A Data Science Central Community

The formula e^{Pi * i) = -1 (see picture below) has been deemed one of the most beautiful mathematical equations, see for example a Quora discussion on the subject. Here Pi = 3.1415... and i is the imaginary number with i^2 = -1.

As I was trying to find if there is a simple relation between e and Pi not involving imaginary numbers, but instead just a finite number of basic operations and functions (not even integrals of course), I came with the following:

- e^{2 * Pi * i} = 1
- Take the logarithm on both sides, you get 2 * Pi * i = 0
- Thus i = 0.

Can you explain this paradox? The solution is straightforward if you are familiar with the theory of functions of complex argument.

It does not seem that you can find the basic relationship I was hoping for between e and Pi, so these two fundamental mathematical constants are not redundant, it seems. Actually, this is still an unsolved mathematical conjecture, and one of the most famous ones.

Tags:

© 2019 AnalyticBridge.com is a subsidiary and dedicated channel of Data Science Central LLC Powered by

Badges | Report an Issue | Privacy Policy | Terms of Service

**Most Popular Content on DSC**

To not miss this type of content in the future, subscribe to our newsletter.

- Book: Classification and Regression In a Weekend - With Python
- Book: Applied Stochastic Processes
- Long-range Correlations in Time Series: Modeling, Testing, Case Study
- How to Automatically Determine the Number of Clusters in your Data
- New Machine Learning Cheat Sheet | Old one
- Confidence Intervals Without Pain - With Resampling
- Advanced Machine Learning with Basic Excel
- New Perspectives on Statistical Distributions and Deep Learning
- Fascinating New Results in the Theory of Randomness
- Fast Combinatorial Feature Selection

**Other popular resources**

- Comprehensive Repository of Data Science and ML Resources
- Statistical Concepts Explained in Simple English
- Machine Learning Concepts Explained in One Picture
- 100 Data Science Interview Questions and Answers
- Cheat Sheets | Curated Articles | Search | Jobs | Courses
- Post a Blog | Forum Questions | Books | Salaries | News

**Archives:** 2008-2014 |
2015-2016 |
2017-2019 |
Book 1 |
Book 2 |
More

**Most popular articles**

- Free Book and Resources for DSC Members
- New Perspectives on Statistical Distributions and Deep Learning
- Time series, Growth Modeling and Data Science Wizardy
- Statistical Concepts Explained in Simple English
- Machine Learning Concepts Explained in One Picture
- Comprehensive Repository of Data Science and ML Resources
- Advanced Machine Learning with Basic Excel
- Difference between ML, Data Science, AI, Deep Learning, and Statistics
- Selected Business Analytics, Data Science and ML articles
- How to Automatically Determine the Number of Clusters in your Data
- Fascinating New Results in the Theory of Randomness
- Hire a Data Scientist | Search DSC | Find a Job
- Post a Blog | Forum Questions