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What do you think was going through the minds of the group of astronomers and mathematicians that came up with the idea of the unit circle?

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    Complex thoughts. – 2017-02-04
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    "Oh my goodness, why has it taken us so long to think of this wonderful idea?" – 2017-02-04
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    Maybe they thought "hmmm this could make calculus a lot easier". – 2017-02-06

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"What will we call a circle whose radius is one unit? It sure comes up a lot in models and calculations."

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    "I say we table the discussion." "Geez, Galahad, enough with the Table." – 2017-02-04
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We happened to have a thing called trigonometry, and since all similar triangles have the same trig functions, we decided to call the hypotenuse one unit for simplicity, hence:

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One could also note that the unit circle plays a major role in complex numbers, since we have Euler's formula for complex exponentiation.

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    I think your signature is what was going through their minds when they thought of this idea: "Wow, simply beautiful art!" – 2017-02-04
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    @DavidK :D Thanks! Or, well, not sure if that comment was meant for me or the dead, but I'll take it! – 2017-02-04