Mar 17, 2020 | Books, Events |
Image by Karin Henseler from Pixabay
I have long been fascinated by the Fibonacci sequence because it seems to show up everywhere. You might have noticed it, that certain swirl that shows up on things. Here are a few examples:
In An Elf’s Equations, Sagara describes it like this:
Start with 1, then add the previous number to it (in that case, 0), then add the previous number to that number… 1, 1, 2, 3, 5, 8, 13, 21… Sagara could describe this elegantly as an equation: xn= xn-1+ xn-2. Not that anyone else she knew appreciated that elegance. She could draw this as a series of blocks, then draw a line through their intersections to make a spiral, the same spiral on snail shells and flower petals and pine cones, even faces. Taking the ratio between any two consecutive numbers in the sequence and averaging them gave Sagara the Golden Ratio, 1.618034, which could usually be simplified to 1.6. This number appears over and over and over again in nature. Sagara’s mother told her it even determined the shape of great storms and swirls of stars in the sky. –pp. 46-47
I think Sagara does an okay job of describing the Fibonacci sequence, but I know someone else who does a spectacular job of explaining it: Vi Hart. Her Doodling in Math Class YouTube series shows just how much fun math can be, and how much it influences art. She has three videos on the Fibonacci sequence. The first is the simplest, Part 2 gets a little more complicated, and Part 3 is very complicated, so see how much you can challenge yourself! I recommend you watch them several times because Vi Hart talks REALLY fast.
Want to find some spirals yourself? Ordinarily, I’d suggest that you go shopping in the grocery aisle of your supermarket and look for pineapples, artichokes, cauliflower, and stalks of brussels sprouts to try out, but since we’re all avoiding grocery stores, go outside! Pine cones, leaves on stalks, flowers (if they’re up and growing in your part of the world), and even acorn caps all have Fibonacci spirals on them. Can you find them? Can you find other spirally things in your yard?
And if you can’t, try drawing slug cats and flowers and pine cones, or come up with new creatures made out of spirals, Sagara, for example, draws spiral dragons.
Tomorrow, I’ll give you a template so you can build your own model of Thea!
Mar 16, 2020 | Activities, Books |
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.
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:
via GIPHY
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!
Mar 14, 2020 | Books, Events |
At long last, An Elf’s Equations is available for purchase on Amazon.com 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!
Mar 13, 2020 | Uncategorized |
I was going to have a launch party for An Elf’s Equations. It was a private party to celebrate friends and family and fellow writers who helped me produce the toughest novel I’ve ever written. I was planning a reading and games and, of course, pie for Pi Day.
But I live in Cambridge, the epicenter of the coronavirus outbreak in Massachusetts. We started getting reports of people infected, people self-quarantining because they worked in the same building. I realized that, as much as I wanted to celebrate my third novel and thank all the people who helped me create it, I didn’t want to put them at risk. And the whole prospect was causing me and my family undue stress. So I cancelled the party, about the same time that the NBA was cancelling the season, and Harvard was telling students not to come back after spring break.
I thought, Fine, I’ll have a Facebook party instead. With the help of a self-quarantined friend over Skype, I came up with a schedule for all the fun things I’d do. And then all the public schools started closing, including the ones my children attend. Today was their last day of class for the next two weeks at least. My teenager reports that none of her teachers came to school today, so she came home early. Now, I’m scrambling to plan out what to do with them for the next two weeks so that we don’t all go completely stir-crazy.
Ah! I thought. Other parents are in the same boat. So rather than concentrating all my activities tomorrow, I think I’ll try to post a new activity every day, something fun and interesting connected to An Elf’s Equations that kids can do while stuck at home. I won’t promise to keep to a daily schedule because who knows what will happen? But I’ll do a live reading around 2pm tomorrow, March 14, 2020, and starting Monday, I’ll do my best to post something every day around 11am. Stay tuned here and on Facebook for whatever surprises I can come up with.
Honestly, when I was twelve, being stuck at home for two weeks would have meant a paradise of reading and rereading all my books, over and over. Of course, there was no Internet, no livestreaming, no cell phones, no VCR even! We had six or seven measly TV channels and a bunch of classic board games, and books. Lots of books. Y’know what? I think they’re just as good today. I hope that those of you who’ve bought An Elf’s Equations enjoy it as we drift down the surreal river of social distancing. And if you haven’t bought it yet, this is the perfect time to acquire a new book.
Be well, stay safe, and read.
Dec 10, 2019 | Cooking |
Because it’s Tuesday.
Oct 15, 2019 | Uncategorized |
At long last, An Elf’s Equations is done, and today Dreaming Robot Press launched the Kickstarter campaign. I’m delighted and a little surprised. After all the hard work of making this book, which seemed to take forever, the Kickstarter took flight with head-spinning efficiency. And as of this writing, about six hours after launch, the project is already 24% funded! THANK YOU!!!
An Elf’s Equations is the third novel in my Enchanted Kitchen series and focuses on Sagara, a thirteen-year-old from a high-ranking elf family who is obsessed with math but despises the arbitrary and sometimes cruel rules of her society. However, when her friend Thea, a rare sentient tree called a dodonas and also just a baby, is kidnapped and taken to the nearby Realm of Vanaheim, Sagara finds that she must use all the etiquette her grandmother has been stuffing into her to negotiate with the god-like Vanir, the warring Frost Giants, and even stranger creatures. But rest assured, her math skills also come in handy!
As in A Witch’s Kitchen and A Pixie’s Promise, I’ve put in lots of scrumptious food, including a Viking-inspired feast and a gingerbread house. New in this installment is a bunch of math and logic puzzles that I hope with both challenge and delight you.
In the next few weeks, I’ll talk about some of my inspiration for Sagara and the Realm of Vanaheim, as well as some of the challenges I ran into when writing this book. Please feel free to ask questions in the comments or on my Facebook page.
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