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. When you have a hundred acrobats doing this at once, it becomes even more mindblowing. That’s what we see in this video of the Chinese Youth Olympics last month. In the opening ceremony, 100 acrobats do the most amazing dance in the sky, dangling from ropes held by hundreds of people on the ground. The acrobats stack themselves into a tall pillar, then explode outward and back in like a glowing jellyfish, then tumble and spin. Even the rope pullers down on the ground form beautiful patterns — and with lots of math in them. When you’re helping to hold up 12 people hanging from their feet — or you’re in the air hoping the rope people hold you up — everyone had 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 6 times as many rope pullers holding them up, how many rope pullers are there?
Big kids: If the cone shape they make 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: 600 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 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.
And thank you Josh W. for sharing this inspiring and incredibly mathematical video!