[Thread] What is your favourite math equation?
TLDR: I was reading up on the Navier Stokes equations today and it is so elegant that it might be my favourite math equation.
Equation 1: ∇u = 0 (conservation of mass) states that the divergence of the velocity vector u is zero, meaning there is no net change in fluid mass.
Equation 2: ρ Du/Dt = -∇p + μ∇^2 u + ρF (conservation of momentum) expresses Newton's second law for fluid flow. It balances the acceleration of fluid particles (LHS) with internal forces (pressure and viscosity) and external forces (gravity or other external influences) on the RHS.
This equation is foundational for modelling various fluid dynamics scenarios, from celestial bodies like stars and galaxies to F1 cars.
Long Version: Here's how it works:
Equation 1:
∇u = 0 (conservation of mass)
So, u is velocity that can be represented as (u,v,w) vector, where u,v,w are x,y,z components of the vector.
∇u tells us that we need to do a partial derivative on u.
So, ∇u = ∂u/∂x + ∂v/∂y + ∂w/∂z = 0
or, the partial derivative of every component wrt corresponding direction is 0.
Equation 2:
ρ Du/Dt = -∇p + μ∇^2 u + ρ F (conservation of momentum)
LHS: Since, u is velocity, then Du/Dt is acceleration and ρ is density. Newton's second law, F = m x a, applies here. Wherein, Du/Dt is acceleration of fluid particles and m is the density of the fluid.
RHS: -∇p + μ∇^2 are the internal forces of particles hitting into each other while F represents the external force.
F in most cases is gravity, so one can replace it with g. However, if you put in electromagnetism then, you can combine Navier-Stokes with Maxwell's equations.
This has over time led to the development of magnetohydrodynamics, ie how stars and galaxies form. You can model the growth of our sun with this.
∇p is our pressure gradient and represents the change in pressure. Essentially, fluids move from high pressure to low pressure.
μ∇^2 represents viscous forces yielding from viscosity.
Imagine this can model aerodynamics of F1 cars.
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Most people don’t have a favourite math equation 😂 But good to see this interest, and love the effort to write this down
e^(iπ) + 1 = 0 is often considered the favourite of many because it is elegant, combines five of the most important numbers in math.
e is the base of natural log pi, the ratio of circles circumference to its diameter 1, the multiplicative identity 0, the additive identity i, the imaginary unit
r/math will love you
nothing can beat the basic Pythagorean theorem (a² + b² = c²) when used in real life 😂😅
Not equation but graph - https://images.app.goo.gl/MYP487dbQsUkm4zbA
It's called the nuclear binding energy graph. We all learnt it in 12th standard (didn't remember what it was called lul so just googled it)
This single graph explains why fission and fusion works if you start from hydrogen you can go all the way to iron and each higher element fusion reaction will release energy. That's basically how stars do it like our sun.
If you go reverse you can start from something like Uranium and start breaking it. Then it again releases energy till iron and that's how your boi Oppenheimer did the nukes aka fission.
Now let's blow it up.
You know when a Star goes Nova💥? It does because in its core Iron starts to get formed.
From hydrogen -> Iron, a star releases energy but as soon as you get Iron, it stops being an exothermic process.
So now the star has no energy to fight the extreme gravity of its core and the gravity collapses the star and it blows up it's outer layers and depending on the stellar mass can go from a -
Small star -> red giant -> small boom-> white dwarf
to a
Big star -> hypernova -> black hole.
So all the Iron in your blood? That came because somewhere out there a star died to create it. So all you bitches who think you are not special remember that you literally are a star child created by the universe itself.
Hahahaha I love the ending.
Yes, this was Modern Physics I think. But I really love this graph.
Love needing out hahaha. Fusion is at the precipice of something new.
I don't think we will see a fusion reactor powering a city in our lifetime. They have been at it for decades now and it's still not there yet
income - expense > 0
if my favourite equation when true.
🤣💀
For me it's always going to be fractals. Mesmerising to say the least. And then you have 1==1 :). @salt GoJek? More like GoGeek hehe. 😂
Love geeking or nerding out. It is insane. Fractals are really great.
Maybe try reading about the human body. Maybe it was my tutor who made it so interesting back in the day, but my Gawd, the way the body works. Speechless. Puts a fine mechanical watch to shame. (Not even a valid comparison)
Euler Lagrange I studied it in my first year. Really enjoyed solving problems
And the maths equation Michael Massi used to rob the 8th tittle of most deserving, the greatest F1 driver of all time, Sir Lewis Hamilton
Was a big Verstappen fan. Can’t handle the RB domination now.
Need Alonso and LeClerc to step it up.
No one's touching RB as of now. McLaren and Mercedes are far off. Ferrari is Ferrari. Alonso racing, I mean Aston Martin ain't it. 24 is all gonna be Verstappen again
