# Going Slideways

February 13, 2020

When cavemen invented the wheel thousands of years ago, it was probably wood or rock. It probably wasn’t a rubber tire full of air, and they probably didn’t use it to go sledding. That’s called inner tubing: you sit or lie down on a giant donut-shaped balloon, someone gives you a push, and you slide down the snowy, slippery hill. It’s called an “inner” tube because it’s from inside an even bigger circle: a truck tire. Humans first started snow tubing in 1820 in Switzerland, a long time after the cavemen – but a long time before cars and trucks, so where did they get their tubes? More importantly, what happens when you spin as you slide? Lots of math, as you’ll see here!

Wee ones: If your inner tube spins once to the left, then once to the right, then once to the left, then once to the right…which way do you spin next?

Little kids: If you, 3 friends, and 2 snow-loving dogs all pile onto an inner tube, how many riders are there?  Bonus: You can also ride tubes on waterslides. If you go 10 miles an hour on snow but twice as fast in water, how fast do you tube on the water?

Big kids: If you start sliding facing downhill, with the hill’s right side on your right, and as you slide you spin 1/2 turn to your left, then 1/4 of a turn to your right, then 3/4 turn to the left, which way are you facing now?  Bonus: If 1/2 the tubes are double tubes (seating 2 people) and the other 1/2 are single tubes, how many tubes are there if they hold 18 people total?

The sky’s the limit: If your tube spins once around every 2 seconds, your friend spins once every 3 seconds, another friend spins once every 4 seconds, and the last friend spins once every 5 seconds, what’s the soonest you’ll all face forward at the same time if you all started facing forward?