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If possible, show the equation, mention its name and indicate why you consider it special.
 

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The simplicity behind oxidation and reduction. It's amusing how my old man taught me about refilling old lead batteries with water, and how I'm now teaching him about equation imbalance and electrolysis. At the top of the white board in green there's just some acidic behavior.

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I only have a "Chemistry 1" education at university, which is the minimum required for an electroengineer.

Now that plain old algebra has become such a breeze I have a much healthier appreciation for it.

I'm not a big fan of integration and differential equations.
 

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Hi @Skimt !
Thanks for your answer!


The simplicity behind oxidation and reduction. It's amusing how my old man taught me about refilling old lead batteries with water, and how I'm now teaching him about equation imbalance and electrolysis
Great, I've had this kind of conversation with my father too.

At the top of the white board in green there's just some acidic behavior.
I'm not very good with this. If at any time you have some chance to explain this to me, I would appreciate it, but don't feel compromised.

I'm not a big fan of integration and differential equations
Differential equations are really fascinating to me
 
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I will share the equation that I have chosen: Snell's law

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It is honestly not my favorite, it is not the most spectacular, as you can see. I could say that I am fascinated by Maxwell's equations, but I have made a more personal choice. I like this equation for its derivation from the electric and magnetic fields corresponding to the incident electromagnetic wave. This derivation seems particularly beautiful to me since I saw it in an electromagnetic theory class.
 

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I'm not a professor of chemistry so I might not have fully grasped it myself and might say something I shouldn't have. Take it with a pinch of phosphate :sneaky: (You'll get it.)

There are weak and strong acids, and the only thing I can tell you about strong acids is that their chemical compound differs from weak acids. H3xO4 is considered a weak acid, where H3 and O4 are constant, and x is an atomic variable. The particular acid used on the board is P (phosphor), making it a "phosphoric acid" (H3PO4). In Norwegian the naming convention is "x-syre", while in English it's "x-ic acid". The naming convention for acids should be all the same whether they're weak or strong.

Whenever a Hydrogen splits from this acid (H3xO4), the Oxygen loses the electron that the Hydrogen provided it with. The H-atom then becomes positively charged and the O-atom becomes negatively charged (ionization). This new compound is not considered an acid anymore.

In Norway, we simply refer to H2PO4, HPO4, and PO4 as "phosphate" (or "fosfat"; "x-at"), and when we want to go into depth we call them "dihydrogen phosphate" and "hydrogen phosphate", respectively. The "di-" is greek for two, indicating that there are two Hydrogen atoms. These are all called salts, or "leftover salts".

The basic rule of thumb here is that they can go both ways (equations after all). So, these leftover salts can turn into acids again .

Chemical equations uses basic algebra, so once you know how electrons work and you've seen how it's done, you should be able to get the hang of it relatively quick.

I will share the equation that I have chosen: Snell's law

View attachment 865453

It is honestly not my favorite, it is not the most spectacular, as you can see. I could say that I am fascinated by Maxwell's equations, but I have made a more personal choice. I like this equation for its derivation from the electric and magnetic fields corresponding to the incident electromagnetic wave. This derivation seems particularly beautiful to me since I saw it in an electromagnetic theory class.
What happens when you derive them? Sinus turns into Cosinus, and Cosinus turns into negative Sinus (I don't have the formula in front of me), and then there's the product rule.
 

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Take it with a pinch of phosphate :sneaky: (You'll get it.)
Ok, i've got it! (y)

There are weak and strong acids, and the only thing I can tell you about strong acids is that their chemical compound differs from weak acids. H3xO4 is considered a weak acid, where H3 and O4 are constant, and x is an atomic variable. The particular acid used on the board is P (phosphor), making it a "phosphoric acid" (H3PO4). In Norwegian the naming convention is "x-syre", while in English it's "x-ic acid". The naming convention for acids should be all the same whether they're weak or strong.

Whenever a Hydrogen splits from this acid (H3xO4), the Oxygen loses the electron that the Hydrogen provided it with. The H-atom then becomes positively charged and the O-atom becomes negatively charged (ionization). This new compound is not considered an acid anymore.

In Norway, we simply refer to H2PO4, HPO4, and PO4 as "phosphate" (or "fosfat"; "x-at"), and when we want to go into depth we call them "dihydrogen phosphate" and "hydrogen phosphate", respectively. The "di-" is greek for two, indicating that there are two Hydrogen atoms. These are all called salts, or "leftover salts".

The basic rule of thumb here is that they can go both ways (equations after all). So, these leftover salts can turn into acids again .

Chemical equations uses basic algebra, so once you know how electrons work and you've seen how it's done, you should be able to get the hang of it relatively quick.

I definitely need to study this


What happens when you derive them? Sinus turns into Cosinus, and Cosinus turns into negative Sinus (I don't have the formula in front of me), and then there's the product rule.
Well, by "derivation" I was referring rather to the deduction of Snell's Law (Also known as "Law of Refraction")
This derivation is usually made from the Fermat principle, with a much simpler development.

Deriving (deducting) Snell's law from electrodynamics is more complex (and beautiful). I honestly do not remember the whole development, but I leave you a part of the approach
(sorry for the image quality)
20200527_000823-1.jpg
 
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I figured if they're interested in differential equations then the Gauss-Jordan elimination (among others) might interest them.
 

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1 + 1 = 2
It's one plus one equals two.
Because you can do it with one hand and do it again with another hand.
You can also do it with both hands.
 

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My favourite is the Navier Stokes Equation for a rotating body.

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I like it because it's a pretty mean equation, and I used it extensively during the final year of my undergrad to study and derive a shitload of very interesting laws in geophysical fluid dynamics.

It's special because it sets the basis for the entire human understanding of how oceans and atmospheres flow around a planet.
 

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I like it because it's a pretty mean equation
I agree with you, it's a fascinating equation!

and I used it extensively during the final year of my undergrad to study and derive a shitload of very interesting laws in geophysical fluid dynamics.
Amazing!

Would you mind telling me a little more about your work?
I have been working in the geophysics area for a long time, but never with fluid mechanics.

It's special because it sets the basis for the entire human understanding of how oceans and atmospheres flow around a planet.
Beautiful!
I don't consider myself good at fluid mechanics. Despite that I think it is one of the most fascinating areas of physics.
I honestly haven't studied much about applications to geophysics.
Are you a physicist or did you study a different career?

thanks for your answer @HAL !
 
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I agree with you, it's a fascinating equation!



Amazing!

Would you mind telling me a little more about your work?
I have been working in the geophysics area for a long time, but never with fluid mechanics.



Beautiful!
I don't consider myself good at fluid mechanics. Despite that I think it is one of the most fascinating areas of physics.
I honestly haven't studied much about applications to geophysics.
Are you a physicist or did you study a different career?

thanks for your answer @HAL !
I'm not a physicist at all haha. I studied physics for undergrad and fluid dynamics was a favourite topic, and then in my final year geophysical fluid dynamics was the icing on the cake. Super interesting! But, aside from that, I got pretty bored of academia and went into programming.

I can tell you a bit about the geophysical fluid dynamics stuff I studied though... It was absolutely fascinating, it pretty much explained the movement of all major planetary flows in the ocean and atmosphere.

First there's the obvious one, the coriolis force, which causes wind to deflect eastwards as it heads to the poles. But there's actually so much more that happens due to coriolis effects. For example, when wind is blowing over the ocean, it causes currents in the ocean (almost all ocean movement is due to wind), but the coriolis force causes the water to move perpendicular to the direction of the wind. This means that easterly winds either side of the equator push oceans in to the equator, leaving the water with nowhere to go. And THAT is why there's a jet of water (aka the gulf stream) racing up the western Atlantic. It's just escaping the pressure of all the water being driven into the equator!

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The equation for the gulf stream looks like this:
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Sadly I can't even remember what half of the variables mean, other than to say they represent things like wind force, friction with the ocean floor, or the angle of latitude that you want to calculate for.

What else? Geostrophic balance. This one's amazing. Typically you would imagine wind to move from regions of high pressure to regions of low pressure. Common sense, right? Well, Coriolis effects cause flows to move around regions of differing pressure. We actually witness this every day in weather reports.

In the image below, black arrows are showing wind direction. Common sense says wind should move directly from H regions to L regions, but it doesn't. It goes around them!

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The equation for geostrophic balance looks like this:

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It's basically saying that the coriolis forces that want to send the flow sideways are equal to the inertial forces that want to move the flow by direct pushing/pulling, and so you end up with flows that simply go around the push/pull (pressure) regions.

What else?

Rossby waves. These are the thing causing the 'concertina' pattern in the jet stream. They're caused by a thing called 'conservation of vorticity'. It's similar to the the more widely known principles of 'conservation of momentum', or at a more fundamental level, conservation of energy. Wind on the equator is at a much wider radius of global rotation than winds on the poles. As the wind moves to the poles, it attempts to maintain the rotation, which manifests as a concertina pattern in the jet stream.



The equation for Rossby waves looks like this:

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It's a fairly standard wave equation, where the wave speed,
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, is defined primarily by the angle of latitude you're looking at.

I think that's enough for now :D

I think what fascinated me most about this topic is that there are actual mathematical equations to describe such huge, complex and seemingly chaotic events at the planetary scale. And all those equations come from that one main rotational navier stokes equation that I posted earlier.
 

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1*0=0. It's special because of the Interesting number paradox, but this time it's "Special equation". Though I suppose it has some properties that could be interesting... I feel that there are many beautiful equations out there, but this one just seems quite well-rounded.
 
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