Remarkable Curves (Little Mathematics Library)
Remarkable Curves by A. I. Markushevich in Little Mathematics LibraryAs
the title suggests the books takes the reader through various curves
and how they can be materialised, just have a look at the table of
contents below. The preface of the book says:This
book has been written mainly for high school students, but it will also
be helpful to anyone studying on their own whose mathematical education
is confined to high school mathematics. The book is based on a lecture I
gave to Moscow schoolchildren of grades 7 and 8 (13 and 14 years old).In
preparing the lecture for publication I expanded the material,while at
the same time trying not to make the treatment any less accessible. The
most substantial addition is Section 13 on the ellipse, hyperbola and
parabola viewed as conic sections.For the sake of brevity most of the results on curves are given with- out proof, although in many cases their proofs could have been given in a form that readers could understand.The third Russian edition is enlarged by including the results on Pascal's and Brianchon's theorems (on inscribed and circumscribed hexagons), the spiral of Archimedes, the catenary, the logarithmic spiral and the involute of a circle.The book was translated from the Russian by Yu. A. Zdorovov and was first published by Mir in 1980.The table of contents is as below:Preface to the Third Russian Edition 1. The Path Traced Out by a Moving Point 2. The Straight Line and the Circle 3. The Ellipse 4. The Foci of an Ellipse 5. The Ellipse is a Flattened Circle 6. Ellipses in Everyday Life and in Nature 7. The Parabola 8. The Parabolic Mirror 9. The Flight of a Stone and a Projectile 10. The Hyperbola 11. The Axes and Asymptotes of the Hyperbola 12. The Equilateral Hyperbola 13. Conic Sections 14. Pascal's Theorem 15. Brianchon's Theorem 16. The Lemniscate of Bernoulli 17. The Lemniscate with Two Foci 18. The Lemniscate with Arbitrary Number of Foci 19. The Cycloid 20. The Curve of Fastest Descent 21. The Spiral of Archimedes 22. Two Problems of Archimedes 23. The Chain of Galilei 24. The Catenary 25. The Graph of the Exponential Function 26. Choosing the Length of the Chain 27. And What if the Length is Different? 28. All Catenarics are Similar 29. The Logarithmic Spiral 30. The Involute of a Circle Conclusion
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