Formulating definitions is an important part of creating mathematics. The definition you choose has implications for how you sort examples and non-examples of a particular term. The mathematical term *trapezoid* is a well-known (and often debated) example of this choice. Here are two definitions of trapezoid.

**Definition 1:** A trapezoid is a quadrilateral with *exactly* one pair of parallel sides.

**Definition 2:** A trapezoid is a quadrilateral with at *least one* pair of parallel sides.

If you are using definition 1, a rectangle (see rectangle ABCD shown below) is *not *a trapezoid because it has two pairs of parallel sides ( sides AB and DC are parallel as are sides BC and AD. Sorry about the bad notation, ie., segments over AB, DC, stilling learning learn how to insert equations in wordpress.).

For many, a rectangle doesn’t fit their image of what a trapezoid should be. But if you are using definition 2, rectangle ABCD is a trapezoid. For more about why anyone would choose definition 2 over definition 1, go here.

While there are many un-magical math books, I promise that are many magical ones to be found. Before I share examples of magical math books, I’ll describe my process for formulating a definition for a *magical math book*.

First, I recalled the math books I’ve read as a student, teacher, and parent. I use the term *math book* to refer to picture books with explicit mathematical themes, math problem-solving books, math textbooks, and any other math-focused book on the market (electronic formats included).

Using my intuitive sense of what magic is to me, I separated these books into two categories: magical and un-magical. [You may want to do this for yourself. If you do, I’d love to hear about your magical booklists and/or your thoughts about this process in the comments.] With my magical math booklist in hand, I made a list of qualities I felt these books shared.

Next, I searched dictionary definitions of magic and used these to formulate a definition of magic that aligned best with the qualities of my magical math booklist books. Below is the definition of magic that I chose.

*Magic:** A quality that inspires wonder, excitement, and delight.*

However, once I came up with this definition, I felt something was missing. I have read math books that are good, but on a first read through, I don’t feel much wonder, excitement, and/or delight. Then I read them to my children or my friend’s children and something magical happens. This has been particularly true of math picture books. Thus, I have found that the search for math book magic should be a joint one. Here is the complete definition of a *magical math book* that I will use to sort math books for this blog.

**Magical math book:** A math book that inspires wonder, excitement, and/or delight for both reader and listener.

There. Done. A definition. Now we can move on to the fun stuff.

Magical moments aren’t easily explained with words. I will try my best through the blog posts to share the magic that particular math books inspire. I realize that what is magical to one person may not be magical to another. However, my hope is that this blog will inspire others to find and share their ideas about magical math books. In the [revised] words of the magical children’s book writer and poet Jane Yolen, my hope is that blog readers will “__Touch [math book] magic…pass it on__.”

Have you already read a math book that inspires wonder, excitement, and/or delight for both reader and listener? Connect on twitter @KellyDarkeMath and use the hashtag #mathbookmagic to share and/or share through process described in the *Shared Booklist* .

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