the.com/graduation cap

A flat square that says you survived, thrown skyward like proof you're finally free.

means The flat, square-topped academic hat worn at graduation ceremonies, traditionally tossed in the air once the diplomas are handed out.

from Properly called a mortarboard, the cap takes its name from the flat board a bricklayer uses to hold mortar — the resemblance of that square, flat slab is unmistakable. The academic version descends from medieval scholarly headgear; the soft caps worn by clergy and university men gradually stiffened into the rigid square we know. The tassel and the stylized name 'mortarboard' both took hold in the 19th century, by which point the cap had become firmly tied to scholarship and the rituals of the gown-wearing classes.

Proper name
It's called a mortarboard, after the bricklayer's tool.
Tassel logic
Moving it left-to-right signals you've officially graduated.
Oxford origin
Square caps date back to medieval European universities.
Cap toss risk
Sharp corners have actually injured people at ceremonies.
Decoration craze
Decorating the flat top is now a viral tradition.
for instance

mortarboard — academic headwear worn at university commencement ceremonies since the 16th century oxford and cambridge

biretta — catholic clergy square cap used in formal academic and religious processions

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