What happens if you dig a hole straight down into the ground? How far until you reach the bottom? That’s what Bedtime Math fan Ajax wants to know. Well, it depends what you mean by “bottom.” Earth is a ball, so if you want to dig to the center of it, it’s 3,958 miles. But if you want to dig all the way through and pop out the other side, it’s twice as far, or 7,916 miles. By the way, the deepest humans have ever dug is just 7 1/2 miles, or less than 1/1000th of the way through! By the way, the cool website FreeMapTools shows you the spot exactly on the other side of Earth from you. Just remember that the center of Earth is a 10,000-degree F blob of metal, so if you do dig down, you’ll need your heat suit.
Wee ones: If you dig 7 miles down, then dig 1 more mile to beat the record, how far do you dig?
Little kids: Which is cooler, 1 thousand degrees or 10 thousand degrees? Bonus: Earth is 7,916 miles across. Close your eyes and see if you can remember that number!
Big kids: Who digs farther, you if you dig down 6 miles a day for 6 days, or your friend who digs 5 miles a day for a whole week? Bonus: If you dig exactly 20 miles every day, by how much will you overshoot the exact middle spot at 3,958?
The sky’s the limit: If you dig 10 miles the first day, 10 miles again the 2nd day, then 20 the 3rd day, then 30, then 50… how many miles do you think you dig the day after that?
Wee ones: 8 miles.
Little kids: 1 thousand degrees. Bonus: 7,916…7,916…see how long you can remember that.
Big kids: You dig farther, at 36 miles vs. your friend’s 35. By the way that happens with any number multiplied by itself (squared): the answer will be 1 more than multiplying that number plus 1 by that number minus 1. Try it! Bonus: Just 2 miles, since 3,960 will be a multiple of 20.
The sky’s the limit: 80 miles. If you noticed the pattern, each day you dig as far as the previous two days added together. It’s the famous Fibonacci series multiplied by 10, where the Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13…
And thank you Ajax for digging into math with us!
Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking before she could walk, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.