This was hands-down my favorite variant of the “distracted boyfriend” meme that went around the internet last year.

# Euler’s Equation

Tagged complex numbers, Euler's formula

*Posted by John Quintanilla on January 29, 2018*

https://meangreenmath.com/2018/01/29/eulers-equation/

Leave a comment

### 2 Comments

### Leave a Reply Cancel reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

## Top Posts & Pages

- Engaging students: Finding the domain and range of a function
- Importance of the base case in a proof by induction
- Square roots and logarithms without a calculator (Part 3)
- Engaging students: Proving that two triangles are congruent using SAS
- Engaging students: Using right-triangle trigonometry
- Engaging students: Distinguishing between inductive and deductive reasoning
- Full lesson plan: magic squares
- Engaging students: Translation, rotation, and reflection of figures
- Engaging students: Absolute value
- A Timeline of Mathematics Education

## Archives

- September 2020
- August 2020
- July 2020
- June 2020
- May 2020
- April 2020
- March 2020
- February 2020
- January 2020
- December 2019
- November 2019
- October 2019
- September 2019
- August 2019
- July 2019
- June 2019
- May 2019
- April 2019
- March 2019
- February 2019
- January 2019
- December 2018
- November 2018
- October 2018
- September 2018
- August 2018
- July 2018
- June 2018
- May 2018
- April 2018
- March 2018
- February 2018
- January 2018
- December 2017
- November 2017
- October 2017
- September 2017
- August 2017
- July 2017
- June 2017
- May 2017
- April 2017
- March 2017
- February 2017
- January 2017
- December 2016
- November 2016
- October 2016
- September 2016
- August 2016
- July 2016
- June 2016
- May 2016
- April 2016
- March 2016
- February 2016
- January 2016
- December 2015
- November 2015
- October 2015
- September 2015
- August 2015
- July 2015
- June 2015
- May 2015
- April 2015
- March 2015
- February 2015
- January 2015
- December 2014
- November 2014
- October 2014
- September 2014
- August 2014
- July 2014
- June 2014
- May 2014
- April 2014
- March 2014
- February 2014
- January 2014
- December 2013
- November 2013
- October 2013
- September 2013
- August 2013
- July 2013
- June 2013

## Categories

- Algebra I (198)
- Algebra II (294)
- Bases (44)
- Calculus (234)
- Chemistry (10)
- Computer science (9)
- Discrete mathematics (257)
- Elementary (152)
- Engagement (763)
- Geometry (232)
- Guest presenter (449)
- History (54)
- Humor (267)
- Linear Algebra (12)
- News Clips (130)
- Physics (40)
- Popular Culture (256)
- Pre-Algebra (169)
- Precalculus (509)
- Preparing for college (12)
- Probability (87)
- Statistics (86)
- Tales from the Classroom (222)
- Technology (80)
- Theorems (164)
- Uncategorized (63)

## Tags

angle arccosine arcsine arctangent area circle combinatorics Common Core completing the square complex numbers compound interest conceptual barrier confidence interval convex polygons cosine decimal De Moivre's Theorem derivative differential equation distributive law divisibility division algorithm e exponent exponential factoring fraction function geometric series graph high-stakes testing hypothesis test index to a series of posts induction integral intercepts inverse function limit logarithm logic MAA magic trick matrices multiplication parabola parallel Pascal's triangle perpendicular pi polar coordinates polynomial primes PRIMUS proof Pythagorean theorem Pythagorean trig identities quadratic formula residue sequence series sine slope sphere sports square root system of equations tangent Taylor series textbook problems triangle trigonometry unsolved problems vector volume xkcd## Meta

## masacu

/ March 2, 2018sure here must as say prof dr mircea orasanu and prof horia orasanu as followed

COMPLEX FUNCTIONS AND SINGULAR POINTS

## masacu

/ March 11, 2018also here we see and remember as say prof dr mircea orasanu and prof horia orasanu as followed

COMPLEX NUMBERS AND EULER CONCEPTS OF HYDRODYNAMICS

Author Horia Orasanu

ABSTRACT

Up to now the focus has been fluids at rest. This section deals with fluids that are in motion in a steady fashion such that the fluid velocity at each given point in space is not changing with time. Any flow pattern that is steady in this sense may be seen in terms of a set of streamlines, the trajectories of imaginary particles suspended in the fluid and carried along with it. In steady flow, the fluid is in motion but the streamlines are fixed. Where the streamlines crowd together, the fluid velocity is relatively high; where they open out, the fluid becomes relatively stagnant.

When Euler and Bernoulli were laying the foundations of hydrodynamics, they treated the fluid as an idealized inviscid substance in which, as in a fluid at rest in equilibrium, the shear stresses associated with viscosity are zero and the pressure p is isotropic. They arrived at a simple law relating the variation of p along a streamline to the variation of v (the principle is credited to Bernoulli, but Euler seems to have arrived at it first), which serves to explain many of the phenomena that real fluids in steady motion display. To the inevitable question of when and why it is justifiable to neglect viscosity, there is no single answer. Some answers will be provided later in this article, but other matters will be taken up first.

Consider a small element of fluid of mass m, which—apart from the force on it due to gravity—is acted on only by a pressure p. The latter is isotropic and does not vary with time but may vary from point to point in space. It is a well-known consequence of Newton’s laws of motion that, when a particle of mass m moves under the influence of its weight mg and an additional force F from a point P where its speed is vP and its height is zP to a point Q where its speed is vQ and its height is zQ, the work done by the additional force is equal to the increase in kinetic and potential energy of the particlehttps://adsprod1.pixfuture.com/www/delivery/ck.php?oaparams=2__bannerid=6__zoneid=6__cb=da30a68b6e__oadest=https://www.steepto.com/ghits/2639113/i/7064/0/pp/1/2?h=ViXM2Yz5AVmIwLxBC4HVO_F-kT6EFG8s_njl9TkzvoKVeALruZ-7X1s-QIHgATJi&rid=03a5aafb-2541-11e8-bc82-141877677254&tt=Direct&k=61863fczy7eva_A*fZ!fWIVrn5yfWIVrv7Nf.%3BfT%3AfP%3Df*ff%3BfP%24fl*fY%24faYWKxAfP%3Dfgf%3AfaHR0cHM6Ly9hZHNlcnZlci5hZHRlY2h1cy5jb20vYWRpZnJhbWUvMy4wLzk4MzQuM%248%3DfaHR0cHM6Ly93aW5keW1lZC5jb20vZD9pPWI4MW1wbXVmNmd6dW9pZTU1N3AmYT1kZDY%3DfKysvZD9pPWI4MW1wbXVmNmd6dW9pZTU1N3AmYT1kZDYxNjM3ZGRkZDdiZWE0NDI1OTJhNw%3D%3Df%3BfT%3AfP%3DfS~f%3BfcfT*fUAfQAfWIVrpEhf!fTW96aWxsY%2481LjAgKFdpbmRvd3MgTlQgNi4xOyBydjo1OC4wK%24BHZWNrby8yMDEwMDEwM%24BGaXJlZm94LzU4LjA%3Dff!fV2luMzI%3DfMTIwf%3BfUAfPYfi%3Bfl%3Af*f%2Bf*f*