Angle gives direction
The waggle angle maps food direction relative to the Sun.
Biology
A bee finds flowers two kilometers away, returns to the hive, and tells thousands of sisters where they are. Using dance.
Honeybees communicate food location with a waggle dance: direction is encoded by the angle of the waggle run relative to vertical, and distance is encoded by how long the waggle lasts.

Angle gives direction
The waggle angle maps food direction relative to the Sun.
Duration gives distance
Longer waggles mean farther food sources.
Clouds are not fatal
Bees can infer Sun position from polarized sky light.
Nearby food uses round dance
Close sources trigger a simpler dance.
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