November 23, 2020

One of the most fun things about numbers is the patterns they make. You can say, “OK, my pattern is 1, 4, 7, 10…” and then your friend can guess the next number is 13 because you keep adding 3. Or you can say “1, 3, 9, 27…” what’s next? One of the most interesting patterns out there is the Fibonacci series: you start with 0,1, and each number is always the last two numbers added together, So 0+1 gives us 1, and then 1+1 is 2. Then you add 1+2 to get 3. Then 2+3 makes 5. Then you get 8, 13, 21, 34…and so on. That’s why today is Fibonacci Day, because the date is 11/23 (1-1-2-3). We celebrate Fibonacci numbers because lots of objects in nature grow in shapes driven by them. Snail shells spiral around these numbers, as you see in this picture, and the seeds in the middle of a sunflower, and even the hair on your head! As we’ll see, today isn’t the only good day to celebrate these cool numbers.

*Wee ones:* Can you remember the set of numbers 1, 1, 2, 3, 5, 8? See if you can say it back!

*Little kids:* Which is bigger, the jump from 3 to 5, or the jump from 5 to 8? *Bonus:* What’s the next number in this pattern: 1, 3, 5, 7, 9…?

*Big kids:* What’s the next Fibonacci number after 34? *Bonus:* For any Fibonacci number from 3 onward, which is bigger, 2 times that number, or the next Fibonacci number?

*The sky’s the limit:* If we look at just the single-digit Fibonacci numbers, how many dates this year had some set of consecutive Fibonacci numbers in the right order? (Just look at month and day, and in that order.)

Answers:

*Wee ones:* Try to repeat 1, 1, 2, 3, 5, 8!

*Little kids:* The jump from 5 to 8. The jumps keep getting bigger. *Bonus:* 11, because you’re adding 2.

*Big kids:* 55. *Bonus:* Doubling a Fibonacci number will always give you a bigger number than the next Fibonacci number. Since each number is added to the one before it to make the next one, and since the one before it is always smaller, your new number can’t be fully double the most recent number. 5 has to get added to 3 to make 8, so that’s less than 2×5 (10). And 8 has to get added to 5 to make 13, which is less than 16. As the numbers get really big, each number is about 1.6 times the previous number.

*The sky’s the limit:* 10 dates: 1/1, 1/2, 1/12, 1/23, 2/3, 3/5, 5/8, 11/2, 11/23, and 12/3. By the way, in the year 2058 we’ll get to have the awesome date 11/23/58!

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