics - THEIR HISTORY AND SOLUTION (Heinrich Dorrie)


ARITHMETICAL PROBLEMS

  1. Archimedes' Problema Bovinum
  2. The Weight Problem of Bachet de Meziriac
  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 Power Sum Problem
  12. The Euler Number.
  13. Newton's Exponential Series
  14. Nicolaus Mercator's Logarithmic Series
  15. Newton's Sine and Cosine Series
  16. Andre'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 Transcedence Theorem
PLANIMETRIC PROBLEMS
  1. Euler's Straight Line
  2. The Feuerbach Circle
  3. Castillon's Problem
  4. Malfatti's Problem
  5. Monge's Problem
  6. The Tangency Problem of Apollonius
  7. Macheroni's Compass Problem.
  8. Steiner's Straight-edge Problem
  9. The Deliaii Cube-doubling Problem
  10. Trisection of an Angle
  11. The Regular Heptadecagon
  12. Archimedes' Determination of the Number Pi
  13. Fuss' Problem of the Chord-Tangent Quadrilateral
  14. Annex to a Survey
  15. Alhazen's Billiard Problem
PROBLEMS CONCERNING CONIC SECTIONS AND CYCLOIDS
  1. An Ellipse from Conjugate Radii
  2. An Ellipse in a Parallelogram,
  3. A Parabola from Four Tangents
  4. A Parabola from Four Points.
  5. A Hyperbola from Four Points.
  6. Van Schooten's Locus Problem
  7. Cardan's Spur Wheel Problem.
  8. Newton's Ellipse Problem.
  9. The Poncelet-Brianchon Hyperbola Problem
  10. A Parabola as Envelope
  11. The Astroid
  12. Steiner's Three-pointed Hypocycloid
  13. The Most Nearly Circular Ellipse Circumscribing a Quadrilateral
  14. The Curvature of Conic Sections
  15. Archimedes' Squaring of a Parabola
  16. Squaring a Hyperbola
  17. Rectification of a Parabola
  18. Desargues' Homology Theorem (Theorem of Homologous Triangles)
  19. Steiner's Double Element Construction
  20. Pascal's Hexagon Theorem
  21. Brianchon's Hexagram Theorem
  22. Desargues' Involution Theorem
  23. A Conic Section from Five Elements
  24. A Conic Section and a Straight Line.
  25. A Conic Section and a Point


STEREOMETRIC PROBLEMS
  1. Steiner's Division of Space by Planes
  2. Euler's Tetrahedron Problem
  3. The Shortest Distance Between Skew Lines
  4. The Sphere Circumscribing a Tetrahedron
  5. The Five Regular Solids
  6. The Square as an Image of a Quadrilateral
  7. The Pohlke-Schwartz Theorem
  8. Gauss' Fundamental Theorem of Axonometry
  9. Hipparchus' Stereographic Projection
  10. The Mercator Projection
NAUTICAL AND ASTRONOMICAL PROBLEMS
  1. The Problem of the Loxodrome
  2. Determining the Position of a Ship at Sea
  3. Gauss' Two-Altitude Problem
  4. Gauss' Three-Altitude Problem
  5. The Kepler Equation
  6. Star Setting
  7. The Problem of the Sundial
  8. The Shadow Curve
  9. Solar and Lunar Eclipses
  10. Sidereal and Synodic Revolution Periods
  11. Progressive and Retrograde Motion of Planets
  12. Lambert's Comet Prolem
EXTREMES
  1. Steiner's Problem Concerning the Euler Number.
  2. Fagnano's Altitude Base Point Problem
  3. Fermat's Problem for Torricelli
  4. Tacking Under a Headwind
  5. The Honeybee Cell (Problem by Reaumur)
  6. Regiomontanus' Maximum Problem
  7. The Maximum Brightness of Venus
  8. A Comet Inside the Earth's Orbit
  9. The Problem of the Shortest Twilight
  10. Steiner's Ellipse Problem
  11. Steiner's Circle Problem
  12. Steiner's Sphere Problem 

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