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My daughter is in 6th grade. She likes mathematics, i.e., she likes to learn mathematics at school, is also good at what she has learned at school and is rather quick at picking new things. However, she is currently only limited to text books, which I feel are not inspirational, and don't make you fall in love with mathematics. I am looking for some books that may do exactly this for her age group. (i.e., it should be fun to read while showing the real beauty of mathematics.)

For example, topics like the golden ratio, and symmetry are simple enough and fun to explain, but at the same time can be used to show how mathematics is all around us or to show even beauty can be to some extent quantified.

I have looked at some other questions, some are really for kids who are too young, or adults. (Books in German or with German translation are a plus).

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For your particular case, I highly recommend "The Joy of X" by Dr. Steven Strogatz.

And although you didn't request it, for higher level students and adults I also recommend "Mathematics for Non-Mathematicians" by Morris Kline which serves a similar purpose of opening the world of mathematics to a much broader audience and without the feel of a textbook, which it isn't.

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If you looked at those other topics, you saw the links to the books page at my blog, Math Mama Writes. There are a number of books there that would work for a teen. One of my favorites is Carry On, Mr. Bowditch, by Jean Lee Latham, the (slightly fictionalized) biography of Nathaniel Bowditch, who modernized navigation in the 1700s. But maybe that has too many U.S. connections.

The Man Who Counted, by Malba Tahan, is full of mathematical puzzles in the delightful short stories told.

How to Count Like a Martian, by Glory St. John, deals with different number systems in a delightful way.

Another favorite is Math Girls, by Hiroshi Yuki, though the math in it gets pretty hard. It reminds me of anime or manga. The characters are a bunch of high school students. The narrator is a boy who admires a number of girls who share his joy in math.

In Code, by Sarah Flannery, tells of her own experiences getting involved with math. I would have really liked it at your daughter's age. (But then, I'd have liked all of these.)

When picking books for a teen, it helps to know their other interests. If you want to edit the question to include that, I might think of other books.

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    $\begingroup$ Nice answer, and a nice blog as well. $\endgroup$ – John Coleman Jun 6 '17 at 19:52
  • $\begingroup$ Thanks for the response. To add to the original post, she is particularly interested in geometry. $\endgroup$ – user2219907 Jun 7 '17 at 8:21
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"(Books in German or with German translation are a plus)" and "she is particularly interested in geometry."

The OP's notes suggest:

Ziegler, Günter M. Do I Count?: Stories from Mathematics. CRC Press, 2013. CRC link.


                 
Ziegler, Günter M.: Darf ich Zahlen? Geschichten aus der Mathematik. Piper, München, 2014. Taschenbuchausgabe, 3. Auflage.

This is originally in German and now translated to English. Günter's specialty is discrete geometry. His stories and short, easy to read, entertaining, and often dwell on what it means to really do mathematics. I thoroughly enjoyed it myself.

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    $\begingroup$ Exciting. I just bought a copy. $\endgroup$ – Sue VanHattum Jun 7 '17 at 21:40
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Men of Mathematics by Eric Temple Bell

https://en.wikipedia.org/wiki/Men_of_Mathematics

(Note for PC police, there is a woman in the "Men".)

Book is not 100% historically accurate. But too much is made of the minor dramatizations by critics. Book motivated many young students into math or sciences. Comes up a lot on famous scientist reading lists while young (that and Microbe Hunters).

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