Welcome to the First π Day Activity
from 2025 March 10th to 14th!

In this activity, you will be given 3 brilliant circle-related questions, and the top three participants providing the most brilliant explanations will be awarded the textbooks, reading notes, and lecture handouts that Guanzhong Yang organized!
If you are interested in this activity, email to [email protected] to join it!

Q1 ★★★☆☆
With the help of graphs, try to prove that 3 < π < 4.
HINT: consider the derivation and definition of π.

Q2 ★★★★☆
Suppose there is a person, with 2m high, standing on the surface of the Earth, with 6000km radius. Given that the beams of sunlight are parallel, what is the largest length of the shadow of that human?
HINT: earth is a circle.

Q3 ★★★★★
A clock has 12 portions, and each portion is either blue or red. Totally there are 6 blue portions and 6 red portions. Prove that there exists a line which can divide the clock into two half parts, with each part has 3 blue portions and 3 red portions.
HINT: try to rotate it by yourself at first.

Wish You Have Fun with π and Circle!