Improved version here: https://youtu.be/mvmuCPvRoWQ The enigmatic equation e^{pi i} -1 is usually explained using Taylor's formula during a calculus class. This video offers a different perspective, which involves thinking about numbers as actions, and about e^x as something which turns one action into another. For more information on viewing exponential functions in this new light, check out this article: http://goo.gl/LPyc4R Music: "Wyoming 307" by Time For Three, http://www.tf3.com/

https://themobilestudio.leadpages.co/leadbox/147ee8b73f72a2%3A10eee753fb46dc/5719238044024832/ Filming is currently underway on a special online course which will include videos (such as this one), animations and work-throughs to illustrate, in a visual way, how the Fourier Transform works, what all the maths is about and how it is applied in the real world. In order to describe the Fourier Transform, we need a language. That language is the language of complex numbers. Complex numbers is a baffling subject but one that it is necessary to master if we are to properly understand how the Fourier Transform works. Therefore I have decided to devote a module of the course to the subject of complex numbers, what the imaginary number “i” is and why it is so useful to us when dealing with the Fourier Transform. This video is the introduction to that module. If you would like to reserve your free module in the course then click on the link below and follow the on screen instructions: https://themobilestudio.leadpages.co/leadbox/147ee8b73f72a2%3A10eee753fb46dc/5719238044024832/

Some comments on Carl Friedrich Gauss and his contributions. Part of the Algebra 2 course. By Derek Owens. The distance learning course is available at http://www.derekowens.com

This documentary is dedicated to Leonhard Euler who published the beautiful formula called Euler's identity. It was made in metakloner studies in Valparaiso - Chile. This video was made in the laboratory of metakloner in Valparaiso - Chile. Can make suggestions to: [email protected] This video is free and can occupy any teacher. All rights are reserved and belong to metakloner. -------------------------------------------------- Este documental esta dedicado a Leonhard Euler quien publico la hermosa formula llamada la identidad de Euler. Fue realizado en los estudios de metakloner en Valparaiso - chile Este video fue realizado en el laboratorio de metakloner en Valparaiso - Chile. Las sugerencias pueden hacerlas a: [email protected] Este video es gratuito y cualquier docente puede ocuparlo. Todos los derechos están reservados y pertenecen a metakloner. Puedes ver la obra completa en este link: http://gallica.bnf.fr/ark:/12148/bpt6k69587

This is the introduction to Section 4.1 of Applied Calculus by Denny Burzynski published by XYZ Textbooks. We want students to see that definitions in mathematics become more abstract and complicated the further we go in mathematics. Here we are trying to get them to understand and accept the definition for the number e.

A puzzle to try on your friends and family, using something called an Euler's Trail http://en.wikipedia.org/wiki/Euler_trail Puzzle sent to me by Obivandamme http://www.youtube.com/user/obivandamme All mistakes in the solution are my own.