Puzzle of the week: why is the sum of the first n odd numbers a perfect square? ➗

# Prove it without a formula Here is this week puzzle for the math circle: **1 + 3 + 5 + ... + (2n − 1) = n²**. 数学不是算,是思考。 Everyone can plug in numbers and see it works. But can you *show why* it must be true? My favorite is the picture proof: each odd number is an **L-shaped layer** you add around a square, and the square just keeps growing. No algebra needed. Drop your proof below — picture, induction, or something I have never seen. Best explanation gets pinned. Let us argue about elegance. 🔥