Acrobats do amazing things. They stand on each other’s shoulders, flip upside down in the air, and somehow jump to the ground without breaking their necks. In this video of the Chinese Youth Olympics, we see 100 acrobats do these crazy feats all together. They dangle from ropes held by hundreds of people on the ground. The acrobats then stack up in a tall pillar, then explode outward and back in like a glowing jellyfish. Even the rope pullers on the ground form beautiful patterns — and with lots of numbers behind them. When you’re helping to hold up 12 people high over your head, you’d better do the math right!
Wee ones: What shapes are made by the rope pullers on the ground? (You can see them in the top right picture.)
Little kids: If there are 5 rings of rope pullers, and 3 of them start swirling to the right while the rest swirl to the left, how many rings swirl left? Bonus: If there are 100 acrobats and 200 MORE rope pullers than that, how many rope pullers are there?
Big kids: If the cone shape has 8 layers with 8 acrobats in each, how many acrobats make those 8 layers? Bonus: If instead they made 6 rings on the ground and each had 10 more pullers than the next ring inside it, how many rope pullers would there be if the smallest ring had 80 people? (Hint for a shortcut: How many would the 3rd and 4th rows add up to…then how many in the 2nd and 5th together…)
The sky’s the limit: If there were 3 acrobats in the 1st layer, 6 in the 2nd, 9 in the 3rd layer and so on, how many layers would you need to stack 360 people?
Wee ones: Circles.
Little kids: 2 rings swirl left. Bonus: 300 rope pullers.
Big kids: 64 people. Bonus: 630 people, since the pair of middle rings (3rd and 4th) adds up to 210, and so do the 2nd and 5th rings, and the 1st and 6th. Alternatively you can add 80+90+100…
The sky’s the limit: For each layer, the total count is 3 times the next “triangle number,” where triangle numbers are those that can be stacked as rows of 1, 2, 3, 4, etc. The triangle numbers are 1, 3, 6, 10…here we instead have 3, 9, 18, 30. So 360 will be 3 times some triangle number, which is 120. Any triangle number is the width of the base times the next integer, divided by 2. 120 is half of 15×16, so you would need 15 layers of acrobats to reach 360.