The title is a word analogy puzzle. The plots below are hints. In each pair, the black curve is the same.

### Arctangent

### Exponential function

### Sine function

### x^{4}

Answer: boa constrictor digesting an elephant.

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# Real line : Complex plane :: Hat : ?

### Arctangent

### Exponential function

### Sine function

### x^{4}

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3 thoughts on “Real line : Complex plane :: Hat : ?”

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The title is a word analogy puzzle. The plots below are hints. In each pair, the black curve is the same.

Answer: boa constrictor digesting an elephant.

“A picture is worth a thousand words”, but in this case it’s not true.

It would be essential to mention that each surface is the graph of the real part of the corresponding complex function.

I guess it is not obvious to me what the analytic continuation of the “hat graph” should be, but I did like the Little Prince reference.

My analysis prof sketched this on the board when I was an undergrad: imgur dot com slash eF6OzCc. I was the only person in the classroom chuckling.