Decorate Your Room like Sagara’s Room

Hello, everyone! I hope you’re all finding interesting and fun things to do while practicing social distancing. This week, I’m going to be posting activities for you to do while you’re home. Today’s theme is Sagara’s bedroom, which is decorated with MATH. Here’s an excerpt from An Elf’s Equations:

Sagara turned and ran lightly along a branch as broad as the Path by Millie’s house until she reached her bedroom. Pulling aside a curtain of cultivated ivy, Sagara touched a smooth river stone set in a niche beside the door, and it began to glow with soft, golden light. She entered a room made entirely of living woven branches, much like the classrooms in Master Quercius’s branches at the Enchanted Forest School. This room was much smaller and private, decorated with mathematical constructs: fractal patterns, the Fibonacci spiral, graphs and diagrams. A long strip of paper circled the leafy ceiling with the first two hundred digits of pi. — p. 31

What the heck is all this stuff? Well, here are some brief explanations of what they are and why Sagara thinks they’re cool.

A representation of the number pi

Pi Goes On Forever

Pi is a strange and unusual number. It’s the number we’ve discovered that describes round things: circles, balls, even the orbits of planets (if the orbits were perfect). Draw a circle and put a dot in the exact center of the circle, then draw a line straight through that dot from one side of the circle to the other. We call that line the diameter. Now put a dot anywhere on the circle. The length of the circle if you go all the way around it is called the circumference. So if you have a piece of string, and you make a circle out of it, the length of the string is the circumference. If you measure the circumference and the diameter very carefully, you can find pi.

For example, let’s say you have a string that’s a foot long. If you make a circle out of it and measure its diameter, you’ll find that it’s a little under four inches, about 3.8 inches. Now, divide 12 inches by 3.8 inches. You can use a calculator, it’s okay. You’ll get a number with a lot of digits after it: 3.157847368 is what my calculator says. That’s pretty close to pi, but not exact because we didn’t measure the radius exactly enough. If you measure it really, really carefully, it’s more like 3.14159. Here’s a little video of how that works:


Many, many digits of pi. Image by Andrew Martin from Pixabay

Now here’s the really cool thing. If you could measure the diameter and the circumference absolutely perfectly, the digits would go on forever. What’s more, they never repeat. Mathematicians call this a transcendental number. They have calculated millions of digits of pi, and they still haven’t found the end. Sagara loves this. She loves thinking about the fact that it goes on and on and on forever. So she glued together pieces of paper and copied out as many digits as she could and put them up all around her room. You can do that, too! How many digits of pi can you write out?

A Mobius Strip has Only One Side

Take a piece of paper. Cut it into three strips and tape or glue them into one long strip. Now give the strip one twist and tape the ends together. Here are some good step-by-step instructions. Now, put a dot in the middle of the strip, anywhere, and start drawing a line down the middle of the strip. Keep going. Eventually, you’ll reach the dot again. HOW IS THAT POSSIBLE???

It’s possible because a Mobius strip actually only has one side. That twist you put in the loop means that you connected on side of the paper to the other, making an infinite loop. Sagara thinks this is better than magic, and she has little mobius strips dangling from the branches of her room. When she gets bored, she takes one down, draws that line, and then cuts along the line to see what happens. Try it! I guarantee you’ll be surprised.

Fractals Can Be Infinite

Fractals are repeating patterns that appear in nature. Be warned! Once you start seeing them, you can’t stop.

Here’s a simple example of a fractal. Draw an equilateral triangle – that’s a triangle whose sides are all the same length and whose angles are all the same 60 degrees. Now, draw another, upside down triangle inside that triangle, with each of its points at the middle of the larger triangle’s sides. Suddenly, you have four triangles. Do that again. And again. And again.

via the Boston University Math page on Serpinski Triangles

If you had a big enough triangle, or a good enough magnifying glass, you could keep on doing this forever. The triangle doesn’t even have to be equilateral. Try drawing some triangles of different sizes and see if you can keep dividing them up the same way.

Tangrams: Many Pictures from the Same Shapes

Sagara loves turning things around and seeing them in new and surprising ways. Tangrams are images that you make from a small set of shapes. By courtesy of my friend Rebecca Rapoport, co-author of Math Games Lab for Kids, you can download and print the basic tangrams set and many different tangrams shapes to make (there are some other cool math downloads on that page, too). I recommend coloring the pieces for the tangrams many different colors, then seeing how the colors fit into the shapes. Sagara enjoys trying to create new shapes for herself and has several unique creations posted around her room.

As for Fibonacci spirals, we’ll get to that tomorrow. Happy mathing!

My Book Birthday is Pi Day!

Screenshot of video of Dianna Sanchez reading from An Elf's Equations

At long last, An Elf’s Equations is available for purchase on and available for order at your local bookseller! Today is also Pi Day (3.14), so to celebrate both, I read from the book live on Facebook. You can also watch me read from Chapter 1 here.

As I discussed in my previous post, I’m going to start providing activities related to An Elf’s Equations on Monday and every weekday at 11am EDT while schools are closed for the next two weeks. Here’s my schedule of activities for next week:

Monday, March 16: Decorate your room like Sagara’s room! Sagara loves math, and her room is decorated with all kinds of fun math puzzles and diagrams. Check this blog for downloadable activities.

Tuesday, March 17: Fun with Fibonacci! Draw your own Fibonacci spiral, watch videos about how the spiral is used in art, and go find Fibonacci spirals in nature.

Wednesday, March 18: Make your own Thea with downloadable patterns. Recipe for something chocolate.

Thursday, March 19: Secret message! Use a code to find a message hidden in An Elf’s Equations.

Friday, March 20: Live Question and Answer session. I’ll answer questions asked in the comments on Facebook.

So check back here on Monday at 11am EDT for more fun stuff!

A Witch’s Kitchen is On Sale Right Now!


The algorithm gnomes at have worked their mysterious magic, and right now, A Witch’s Kitchen is just $6.93! So if you are looking for presents to ship to family and friends for Hannukah/Christmas/the sheer joy of it, now is an opportune moment. (You could also get a copy for yourself.) I have no idea how long this will last, so act quickly!

If you prefer to buy your books at a bookstore, I’ll be at the Barnes & Noble in Peabody, MA on December 10, 2018 from 6:30 – 8:30pm to benefit The Room to Write in Wakefield. Many other wonderful local authors will also be there, and what a great opportunity to do some holiday shopping while helping out a great organization that supports local writers.

A Pixie’s Promise is now available!!!

Copies of A Pixie's Promise in shipping box

They’re here and ready for you to read! At long last, A Pixie’s Promise is available for purchase on Amazon (eBook only until Amazon gets their act in gear), Barnes and Noble, and IndiePub. The eBook is also available on Kobo and iTunes. I recommend that you support your local independent bookstore, where you can order a copy through Ingram. My two favorite bookstores in the Boston area are Porter Square Books and Pandemonium Books and Games, both in Cambridge.

If you’d like a signed copy, my book launch party is at Porter Square Books on November 6th, 7-9pm. That’s right, Election Night, so please vote early and then come hang out and eat cupcakes with me!

Thanks to everyone who helped make this book possible, from my critique group partners to my young beta readers to Dreaming Robot Press, my magnificent publishers. And thanks to my awesome family, who inspire me and put up with all my writing shenanigans. I couldn’t have done it without all of you.

Kickstarter has Funded!!!

Thank you!

Thanks to all our supporters for making my next novel possible. You all rock! And thanks especially to Corie and Sean Weaver of Dreaming Robot Press who ran the campaign, and to Bill Wolfe, my co-campaigner. You are the magic.

Stay tuned for more publishing info! The launch party for A Pixie’s Promise is scheduled for September 21st, 7pm, at Porter Square Books in Cambridge.

Cooking is Magic, Part 6: Play with Your Food

Children view robot birthday cake

Robot cake I made for Nora’s third birthday party, with working sugar cookie gears

Writing a novel can be long, grueling work. It took me two years and two months to complete my first novel. The second came in at just under a year, and it looks like the third will be more like six months, so I seem to be getting better at it. Still, it’s sometimes disheartening to pour months of work into something that people will read in a day or two. Sort of like spending hours on cooking a really good meal that your kids then inhale in ten minutes, fifteen if my teenager goes back for seconds.

So why do it at all? Simple: because it’s FUN.

Cooking your own meals and desserts means you have total creative control to do anything and everything you like. Your three-year-old wants a robot birthday cake with moving gears? Sure! Your ten-year-old is obsessed with dragons? Make a cupcake tower with dragon cookies perched on them. Launching your first novel? Make a cake that looks just like your book! I love cooking and baking challenges, and my children do, too. One of my great parenting joys is helping them to realize their own crazy ideas in chocolate and candy and fondant.

And yet… cooking is limited to the available ingredients. In writing, anything is possible. I can create a character who grew up on Mars and needs an exoskeleton to visit Earth, or a frog prince obsessed with baseball, or a village where everyone is a monster, but they’ll never admit it. Right now, I’m writing about a thirteen-year-old elf girl fascinated by math and programming who’s been roped into helping rescue a magical, sentient baby tree who’s been kidnapped by someone who basically thinks he’s a Norse god, all because the elf girl’s grandmother has a secret agenda. Whaaaaat? How does that even make sense?

Well, it makes about as much sense as making candy sushi or books out of marshmallows and graham crackers. And you know what, I love every crazy second of it, even when my plot goes sideways and I have to spend ages revising. i love creating whole worlds and the fascinating people in them who live and strive and fail and pick themselves up and keep on going. It was inevitable, i think, that I’d end up writing about a young witch with a flair for magical baking. And I love that I get to share these stories, not just with my friends and family, but with everyone, everywhere.

For some examples of the crazy, fun, wild things I’ve made, please visit my Facebook page. And for more about that young witch and her friend, the pixie who discovers she has more of a knack for magic than she ever imagined, preorder A Pixie’s Promise before the Kickstarter ends in just a few scant hours. Otherwise, you’ll have to wait until it comes out in September.