Our elementary school recently had a book fair. I purchased three books, and I’d like to tell you a little bit about each of them.

*Optical Illusions* by Gianni A. Sarcone and Marie-Jo Waeber will make a nice addition to my other books on optical illusions. This one is special not only because it has a moveable design on the front cover, but also because it includes instructions on how kids or adults can make their own optical illusions. Mathematics and art often both play a part when an optical illusion is created. There is so much information in this book that I haven’t read it completely yet, but I like what I’ve read so far.

*When Sophie Thinks She Can’t* by Molly Bang brings up several subjects including math anxiety, bullying, and growth mindset. It also introduces tangram puzzles and making rectangles from 12 squares. Anytime you feel inclined to say, “I can’t!” add the very important word, “yet.” I like this book a lot and read it to a class of 5th graders right before I introduced them to the Find the Factors puzzles. (As I handed out the puzzles, one student with a sense of humor called out, “I can’t do these puzzles.” I smiled and said, “That was a good one,” and then proceeded to make sure every kid in the class could at least do the first few levels of the puzzle.)

*All Year Round* by Susan B. Katz with cute pictures by Eiko Ojala. This book uses appealing rhymes to intertwine two important early mathematical concepts: the calendar and simple geometric shapes. Some of the shapes even introduce concepts in solid geometry.

At first, I didn’t buy this book because a few things disappointed me:

- It seems to imply that flowers with four round petals are shaped like a square. (The flowers are in a square box, but the focus in on the flowers, not the box.)
- Baseball diamonds are actually squares. Turning it on its corner does not change it from a square to a diamond, or rhombus, as it is called in mathematics. (I decided to forgive this because every square is technically a rhombus even though not every rhombus is a square. And besides, a baseball playing field really is called a baseball diamond.)
- Unless you cut off the rounded top of a slice of pumpkin pie, you won’t really have a triangle shape; you will have a sector. Yes, sectors look a lot like triangles, but they are not triangles.

However, after going home and thinking about it, I decided that these complaints can be good conversation starters so I went back to the book fair and bought the book. Besides, commonly-used shape names do not necessarily match correct geometric terms. I have read this book to one of my granddaughters, and we enjoyed reading and seeing how the world changes over a calendar year and identifying the simple shapes in the illustrations.

Since this is my 1071st post, I’ll share some facts about the number 1071:

- 1071 is a composite number.
- Prime factorization: 1071 = 3 × 3 × 7 × 17, which can be written 1071 = 3² × 7 × 17
- The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 1071 has exactly 12 factors.
- Factors of 1071: 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071
- Factor pairs: 1071 = 1 × 1071, 3 × 357, 7 × 153, 9 × 119, 17 × 63, or 21 × 51,
- Taking the factor pair with the largest square number factor, we get √1071 = (√9)(√119) = 3√119 ≈ 32.72614

1071 is the hypotenuse of a Pythagorean triple:

504-945-1071 which is (8-15-**17**) times **63**

OEIS.org informs us that 6³ + 7³ + 8³ = 1071, making 1071 the sum of three consecutive cubes.

1071 is consecutive digits 567 in BASE 14 because 5(14²) + 6(14) + 7(1) = 1071