Copilot Certainly! In Scratch, you can approximate the value of π (pi) using various methods. Let’s explore a couple of approaches: Gregory-Leibniz Series: The Gregory-Leibniz series is a simple method to calculate π. It involves an infinite series: ? = 4 − 4 3 + 4 5 − 4 7 + 4 9 − 4 11 + … π=4−34+54−74+94−114+… Here’s how you can implement it in Scratch: when green flag clicked set [pi v] to (4) set [Refreshes v] to (1) forever change [Refreshes v] by (2) set [pi v] to ((pi) - ((4) / (Refreshes))) change [Refreshes v] by (2) set [pi v] to ((pi) + ((4) / (Refreshes))) end This script continuously updates the variable pi to get closer to the actual value of π. Nilakantha Series: The Nilakantha series converges to π faster than the Gregory-Leibniz series: ? = 3 + 4 2 ⋅ 3 ⋅ 4 − 4 4 ⋅ 5 ⋅ 6 + 4 6 ⋅ 7 ⋅ 8 − 4 8 ⋅ 9 ⋅ 10 + … π=3+2⋅3⋅44−4⋅5⋅64+6⋅7⋅84−8⋅9⋅104+… Here’s how you can implement it in Scratch: when gf clicked set [pi v] to (3) set [Refreshes v] to (2) forever set [pi v] to ((pi) + ((4) / ((Refreshes) * (((Refreshes) + (1)) * ((Refreshes) + (2)))))) change [Refreshes v] by (2) set [pi v] to ((pi) - ((4) / ((Refreshes) * (((Refreshes) + (1)) * ((Refreshes) + (2)))))) change [Refreshes v] by (2) end This method converges more quickly but involves more complex calculations. Remember that these approximations won’t give you the exact value of π, but they provide sufficient precision for most projects in Scratch. Feel free to experiment and explore other methods! ??
