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basic_tools:eulers_formula

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 basic_tools:eulers_formula [2021/05/15 18:01]boldstonegoson basic_tools:eulers_formula [2021/05/15 18:11] (current)boldstonegoson Both sides previous revision Previous revision 2021/05/15 18:11 boldstonegoson 2021/05/15 18:09 boldstonegoson 2021/05/15 18:04 boldstonegoson [Beauty] 2021/05/15 18:01 boldstonegoson 2021/04/18 11:05 cleonis Added demonstration that Euler's formula follows from the Taylor series expansions2020/04/02 13:44 2018/04/16 07:50 jakobadmin ↷ Page moved from basic_notions:eulers_formula to basic_tools:eulers_formula2018/03/28 13:24 jakobadmin 2017/12/16 13:25 jakobadmin [Student] 2017/12/16 12:58 jakobadmin created Next revision Previous revision 2021/05/15 18:11 boldstonegoson 2021/05/15 18:09 boldstonegoson 2021/05/15 18:04 boldstonegoson [Beauty] 2021/05/15 18:01 boldstonegoson 2021/04/18 11:05 cleonis Added demonstration that Euler's formula follows from the Taylor series expansions2020/04/02 13:44 2018/04/16 07:50 jakobadmin ↷ Page moved from basic_notions:eulers_formula to basic_tools:eulers_formula2018/03/28 13:24 jakobadmin 2017/12/16 13:25 jakobadmin [Student] 2017/12/16 12:58 jakobadmin created Line 95: Line 95: This shows a deep relationship between the exponential function, the [[basic_tools:​imaginary_numbers|imaginary unit]] $i$ and $\pi$. (Pi is the ratio between circumference and diameter shared by all circles.) This shows a deep relationship between the exponential function, the [[basic_tools:​imaginary_numbers|imaginary unit]] $i$ and $\pi$. (Pi is the ratio between circumference and diameter shared by all circles.) - -  ​ <​blockquote>​ Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler'​s equation reaches down into the very depths of existence. <​cite>​[[https://​books.google.com/​books?​id=GvSg5HQ7WPcC&​pg=PA1#​v=onepage&​q&​f=false|Keith Devlin]]​ <​blockquote>​ Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler'​s equation reaches down into the very depths of existence. <​cite>​[[https://​books.google.com/​books?​id=GvSg5HQ7WPcC&​pg=PA1#​v=onepage&​q&​f=false|Keith Devlin]]​ + <​blockquote>​ [Euler'​s equation] is absolutely paradoxical;​ we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth"​. <​cite>​[[https://​books.google.com/​books?​id=eIsyLD_bDKkC&​pg=PA160|Benjamin Peirce]]