In the Little Mathematics Library series we now come to Remarkable Curves, by a very remarkable author A. I. Markushevich. I am saying that he is remarkable as he has many good books under his sleeve, some of which we may see in the future.
As 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.
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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