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If I understand you correctly, you are saying that a bird flying in the sky does not have a shadow. If this is the case, it is not true. Birds do have shadows. I have noticed shadows of birds flying overhead, like a hawk, for example.

I believe, that for small birds, the shadows are probably so small we just don't notice them.

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Q: How can you prove mathematically not formation of shadow of bird flying in the sky?
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