Why are squared values so common ?

[Anonymous No.12655408]

It:
- abates negative effects by creating only positive numbers
- exacerbates effects as the value increases
- it denotes a number multiplying the same number
- analyzing it with visual methods I capture what non-linear relations are

My real question is: - where do I find it in real life/examples ? I’m kind of sleepy but could you help me unveil this ? I feel I can’t grasp the totality of its use, where is it in real life this squared number, rise/run variations ?

[Anonymous No.12655434]

>>12655408
>where is it in real life this squared number

Area?

[Anonymous No.12655435]

>>12655408
Originally the square was literally about a geometric square and it's area.

[Anonymous No.12655440]

>>12655434
>>12655435
You mean the area of a parallelogram ? I have a slight understanding on how one can visually “disarm” other shapes as triangles or parallelograms and analyzing it with the Area formula but is that all ? Or what do you mean with Area ? I might be doing stupid questions but please tolerate my confusion

[Anonymous No.12655452]

>>12655440
>You mean the area of a parallelogram ?

Why not the area of a city or property? That's a direct use where 'squared' comes into play.

[Anonymous No.12655458]

>>12655452
I never thought about it like that, perhaps I have brain damage. You’ve got any other real life examples that do not relate to geometry ? I find this very helpful

[Anonymous No.12655476]

>>12655408
By the central limit theorem, pretty much everywhere. When you combine a number of random variables in some way, they'll follow a Gaussian distribution, which is roughly exp(-x^2).
The negative log-likelihood is x^2, and that's why you see squares everywhere - kinetic energy, strain energy, area, and so on.

[Anonymous No.12655479]

>>12655458
Because you asked nicely I've decided it worth brainstorming for you.

It pops up all the time in physics and chemistry. A basic kinematic equation for displacement is d=Vi(t)+1/2a(t)^2 where Vi is the initial velocity (so you can see why it's multiplied by time once) and a is the acceleration, which continues to increase the speed as time continues, which is why it must be multiplied by time twice.

[Anonymous No.12655483]

>>12655408
You mean why are squared values so common in physics equations?
Like why its not E=mc^3
Dunno honestly, probably reflects the nature of spacetime.
Gravity and charge are inverse square laws because the distortion of spacetime goes out in a sphere from the objects

[Anonymous No.12655493]

>>12655408
because they make things positive like you say, and are differentiable. also because many functions can be expanded as a taylor series, and lower order terms are often important

[Anonymous No.12655506]

>>12655458
Generally things that radiate from a center decrease proportionally to the inverse of the square of the distance. Electromagnetism, gravity for esample. That is related to the area though, because you can imagine the object that receives the effect eats up a proportion of the effect that depends on the proportion of the surface area of the sphere, so a ratio like x/r^2

[Anonymous No.12655867]

>>12655408
If your distance from an object is D, then the percieved size of that object will be 1/D^2. So as an object is further away, it seems smaller, but an exponentially slowing rate.