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#### Project Title

eπi + 1=0: The History & Development

#### Abstract/Description

I have on occasion run across the equation in books, articles and in conversation with other mathematicians. In each of these encounters the person alluded to a fascination with this equation which links the five most important constants in the whole of analysis:

• 0 = The additive identity
• 1 = The multiplicative identity
• π = The circular constant
• e = The base of the natural logarithms
• i = The imaginary unit

Being a novice mathematician, I wondered how all these fundamental constants could end up in one equation and what it meant. Along with this thought came the realization that there was some fun investigating to be done. In this paper I will trace the growth of trigonometric ratios and sequences of exponential growth that lead to the equation:eπi + 1=0. My objective is to appreciate and understand the math that lead up to this equation and help the reader understand how it came to be over two thousand years.

#### Note on the Author

Dawne Charters-Nelson is a senior and mathematics major with two prior degrees in art and engineering. She wrote this paper for a Math History course under the encouragement and mentorship of Dr. Philip Scalisi.

#### Rights Statement

Articles published in The Undergraduate Review are the property of the individual contributors and may not be reprinted, reformatted, repurposed or duplicated, without the contributor’s consent.

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